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\DOI{10.5802/crgeos.259}
\datereceived{2023-12-08}
\daterevised{2024-04-12}
\dateaccepted{2024-04-15}
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\dateposted{2024-05-21}
\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}
%
%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{Geodynamics of continents and oceans - A tribute to Jean Aubouin}
%\def\cdr@specialtitle@french{G\'eodynamique des continents et des Oc\'eans - Hommage \`a Jean Aubouin}
%\makeatother

\title{Fluids, faulting and earthquakes in the brittle crust: recent
advances and new challenges}

\alttitle{Fluides, failles et s\'{e}ismes dans la cro\^{u}te fragile :
avanc\'{e}es r\'{e}centes et nouveaux d\'{e}fis}

\author{\firstname{Olivier} \lastname{Fabbri}\CDRorcid{0000-0001-8646-9368}\IsCorresp}
\address{UMR 6249, universit\'{e} de Franche-Comt\'{e}, 16 route de Gray, 25030 Besan\c{c}on cedex,~France}
\email[O. Fabbri]{olivier.fabbri@univ-fcomte.fr}

\author{\firstname{Hugues} \lastname{Raimbourg}\CDRorcid{0000-0002-9160-0989}}
\address{UMR 7327, universite d'Orl\'{e}ans, 1A rue de la F\'{e}rollerie, 45071 Orl\'{e}ans cedex~2,~France}

\author{\firstname{Henri} \lastname{Lecl\`{e}re}\CDRorcid{0000-0002-3644-3183}}
\addressSameAs{1}{UMR 6249, universit\'{e} de Franche-Comt\'{e}, 16 route de Gray, 25030 Besan\c{c}on cedex,~France}

\shortrunauthors

\begin{abstract}
Interactions between fluids and deformation are widespread in the
brittle crust. As experimentally shown, a high pore fluid pressure
$p_{f}$ can fracture intact rocks or reactivate
pre-existing fractures. The preference of reactivation over the
formation of a new fracture depends on the orientation of the
pre-existing fracture with respect to the stress axes and on
$p_{f}$. In nature, the predominant reactivation of
misoriented pre-existing faults rather than the formation of new faults
with more favorable orientations suggests that pressurized fluids are
present in the brittle crust. There is a large body of evidence
indicating that supra-hydrostatic $p_{f}$
contributes to the reactivation of low-angle thrust faults or normal
faults. Conversely, supra-hydrostatic $p_{f}$
values are less common along vertical or steeply dipping plate boundary
transform faults or intra-continental strike-slip faults. If these
faults are severely misoriented with respect to the ambient stress
field, their reactivation may not be due to supra-hydrostatic
$p_{f}$ but to other mechanisms such as
shear-enhanced compaction or thermal pressurization. Supra-hydrostatic
$p_{f}$ also plays a role in the nucleation or
propagation of seismic ruptures in the continental or oceanic crust,
and in subducting slabs in convergent margins, as reported for
aftershocks, swarms, slow earthquakes, and to a lesser extent for major
earthquakes. Lastly, increase or decrease of
$p_{f}$ in depth due to human activities such as
hydrocarbon extraction, dam impoundment, gas storage or geothermal
energy production result in many cases in the inception or enhancement
of seismic activiy, adding clues in favor of a relationship between
fluids and\unskip\break earthquakes.
\end{abstract}

\begin{altabstract}
Les interactions m\'{e}caniques entre fluides et d\'{e}formation sont
omnipr\'{e}sentes dans la cro\^{u}te fragile. Comme d\'{e}montr\'{e}
exp\'{e}rimentalement, une pression de fluide
$p_{f}$ \'{e}lev\'{e}e peut fracturer des roches
intactes ou r\'{e}activer des fractures pr\'{e}-existantes. La
pr\'{e}f\'{e}rence de la r\'{e}activation sur la formation d'une
nouvelle fracture d\'{e}pend de l'orientation de la fracture
pr\'{e}-existante par rapport aux orientations des axes de contrainte
et de la valeur de $p_{f}$. Dans la nature, la
pr\'{e}dominance de la r\'{e}activation de failles d\'{e}favorablement
orient\'{e}es sur la cr\'{e}ation de nouvelles surfaces optimalement
orient\'{e}es sugg\`{e}re que les fluides pressuris\'{e}s sont
omnipr\'{e}sents dans la cro\^{u}te fragile. De nombreuses \'{e}tudes
sugg\`{e}rent que des pressions de fluide supra-hydrostatiques rendent
possible des d\'{e}placements le long de failles inverses ou normales
\`{a} faible pendage, donc d\'{e}favorablement orient\'{e}es par
rapport aux axes de contrainte. Par contre, les \'{e}vidences de
pressions de fluide \'{e}lev\'{e}es au voisinage des failles
transformantes ou d\'{e}crochantes sont moins document\'{e}es,
sugg\'{e}rant que d'autres m\'{e}canismes d'affaiblissement, tels
que la compaction par cisaillement ou la pressurisation thermique,
interviennent. Des pressions supra-hydrostatiques jouent un r\^{o}le
dans la nucl\'{e}ation ou la propagation des s\'{e}ismes dans la
cro\^{u}te sup\'{e}rieure et dans les lithosph\`{e}res plongeantes dans
les zones de subduction, comme en t\'{e}moignent les s\'{e}quences de
r\'{e}pliques, les essaims sismiques, les s\'{e}ismes lents et, dans
une moindre mesure, les ruptures majeures. Des variations de
$p_{f}$ en profondeur li\'{e}es aux activit\'{e}s
humaines, comme l'extraction d'hydrocarbures, le remplissage de
lacs artificiels, le stockage de gaz ou la production d'\'{e}nergie
g\'{e}othermique, r\'{e}sultent fr\'{e}quemment en un d\'{e}clenchement
ou un renforcement de l'activit\'{e} sismique.
\end{altabstract}

\keywords{\kwd{Fluid} 
\kwd{Fault} 
\kwd{Pore fluid pressure}
\kwd{Earthquake}
\kwd{Slow earthquake}
\kwd{Seismic swarm}
\kwd{Crack-seal vein}}


\altkeywords{\kwd{Fluide}
\kwd{Faille}
\kwd{Pression de fluide interstitiel}
\kwd{S\'{e}isme}
\kwd{S\'{e}isme lent}
\kwd{Essaim sismique}
\kwd{Veine rubann\'{e}e}}

\maketitle

\twocolumngrid

\end{noXML}

\section{Introduction}

Whatever their nature, chemical composition or physical state, fluids
play key roles in the evolution of the Earth's lithosphere,
particularly regarding sediment diagenesis, volcanic activity,
hydrothermal alteration, metamorphism, ore deposit formation, among
many other phenomena. Fluids are also important with regard to
deformation, especially brittle deformation. In the upper brittle
crust, fluids can circulate in deforming zones, namely fracture zones
or fault zones, and can chemically or mechanically interact with host
rocks. Such interactions are also conceivable in subduction zones,
where the upper part of the subducting plate keeps a brittle behavior
down to hundreds of kms of depth.

The role that fluids exert on rock deformation is of paramount
importance for human societies. Indeed, fluid extraction (e.g.,
hydrocarbon industry) or fluid injection (geothermal energy, waste
water disposal, gas storage) trigger or enhance seismic activities in
otherwise aseismic or moderately active regions.

This review aims at bridging the gap between the mechanical
interactions between fluids and rocks on one hand and the structural
analysis of deformed rocks from the scale of the hand sample to that of
the deforming plate boundaries. For space reasons, the chemical effects
of fluids, although of considerable importance, will not be addressed
here.


\section{The mechanical interaction between fluids and rocks}

\subsection{The development of abnormally high pore fluid pressures in
the upper crust}

Production of fluid in depth, for instance by magmatic activity or by
metamorphic or metasomatic reactions, can result in an influx of
fluids. If there is a permeability barrier that prevents or hinders
fluid escape, then the pore fluid pressure $p_{f}$ will increase. This
increase can also be generated by pore volume reduction in
low-permeability rocks. For instance, elastic crack relaxation
following an earthquake (seismic pumping, see below 
Section~\ref{sec2.6}) or inelastic pore compaction controlled by the
applied shear stress (shear-enhanced compaction, see below
Section~\ref{sec2.7}) are two important mechanisms responsible for pore
volume decrease. Beside such earthquake-related mechanisms, pore
compaction can also be achieved during diagenesis
\citep{WalderNur1984,Wangetal2022}. As attested by measurements in deep
boreholes, supra-hydrostatic $p_{f}$ values actually develop below
impermeable barriers or seals, and can reach the value of the
lithostatic stress or even exceed it
\citep{Yerkesetal1985,Powley1990,Neuzil1995,Zencheretal2006}.

\subsection{Intact rock fracturing, stress corrosion,\newline hydrofracturing}

Classical rupture criteria for \textit{intact rocks} in the upper crust
are inspired by experimental rock mechanics and state that, as long as
the stress tensor (whose components are $\sigma_{1}$,
$\sigma_{{2}}$, and $\sigma_{3}$, with the convention
$\sigma_{1} > \sigma_{{2}} > \sigma_{3}$) acting on the rock
does not satisfy any criterion, no fracture will form. To the contrary,
once the stress tensor satisfies the criterion, microscopic fractures
will propagate through the rock, eventually leading to the formation of
a macroscopic fracture or fault.

Two rupture criteria are commonly used in the analysis of intact rock
failure. The simplest is the linear Mohr--Coulomb criterion, which
postules that the propagation of macroscopic fractures happens when
{\begin{eqnarray*}
\tau = \mu_{i} \sigma_{n} + C
\end{eqnarray*}}\unskip
with $\tau$ being the tangential stress acting along the fracture,
$\sigma_{n}$ the normal stress acting on the fracture, $\mu_{i}$
and $C$ being respectively the intrinsic coefficient of friction and
the intrinsic cohesion, both depending on rock type. The more
elaborated parabolic Griffith failure criterion can be expressed as
{\begin{eqnarray*}
\tau^{2} + 4 T \sigma_{n} = 4 T^{2}
\end{eqnarray*}}\unskip
where $T$ is the tensile strength of the intact rock, counted positive.
Both Mohr--Coulomb and Griffith criteria can be combined in a composite
criterion for which the parabolic criterion will apply to negative
normal stress values and the linear criterion will apply for the
positive normal stress values [\citealp{SibsonScott1998};
Figure~\ref{fig1}]. 

\begin{figure}
\includegraphics{fig01}
\vspace*{-9pt}
\bcaption{\label{fig1}The role of pore fluid pressure 
in fracturing intact rocks as
representated in the Mohr space. The intact rock rupture criterion is
composite, that is, it consists of the Griffith criterion for the
negative normal stresses, and of the linear Mohr--Coulomb criterion for
the positive normal stresses. $\sigma_{n}'$: effective normal stress
acting on the surface ($\sigma_{n}'=\sigma_{n} - p_{f}$). (a) A pore
fluid pressure $p_{f1}$ decreases the normal stresses and shifts the
Mohr circle until it tangents the failure envelope. The orientation of
the newly formed fracture with respect to the stress axes is optimal.
(b) Due to a lower differential stress, a pore fluid pressure $p_{f2}$
displaces the Mohr circle until it tangents the failure envelope in the
parabolic part, resulting in the formation of hybrid shear-extensional
fractures.}{0}{(c) Due to a still lower differential stress, a pore fluid
pressure $p_{f3}$ displaces the Mohr circle until it tangents the
failure envelope at $\tau = 0$, resulting in the formation of pure
dilatant fractures.}
\vspace*{-6pt}
\end{figure}


In the absence of pore fluid in the rock, the convergence between the
tensor and the criterion can be achieved only by increasing the
differential (deviatoric) stress $\sigma_{{D}} = \sigma_{1}
-\sigma_{3}$, that is, either by decreasing $\sigma_{3}$, by
increasing $\sigma_{1}$, or by acting on both $\sigma_{3}$ and
$\sigma_{1}$. If a fluid is present inside the rock (so-called pore
fluid), then two processes can lead to the formation of macroscopic
fractures. In the first process, called stress corrosion, the fluid
will \textit{chemically} react at the atomic scale with the rock at the
tip of a pre-existing loaded crack, so that the critical stress
intensity factor at this location gets lower and lower. When the stress
intensity factor at the tip of the crack reaches the fracture toughness
of the altered rock, the fracture will propagate. This phenomenon is
called sub-critical crack growth
\citep{AndersonGrew1977,Atkinson1984,Brantutetal2013}. The second
process requires that the pore fluid is elevated at a pressure
$p_{f}$. If so, the components $\sigma_{{i}}$ of the tensor will
then be changed into \textit{effective} components $\sigma_{{i}}^* =
\sigma_{{i}} - p_{f}$, and the rupture criterion is assessed using
effective stress. If $p_{f}$ is increased enough, the effective
stress tensor will satisfy the rupture criteron (Figures~\ref{fig1}
and~\ref{fig2}). Note that, unlike the $\sigma_{{i}}$ components of
the tensor, $\sigma_{{D}}$ is not modified by any variation of
$p_{f}$. A failure mode diagram \citep{Cox2010} allows to estimate
$\sigma_{{D}}$ and $p_{f}$ required for rock failure
(Figure~\ref{fig3}). 
In this diagram, $p_{f}$ is expressed by the
pore fluid factor (also called pore fluid pressure ratio) $\lambda =
p_{f} / \rho gz$, where $\rho gz$ is the lithostatic stress,
$\rho$ the mean density of the rock column from the surface to depth
$z$, and $g$ the gravity acceleration. The values of $\lambda$ are
between 0.3--0.4 (hydrostatic $p_{f}$) and 1 (lithostatic $p_{f}$).
In a Mohr--Coulomb diagram, if the tangent point between the Mohr circle
and the envelope is located in positive $\sigma_{n}$ values, the
rupture is said to be of shear failure type. This is illustrated in the
failure mode diagram by the blue line on the failure envelope
(Figures~\ref{fig1}a and~\ref{fig3}). If $\sigma_{3}^* = -T$, $T$
being the tensile strength of the intact rock, counted positive, the
rupture is purely extensional (dilatant), and is illustrated in the
failure mode diagram by the red line on the failure envelope
(Figures~\ref{fig1}c and~\ref{fig3}). It is important to note that the use
of extension here does not reflect an extensional tectonic regime (for
which $\sigma_{{V}} = \sigma_{1}$, $\sigma_{{V}}$ being the
principal vertical stress component, in an Andersonian framework).
Intermediate locations correspond to hybrid extensional-shear failures
illustrated in the failure mode diagram by the green line on the
failure envelope (Figures~\ref{fig1}b and~\ref{fig3}).

\begin{figure}
\vspace*{-3pt} 
\includegraphics{fig02}
\vspace*{-5pt} 
\bcaption{\label{fig2}\fontsize{9.6}{12}\selectfont
Competition between reactivation of pre-existing fractures and
formation of a new fracture [after \citealp{Handin1969,Sibson1985}].
The failure envelope for intact rock follows a composite
Griffith--Mohr--Coulomb criterion. The reactivation envelope is linear,
and its cohesion is neglected. $\sigma_{n}'$: effective normal stress
acting on the surface ($\sigma_{n}'= \sigma_{n} - p_{f}$). (a) The
pre-existing fracture (black dot on the circle) is \textit{favorably
oriented} with respect to the $\sigma_{1}$ stress axis. The pore fluid
pressure $p_{f1}$ is large enough to allow its reactivation. (b) The
pre-existing fracture is \textit{unfavorably oriented} with respect to
the $\sigma_{1}$ stress axis, but the \textit{misorientation is
moderate}. The pore fluid pressure $p_{f2}$, larger than $p_{f1}$, is
necessary to allow its reactivation. (c) The pre-existing fracture is
\textit{unfavorably oriented} with respect to the $\sigma_{1}$ stress
axis, and the \textit{misorientation is severe}.}{1}{\fontsize{9.6}{12}\selectfont Due to an increasing
pore fluid pressure, the Mohr circle shifts towards smaller normal
stresses. It eventually tangents the intact rock failure envelope (grey
dot) before the pre-existing fracture (black dot) can be reactivated.
In~this case, a new fracture (grey dot) with a favorable orientation is
formed for a pore fluid pressure $p_{f3}$.}
{\vspace*{2pt}}
\end{figure}


\begin{figure}
{\vspace*{2pt}}
\includegraphics{fig03}
\caption{Failure mode diagram for reverse and normal faulting based on
the Mohr--Coulomb theory. Red, green and blue lines correspond
respectively to pure extensional (dilatant) veins, hybrid veins and
shear fractures. Oblique black lines correspond to the reactivation
conditions for a favorably oriented fracture or a severely misoriented
fracture. The diagram is drawn for a depth $z$ of 7~km, a rock density
$\rho$ of 2.7, a friction coefficient $\mu$ of 0.75 and a
tensile strength $T$ of 5~MPa. See text for explanation of points A, B
and C.\label{fig3}}
{\vspace*{2pt}}
\end{figure}

Dilatant breccias form when the three effective principal stresses are
negative ($\sigma_{3}^* < \sigma_{{2}}^*< \sigma_{1}^* < 0$), while
\textit{pure} dilatant breccias, that is, breccias without any
preferred orientation of dilatancy (Figure~\ref{fig4}), form when the
stress tensor is hydrostatic, the common stress magnitude being the
opposite of the tensile strength of the rock: $\sigma_{1}^* =
\sigma_{{2}}^* = \sigma_{3}^* = - T$ [hydrostatic stress state;
\citealp{Cosgrove1995}].

\begin{figure}
\vspace*{-2pt}
\includegraphics{fig04}
\vspace*{-.3pc}
\caption{Purely dilatant
breccias (hydraulic breccias) suggesting a
hydrostatic stress state ($\sigma_{1}^* = \sigma_{2}^* = \sigma_{3}^* =
- T$). (A) Saw-cut hand sample showing dark green serpentinite
fragments cemented by white calcite along a paleo-detachment fault,
Schistes Lustr\'{e}s Zone, Queyras serpentinite, French Alps. Width of
photograph: 25~cm. (B) River bed exposure of a dilatant breccia
composed of low-porosity sandstone fragments (grey color) cemented by
quartz (white color) along a vertical fault (white arrows), Oligocene
Hyuga Group, Shimanto accretionary prism, Japan. (C) Saw-cut 
sandstone hand sample from nearby (B) exposure. Width of photograph:
15~cm.\label{fig4}}
\vspace*{-1pc}
\end{figure}

Mineralized extensional joints (tension gashes)~are typical and
widespread geological structures resulting from failure of intact rocks
by pure extension (Figure~\ref{fig1}c). Pure extension is achieved by
the condition $\sigma_{3}^* = - T$, that is, $p_{f} =
\sigma_{3} + T$ \citep{HubbertWillis1957,Secor1965,Hancock1985}.
The regular and symmetrical layering of the minerals filling extension
joints suggests a cyclical process with incremental opening stages
alternating through time with fluid ingression and crystallization
\citep{Ramsay1980}. This so-called crack-seal mechanism, reminiscent of
the cyclical nature of earthquakes, is often considered as a geological
expression of the seismic cycle 
\citep[see below and][]{Raimbourgetal2021,Raimbourgetal2022}.

Shear fractures result from a combination of extension and shear
(hybrid failure). They classically form conjugate systems of \textit{en
\'{e}chelon} fractures {(Figure~\ref{fig5}),} where the long axis of the
mineral fibers indicates the combination of extension and shear\unskip\break
(Figure~\ref{fig6}).


\begin{figure}
\includegraphics{fig05}
\vspace*{2pt}
\caption{Calcite-filled mode I and hybrid mineralized fractures
associated with conjugate faults (arrows). The fractures are
perpendicular to the steeply dipping bedding surface. Cretaceous
limestones, Pyrenean foreland, Corbi\`{e}res, France (height of
photograph: 2~m).\label{fig5}}
\vspace*{6pt}
\end{figure}


\begin{figure}
\includegraphics{fig06}
\vspace*{2pt}
\caption{Mode I quartz-filled fracture in low-porosity Oligocene
sandstones, Shimanto accretionary prism, Japan. The quartz fibers show
an S shape, suggesting a component of displacement parallel to the
fracture. Thickness of the vein: 15~mm.\label{fig6}}
\end{figure}


\subsection{Fracture reactivation vs. fracture\newline neoformation}

Unlike in laboratory experiments, rock masses in the brittle crust are
fractured. Therefore, it is not the intact rock strength that will
dictate the stability of rock masses, but rather the strength of
discontinuity (fault or fracture) surfaces \citep{Byerlee1978}. Intact
rock rupture criteria are replaced by more realistic
\textit{reactivation} criteria. The simplest and most widely used
criterion is the Mohr--Coulomb reactivation criterion
\citep{Handin1969}, quite similar to the Mohr--Coulomb criterion for the
intact rock, and which can be written as
{\begin{eqnarray*}
\tau = {\mu} \sigma_{n} + C.
\end{eqnarray*}}\unskip
The criterion postulates that the stability of fractured rock masses in
the brittle crust is controlled by two basic parameters that can act in
concert: (1) the coefficient of friction $\mu$ of the rock in contact
or of the material filling the space between the two slipping surface
walls, if any (e.g., fault gouge); (2) the normal stress component
$\sigma_{n}$, acting perpendicularly to the discontinuity surface.
The cohesion $C$ is usually assumed to be equal to zero, given its
negligible value for most rocks. \citet{Handin1969} showed
experimentally that if a pre-existing fracture is unfavorably oriented
with respect to the principal stress axes, a new fracture with a more
favorable orientation will form, leaving the pre-existing one
unreactivated. This can be illustrated by a construction in the Mohr
diagram (Figure~\ref{fig2}c) where the Mohr circle tangents the intact
rock failure envelope before the point corresponding to the
pre-existing fracture reaches the reactivation envelope.


\subsection{The reactivation of moderately to severely misoriented
fault surfaces}

In the brittle crust, the experimentally demonstrated preference of
fracture neoformation over preexisting misoriented fracture
reactivation does not seems to be a general rule. Indeed, in many
instances, moderately to severely misoriented fault surfaces are
reactivated, while no propagation of new surfaces is \mbox{observed}. Several
mechanisms are proposed to solve this paradox, among which the most
frequently invoked are as follows.


(1) The fault zone consists of a continuous layer of weak rocks, for
instance rocks whose rheology can be regarded as plastic,
visco-elastic, or elasto-plastic. This is the case with clay-rich or
evaporite-rich strata (so-called d\'{e}collement layers). Such a weak
and continuous d\'{e}collement layer will allow the displacement of
allochton units over significant distances whatever the orientation of
the fault zone with respect to the stress axes is favorable or not
\citep{DavisEngelder1985,Weijermarsetal1993,CostaVendeville2002,
Vendevilleetal2017}.


(2) The fault surface is coated by low-friction\unskip\break 
($\mu< 0.2$) material such as low-friction clay (e.g.,
montmorillonite) or talc \citep{Morrowetal1992,Morrowetal2017,
MooreLockner2011,Boutareaudetal2012,Chenetal2017}.
Leaving aside the stress corrosion process mentioned above, which
concerns the nucleation of a mesoscopic fracture rather than
reactivation of a macroscopic fracture or fault, fluids can weaken a
fault by chemically reacting with the rocks or minerals along the
damage zones or core zones of the fault. The chemically produced
minerals can be frictionally weaker (so-called reaction softening).
Examples of chemical weakening of fault rocks are described by 
\citet{WhiteKnipe1978,EvansChester1995,Wintschetal1995,
Gueydanetal2003,CollettiniHoldsworth2004,Matsudaetal2004,
Jefferiesetal2006,MooreRymer2007,Collettinietal2009B}. 
As indicated above, this reaction-softening effect will not be
developed\unskip\break here.


(3) Along long-lived mature faults, damaged rocks inside the fault
zone get their mechanical constants, such as their Young moduli or
Poisson ratios, modified \citep{Faulkneretal2006}. These modifications
lead to a rotation of the stress axes in the vicinity of the fault
\citep{Healy2008}. The angle between $\sigma_{1}$ and the fault
surface can thus be decreased and a very unfavorably oriented fault can
become favorably oriented for reactivation. The studies of 
\citet{ProvostHouston2001,HardebeckMichael2004,Faminetal2014}
suggest that vertical or steeply dipping strike-slip faults such as the
San Andreas fault in California or the Median Tectonic Line in Japan
can be reactivated following a rotation of the horizontal
$\sigma_{1}$ axis to a more favorable value.


(4) The last mechanism, which is the main purpose of this paper, calls
for the development of abnormally high $p_{f}$, which will decrease
the normal stress $\sigma_{n}$ to the effective $\sigma_{n}^*$
\citep{HubbertRubey1959,Chapple1978}. The analysis of 
\citet{Sibson1985}, which considers only the role of abnormally high
$p_{f}$, without taking into account the role of the three other
mechanisms, distinguishes three classes of fractures: (1) surfaces
\textit{favorably oriented} with respect to the stress axes, which can
be reactivated with a hydrostatic $p_{f}$ for given differential
stresses (see oblique dashed black lines and point A,
Figure~\ref{fig3}); (2) surfaces \textit{moderately misoriented} with
respect to the stress axes that will require large differential
stresses or supra-hydrostatic $p_{f}$ to be reactivated; (3)
\textit{severely misoriented} surfaces that will require, to be
reactivated, $p_{f}$ values larger than in cases (1) or (2), with
$\sigma_{3}^* < 0$ (see oblique black lines on Figure~\ref{fig3}).
The maximum differential stress allowing reactivation of severely
misoriented surfaces is limited by the failure envelope. If the
differential stress gets too high, a new and more favorably oriented
shear surface or a vein will form instead of reactivating the severely
misoriented surface (points B and C on Figure~\ref{fig3}). In all
cases, for a given value of differential stress, the $p_{f}$ value
required to reactivate a severely misoriented surface is higher than
that necessary for reactivation of a favorably oriented surface. The
tectonic regime also has an impact on the $\lambda$ values for
reactivation and vein formation. Indeed, reverse tectonic regimes
generally require higher $p_{f}$ than normal stress regimes do
(Figure~\ref{fig3}).


\subsection{The fault valve model}

The \textit{fault-valve} model, which is a consequence of the stress
analysis of \citet{Sibson1985}, is based on the existence, in faulted
regions, of fault planes moderately or severely misoriented with
respect to the stress axes at the time of the fault activity 
\citep{Sibsonetal1988,Sibson1989,Sibson1990}. The model is based on the
following assumptions: (1) the coefficient of friction on the
preexisting (misoriented) fault is of ``Byerlee'' type, that is, its
value is between 0.6 and 0.85; (2) the cohesion $C$ of the surface is
neglected; (3) the fluid does not chemically react with the rock, that
is, only the fluid pressure $p_{f}$ plays a role.

The typical fault-valve behavior of a fault or fault system involves
cyclical variations of $p_{f}$. A cycle consists of four stages: (1)
$p_{f}$ increases up to supra-hydrostatic values below a hydraulic
barrier, (2) rupture of the fault plane following a Mohr--Coulomb type
criterion \citep{Sibson1985}, (3) fluid escape (upward or sideward)
following increase of the rock permeability by fracturing and
cataclasis associated with fault and hydraulic barrier ruptures, (4)
fracture or pore sealing by mineral precipitation due to the sudden
decrease of $p_{f}$ down to hydrostatic values. This~last stage
eventually results in a restauration of the former seal, thus bringing
back the faulted rock mass to a state before stage (1), allowing a
repetition of the cycle. Following the  initial discovery of this
mechanism in mesothermal gold-quartz deposits by
\citet{Sibsonetal1988}, this behavior was recognized in ancient fault
systems 
\citep{Cox1995,Robertetal1995,Hacker1997,Nguyenetal1998,SibsonScott1998,Faleirosetal2007}.
The extensive damage to the rocks adjacent to the faults suggests that
reactivation might have been seismogenic. The fault-valve model is
proposed to account for present-day seismic reactivation of
unfavourably oriented faults (see Section~\ref{sec4}).


\subsection{The seismic pumping mechanism}\label{sec2.6}

Seismic pumping provides a mechanism of formation of zoned mineralized
veins along faults in the brittle crust by calling for fluid flow
during earthquakes \citep{Sibsonetal1975,Kerrichetal1987}. The mineral
zonation is interpreted as the result of repeated arrivals of fluids,
each arrival leaving an imprint in the vein. In the pre-seismic stage,
due to tectonic loading along the fault, dilatant structures such as
tension cracks will create voids along and near the fault, aspirating
nearby fluids. In the post-seismic stage, fluids will be expelled
upwards or sidewards, before the cycle starts again. In itself, the
seismic pumping mechanism does not increase directly the $p_{f}$ value,
but contributes to it by injecting volumes of fluids from remote areas
towards active fault zones. It can also be active during diagenesis in
faulted sedimentary basins  \citep{WoodBoles1991}.


\subsection{Shear stress-enhanced compaction}\label{sec2.7}

In most cases, the central part, or core, of a fault zone is
constituted by a weak material (clayey gouge, poorly consolidated
breccia and so on). When tectonically loaded, a core material may
undergo more compaction than the stronger surrounding rocks (damage
zone, country rocks). If the core zone is (i) saturated by fluids and
(ii) sealed (i.e., the fluid cannot escape), then tectonic load-induced
compaction will increase $p_{f}$ 
\citep{Byerlee1990,Blanpiedetal1992,SleepBlanpied1992}. The $p_{f}$
increase will then decrease the effective normal stress
$\sigma_{n}^*$, therefore allowing or favoring fault slip. Note
that this mechanism does not require any temperature\unskip\break increase.

\subsection{Thermal pressurization}

Thermal pressurization, also called ``dynamic'' pressurization,
concerns thin  (a few millimeters to a few centimeters) fault core zones
which are the site of coseismic slip along faults in the upper crust
\citep{Sibson1973,Lachenbruch1980,MaseSmith1987,WibberleyShimamoto2005}.
The phenomenon is based on a contrast between the thermal expansion of
aqueous fluids trapped in the very-low-permeability fault core rock
(clayey gouge in most cases) and the thermal expansion of the fault
core rock matrix itself. During co-seismic, slip, the fluid-saturated
rock will thermally expand due to shear heating, but fluids will expand
in larger proportions than the pores. As long as the rock permeability
remains low (e.g., in the absence of fracturing), the fluid cannot
escape from the core zone and, following expansion, its pressure will
increase drastically, resulting in a decrease of the normal stress
acting on the surface.


The recognition of thermal pressurization processes during earthquakes
or in the geological record is a challenge and, in addition to
observations of natural microstructures 
\citep{Ujiieetal2007,Ujiieetal2010,Boullieretal2009,Boullier2011}, 
must rely on experimental reproduction of seismic slip and on numerical
modeling 
\citep{NodaShimamoto2003,SegallRice2006,Ujiieetal2011,Boutareaudetal2008,
Ferrietal2010,Kitajimaetal2011,ViescaGaragash2015}.
In addition to thermal pressurization strictly speaking, frictional
heating can also lead to thermal decomposition of minerals such as
phyllosilicates or carbonates (calcite, siderite), resulting in the
release of fluids ($\mathrm{H}_{2}\mathrm{O},\mathrm{CO}_{2}$) that can
then be pressurized 
\citep{Brantutetal2008,Brantutetal2010,Hironoetal2008,Ferrietal2010,
Jeanneetal2014}.
Frictional melting of the fault surface during co-seismic slip in
carbonate-rich rocks can also result in a release of large amounts of
$\mathrm{CO}_{2}$ following volatile exsolution from the melt
\citep{Faminetal2008}. In the thermal decomposition or exsolution
processes, the released fluids are considered to be pressurized and can
consequently decrease the normal stress acting on the faults. Some
authors contend that so-called injected cataclasites or injected gouges
may result from\unskip\break co-seismic thermal pressurization
\citep{Linetal2013,Lin2019}.


\section{Role of abnormally high $p_{f}$ in crustal\newline tectonics}

\subsection{Role of abnormally high $p_{f}$ in thrust\newline tectonics}

In areas dominated by thin-skinned tectonics, thrust faults can
accommodate significant (${>}$10~km) horizontal
displacements. To overcome the mechanical resistance of the
allochtonous units to displacement, two mechanisms among the ones
described above are frequently called for. The first mechanism (the
translation made possible by weak ductile d\'{e}collement layers)
allows to account for the formation of several foreland thrust-and-fold
belts such as the French-Swiss Jura belt or the Iranian Zagros belt
\citep{Jordan1992,Sherkatietal2006,Sommarugaetal2017,LacombeMouthereau2002}.


The other mechanism, that is, the translation of thrust sheets
triggered or favored by supra-hydrostatic $p_{f}$, is inferred or
ascertained in various tectonic settings. Table~\ref{tab1} provides
examples of studies that call for supra-hydrostatic $p_{f}$ to
account for horizontal displacements along thrusts in collision belts
or foreland fold-and-thrust belts. The supra-hydrostatic $p_{f}$
lowers $\sigma_{n}^*$, thereby reducing the frictional resistance to
motion and allowing a smooth displacement of the allochton units over
their relative autochthonous basement. Evidence for supra-hydrostatic
$p_{f}$ either come from direct methods, namely $p_{f}$
measurements in exploration boreholes, or from indirect methods, such
as analyses of geological structures (e.g., dilatant crack-seal veins
or implosion breccias) or modeling (critical Coulomb wedge, Coulomb
stress change). Fluid inclusions preserved in mineralized veins can
provide estimates of $p_{f}$ at the time of vein formation. As such,
they are a powerful and reliable method for $p_{f}$ estimates.\looseness=-1


\begin{table*}
\caption{Examples of geological or geophysical evidence for
displacement along low-angle reverse faults triggered or favored by
supra-hydrostatic pore fluid pressures $p_{f}$ inside or near fault
zones in collision belts or foreland fold-and-thrust belts, with pore
fluid ratio $\lambda$ estimates where available\label{tab1}}
\begin{tabular}{ccc}
\thead
Area & Name of structure & Evidence \\
\endthead
Central Alps & Glarus thrust & 
\parbox[t]{8cm}{\centering Fracturing, veining, brecciation alternating
with ductile deformation~($\lambda > 1$)$^{[1]\ndash [4]}$} 
\vspace*{4pt}\\

\morerows{1}{Western Alps}  & 
\parbox[t]{4.5cm}{\centering Helvetic Diablerets nappe basal thrust} & 
\parbox[t]{8cm}{\centering Large amounts of connate and metamorphic
waters expelled upward, as indicated by $\delta^{18}\mathrm{O}$,
$\delta^{13}\mathrm{C}$ and $\delta\mathrm{D}$ in calcite or quartz
veins, possibly overpressured by rapid tectonic burial$^{[5]}$} 
\vspace*{4pt}\\

& \parbox[t]{4.5cm}{\centering Sub-Alpine frontal thrust zone (Chartreuse
and Vercors) and foreland (Valence basin)} & 
$p_{f}$ measurements in exploration boreholes$^{[6]}$  \vspace*{4pt}\\ 

Pyrenees & 
\parbox[t]{4.5cm}{\centering Gavarnie thrust and splay faults} & 
\parbox[t]{8cm}{\centering Fluid inclusions in quartz veins indicate fluctuations of $p_{f}$
between lithostatic (${\sim}$500~MPa) and hydrostatic
(${\sim}$200~MPa)$^{[7]}$; combination of shear reactivation
and extension vein opening ($\lambda = 0.77\ndash 0.89$)$^{[8]}$} 
\vspace*{4pt}\\ 

Himalaya & 
\parbox[t]{4.5cm}{\centering Himalayan Main Central Thrust} & 
\parbox[t]{8cm}{\centering Critical Coulomb wedge modeling suggests
${\lambda} =0.8\ndash 0.9^{[9]}$, Coulomb stress change modeling suggests
${\lambda} = 0.3\ndash 0.9^{[10]}$} 
\vspace*{4pt}\\ 

Apennines & 
\parbox[t]{4.5cm}{\centering Apenninic basal thrust zone, Apenninic foreland} & 
\parbox[t]{8cm}{\centering Fluid inclusions in quartz veins indicate
near-lithostatic $p_{f}$ at the time of the emplacement of the Liguride
nappes$^{[11]}$; calcite-cemented implosion breccias filling dilational
jogs ($p_{f}> \sigma_{3}$)$^{[12]}$} 
\vspace*{4pt}\\ 

Taiwan & 
\parbox[t]{4.5cm}{\centering Taiwan fold-and-thrust belt basal
decollement fault, Chelungpu fault} & 
\parbox[t]{8cm}{\centering $p_{f}$ measurements in exploration
boreholes ($\lambda \sim 0.7$)$^{[13]}$, critical Coulomb wedge
modeling$^{[14],[15]}$; discrete hydraulic fractures$^{[16]}$}  
\vspace*{4pt}\\ 

\parbox[t]{1.5cm}{\centering Western California} & 
\parbox[t]{4.5cm}{\centering Coast Ranges and western Great Valley}\vspace*{2pt} & 
$p_{f}$  measurements in exploration boreholes$^{[17], [18]}$ 
\botline
\end{tabular}
\tabnote{References: $^{[1]}$\citet{Burkhardetal1992}, 
$^{[2]}$\citet{BadertscherBurkhard2000}, $^{[3]}$\citet{Badertscheretal2002}, 
$^{[4]}$\citet{HurzelerAbart2008}, $^{[5]}$\citet{CrespoBlancetal1995}, 
$^{[6]}$\citet{Deville2021}, $^{[7]}$\citet{HendersonMcCaig1996}, 
$^{[8]}$\citet{Lacroixetal2013}, $^{[9]}$\citet{Mugnieretal1994}, 
$^{[10]}$\citet{CattinAvouac2000}, $^{[11]}$\citet{Mullis1988}, 
$^{[12]}$\citet{Vannucchietal2010}, $^{[13]}$\citet{SuppeWittke1977}, 
$^{[14]}$\citet{Davisetal1983}, $^{[15]}$\citet{BarrDahlen1990}, 
$^{[16]}$\citet{Boullier2011}, $^{[17]}$\citet{Melchiorreetal1999}, 
$^{[18]}$\citet{Unruhetal1992}.}
\end{table*}

\begin{sidewaystable*}
\vspone
\caption{Examples of geological or geophysical evidence for
supra-hydrostatic pore fluid pressures $p_{f}$ measured or inferred
along low-angle reverse faults in accretionary prisms\label{tab2}}
\fontsize{9}{10.8}\selectfont
\begin{tabular}{cccc}
\thead
Type of prism & Area & Type of structure & Evidence \\ 
\endthead
\morerows{5}{\parbox[t]{2cm}{\centering Active accretionary prisms}}  & 
\parbox[t]{3cm}{\centering Cascadia margin Oregon accretionary prism} & 
\parbox[t]{2.5cm}{\centering Frontal d\'{e}collement} & 
\parbox[t]{28pc}{\centering Seismic velocity variations and negative
polarity reflections in seismic profiles$^{[1]\ndash [3]}$; ODP core
consolidation tests and logging data (${\lambda} = 0.88\ndash
0.99$)$^{[4]}$; supra-hydrostatic $p_{f}$ (${\lambda} = 0.8$) computed
from velocity-depth data$^{[5]}$; reverse polarity reflections from the
d\'{e}collement$^{[6]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Central America Costa Rica and Guatemala margins} & 
\parbox[t]{2.5cm}{\centering Frontal d\'{e}collement} & 
\parbox[t]{28pc}{\centering Direct measurement of $p_{f}$ in DSDP
boreholes ($\lambda = 0.25\ndash 0.48$)$^{[7]}$; consolidation tests on
ODP cores suggest excess $p_{f}$ (1.3--3.1~MPa)$^{[8]}$; numerical modeling
of $p_{f}$ build-up following sediment dewatering in undrained
conditions$^{[9]}$; $p_{f}$ measurements in ODP borehole hydrologic
observatories (${\lambda} = 0.25\ndash 1$)$^{[10]}$; pervasive veining
suggests $p_{f}$ fluctuations in accordance with the seismic cycle$^{[11]}$} 
\vspace*{4pt}\\

& \morerows{1}{\parbox[t]{3cm}{\centering SW Japan Nankai Trough accretionary prism}}  & 
\parbox[t]{2.5cm}{\centering Frontal d\'{e}collement} & 
\parbox[t]{28pc}{\centering Shear tests on saturated clay samples from
the d\'{e}collement indicate that friction drops dramatically with
increasing $p_{f}^{[12]}$; overconsolidation and dilatant fractures
along the d\'{e}collement$^{[13]}$; seismic reflection amplitude
variations along the d\'{e}collement$^{[14]}$; modeling of $p_{f}$
based on acoustic velocity logs$^{[15]}$; modeling of $p_{f}$ based on
laboratory permeability measurements from core samples suggest
$\lambda^* = 0.68 \ndash 0.77^{[16]}$; supra-hydrostatic $p_{f}$
deduced from seismic interval velocities$^{[17]}$; empirical
relationships between $V_{P}$, porosity, and effective $\sigma_{m}$
obtained from laboratory deformation tests on drill core samples
indicate excess $p_{f}$ of 17--87~MPa$^{[18]}$; upward flow of drilling
mud from IODP borehole indicates an initial excess $p_{f}$ of
${\sim}$5--10~MPa above $p_{H}^{[19]}$; estimation of $p_{f}$ from
empirical relationships between $p_{f}$, porosity and $V_{P}$, obtained
from consolidation experiments and from drilling or sonic velocity
data$^{[20]}$} 
\vspace*{4pt}\\

&  & Splay fault\vspace*{2pt} & 
\parbox[t]{28pc}{\centering High-amplitude negative polarity reflections
in seismic profiles$^{[21], [22]}$; low impedance layer$^{[23]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Lesser Antilles Barbados Ridge accretionary prism} & 
\parbox[t]{2.5cm}{\centering Frontal d\'{e}collement} & 
\parbox[t]{28pc}{\centering $p_{f}$ estimated from seismic velocity~or
from negative polarity reflections$^{[24], [25]}$; direct measurements in
ODP boreholes and sediment consolidation tests~($\lambda$ up to
${>}$0.9)$^{[26], [27]}$; high $p_{f}$ suggested by anisotropy of magnetic
susceptibility$^{[28]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering  New Zealand Hikurangi accretionary prism} & 
\parbox[t]{2.5cm}{\centering P\={a}paku splay fault} & 
\parbox[t]{28pc}{\centering Rock deformation experiments on cores from
the fault zone  ($\lambda^* = 0.3\ndash 0.6$)$^{[29]}$} 
\tabularbreaktwo\\ 

\morerows{3}{\parbox[t]{2cm}{\centering Exhumed inactive accretionary prisms}}  & 
\morerows{1}{\parbox[t]{3cm}{\centering Shimanto accretionary prism (Japan)}}  & 
\parbox[t]{2.5cm}{\centering Nobeoka paleo-d\'{e}collement}  & 
\parbox[t]{28pc}{\centering Fluid inclusions and modeling suggest
$p_{f}$ excess values between 5 and 20~MPa$^{[30]}$} 
\vspace*{4pt}\\

& & \parbox[t]{2.5cm}{\centering Nakanomata splay fault} & 
\parbox[t]{28pc}{\centering Quartz-cemented syntectonic dilatant hydraulic breccias$^{[31]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Kodiak accretionary prism (Alaska)} & 
\parbox[t]{2.5cm}{\centering Paleo-d\'{e}collements and m\'{e}lange zones} & 
\parbox[t]{27pc}{\centering Crack-seal quartz veins parallel to ancient
decollements interpreted as resulting from repeated hydrofracturing
($p_{f} > \sigma_{3}$)$^{[32]}$; fluid inclusions indicate
near-lithostatic $p_{f}$ ($p_{f} \sim \sigma_{1}$)~at the time of
quartz vein formation$^{[33], [34]}$; lack of low-friction material and
mechanical analysis of displacement along the d\'{e}collement plead for
supra-hydrostatic $p_{f}^{[35]}$; hydrofractures suggest
supra-hydrostatic $p_{f}^{[36]}$; fluid inclusions in hydrofractures
suggest near-lithostatic $p_{f}^{[37]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Chrystalls Beach accretionary prism (New Zealand)} & 
\parbox[t]{2.5cm}{\centering Mudstone matrix of m\'{e}lange}\vspace*{2pt} & 
\parbox[t]{28pc}{\centering Shear veins severely misoriented with
respect to stress field$^{[38], [39]}$}
\botline
\end{tabular}
\xxtabnote{References: $^{[1]}$\citet{Cochraneetal1994},
$^{[2]}$\citet{Cochraneetal1996}, $^{[3]}$\citet{Mooreetal1995a},
$^{[4]}$\citet{Mooreetal1995b}, $^{[5]}$\citet{Hyndmanetal1993},
$^{[6]}$\citet{Tobinetal1994}, $^{[7]}$\citet{VonHuene1985}, 
$^{[8]}$\citet{Safferetal2000}, $^{[9]}$\citet{ScreatonSaffer2005}, 
$^{[10]}$\citet{DavisVillinger2006}, $^{[11]}$\citet{VannucchiLeoni2007},
$^{[12]}$\citet{Brownetal2003}, $^{[13]}$\citet{Ujiieetal2003},
$^{[14]}$\citet{Bangsetal2004}, $^{[15]}$\citet{Tsujietal2008},
$^{[16]}$\citet{SkarbekSaffer2009}, $^{[17]}$\citet{TobinSaffer2009},
$^{[18]}$\citet{KitajimaSaffer2012}, $^{[19]}$\citet{Hiroseetal2021},
$^{[20]}$\citet{PwavodiDoan2024}, $^{[21]}$\citet{Parketal2000},
$^{[22]}$\citet{Parketal2002}, $^{[23]}$\citet{Bangsetal1990},
$^{[24]}$\citet{Shipleyetal1994}, $^{[25]}$\citet{Mooreetal1995c},
$^{[26]}$\citet{MooreTobin1997}, $^{[27]}$\citet{Mooreetal1998},
$^{[28]}$\citet{Housenetal1996}, $^{[29]}$\citet{FrenchMorgan2020},
$^{[30]}$\citet{Raimbourgetal2015}, $^{[31]}$\citet{Passelegueetal2014},
$^{[32]}$\citet{FisherByrne1987}, $^{[33]}$\citet{Vrolijk1987},
$^{[34]}$\citet{Vrolijketal1988}, $^{[35]}$\citet{ByrneFisher1990},
$^{[36]}$\citet{Fisheretal1995}, $^{[37]}$\citet{Roweetal2009},
$^{[38]}$\citet{Fagerengetal2010}, $^{[39]}$\citet{Fagerengetal2011}.}
\xxtabnote{ODP: Ocean Drilling Program. IODP: International Ocean Drilling
Program. 3D: three-dimensional. $p_{H}$: hydrostatic pressure.
$\sigma_{{m}}$: mean stress ($\sigma_{{m}}= (\sigma_{1}
+ \sigma_{{2}} + \sigma_{3})/3)$. $\lambda^*$: modified
pore fluid factor, $\lambda^* = (p_{f} -
p_{H})/(p_{L} - p_{H}$), where $p_{{H}}$ is the
hydrostatic pressure and $p_{{L}}$ the lithostatic pressure caused by
the weight of the overburden \citep{SafferTobin2011}.}
\end{sidewaystable*}

The role of supra-hydrostatic $p_{f}$ build-up appears critical or
ubiquitous in accretionary prisms, whatever active or inactive 
\citep{MooreVrolijk1992}. \mbox{Table~\ref{tab2}} provides examples of various
continental margins or paleo-margins in which displacement along past
or present (first-order) d\'{e}collement faults or second-order faults
(also referred to as splay faults) branching on d\'{e}collements was or
is possible due to supra-hydrostatic $p_{f}$. Similarly to what is
inferred along large-displacement thrusts, the supra-hydrostatic
$p_{f}$ lowers $\sigma_{n}^*$, thereby reducing the frictional
resistance to motion and allowing a smooth displacement of the
overriding plate oceanwards, at least in the shallowest parts of the
plate interface, before pressure and temperature increases lead to
dehydration and expulsion of fluids. Direct evidence for
supra-hydrostatic $p_{f}$ along the basal d\'{e}collements of
accretionary prisms come form $p_{f}$ measurements in Deep-Sea
Drilling Project (DSDP), Ocean Drilling Program (ODP) or Integrated
Ocean Drilling\unskip\break Program (IODP) boreholes. Porosity measurements and
various mechanical tests (e.g., consolidation tests) on DSDP/ODP/IODP
cores further testify for under-compaction of sediments or rocks along
the d\'{e}collements, accounted for by the assumption of
supra-hydrostatic to nearly lithostatic $p_{f}$. The presence of
hydrofractures along as well as above or below d\'{e}collements is also
direct evidence [Table~\ref{tab2}; see also \citealp{Behrmann1991}].
Indirect evidence come from seismic reflection imaging, with
characteristic negative polarity reflections along d\'{e}collement
surfaces. Lastly, the weakening role of supra-hydrostatically
pressurized fluids along the basal d\'{e}collement of accretionary prisms
can be reproduced by analog modelling
\citep{Cobboldetal2001,MourguesCobbold2003}.

\subsection{Role of abnormally high $p_{f}$ in extensional tectonics}

Large displacement along low-angle normal faults, also referred to as
detachments, is mechanically paradoxical. The different mechanisms
mentioned above to account for the displacement along misoriented fault
surfaces apply to low-angle normal faults 
\citep{ReynoldsLister1987,Yin1989,Axen1992,Westaway1999,Abers2009,Collettini2011}.
Table~\ref{tab3} provides examples of studies which suggest or demonstrate that
reactivation of low-angle normal faults was possible because of
supra-hydrostatic to lithostatic $p_{f}$ values. Regarding inactive
detachments, structural evidence for high $p_{f}$ come from textures of
precipitated minerals in breccia cements (so-called cockade structures)
or in flat-lying crack-seal dilatant veins. Fluid inclusions in the
precipitated minerals also provide indications. Lastly, mechanical
modeling also accounts for overpressured-fluid-aided displacements
along low-angle faults. Regarding active detachments, evidence consist
of vein or breccia cement texture analyses (including fluid
inclusions), mechanical modeling, $p_{f}$ measurements in boreholes,
geophysical investigations (body wave velocity anomalies).

\begin{table*}
\caption{Examples of geological or geophysical evidence for
displacement along low-angle normal faults (detachment faults)
triggered or favored by supra-hydrostatic pore fluid pressures $p_{f}$
inside or near the fault zone\label{tab3}}
\fontsize{9.6}{11.5}\selectfont
\begin{tabular}{ccc}
\thead
\parbox[t]{2.5cm}{\centering Type of low-angle normal fault} &
Name of structure, area\vspace*{2pt} & Evidence \\ 
\endthead
\morerows{2}{\parbox[t]{2cm}{\centering Inactive intra-continental}}  &
\parbox[t]{4.5cm}{\centering Western US Basin and Range (Southern
Mountains MCC deformed zones, Arizona; Whipple detachment, California;
Siever Desert detachment, Utah)} & 
\parbox[t]{7.7cm}{\centering Flat-lying dilatant veins suggest $p_{f} >
\sigma_{3}^{[1]}$; fluid inclusions in quartz veins suggest $p_{f}
\geq 120$~MPa$^{[2],[3]}$; critical Coulomb wedge analysis suggests
$p_{f} \sim 0.6$~$\sigma_{v}^{[4]}$} 
\vspace*{4pt}\\

& \parbox[t]{4.5cm}{\centering Central Alps (Brenner, Simplon and Grimsel faults)} &
\parbox[t]{7.7cm}{\centering Fluid inclusions in veins suggest
supra-hydrostatic $p_{f}^{[5]}$; mylonitic zone embrittlement suggests
episodic supra-hydrostatic $p_{f}^{[6],[7]}$; textural characteristics
of cockade structures in a fault breccia and mechano-chemical
calculations allow to reconstruct $p_{f}$ fluctuations related to
different stages of the seismic cycle$^{[8]}$} 
\vspace*{4pt}\\

& \parbox[t]{4.5cm}{\centering Gulf of Corinth LANF, Greece} & 
\parbox[t]{7.7cm}{\centering Limit Analysis (maximum strength theorem
analysis) suggests $p_{f} = 0.57\ndash 0.77$~$\sigma_{{v}}^{[9]}$} 
\vspace*{4pt}\\ 

\parbox[t]{2cm}{\centering Active intra-continental} &
\parbox[t]{4.5cm}{\centering North Apennines LANFs, including Alto
Tiberina and Tellaro detachments} & 
\parbox[t]{7.7cm}{\centering Limit Analysis (maximum strength thorem
analysis) suggests that $p_{f} = 0.57\ndash 0.77$~$\sigma_{{v}}^{[9]}$; $p_{f}
\sim 0.85$~$\sigma_{v}$ in exploration boreholes$^{[10]}$; brittle
tensile structures and fluid inclusions in calcite veins suggest
episodic supra-hydrostatic $p_{f}^{[11]}$; $V_{P}$ positive anomaly,
$V_{P}/V_{S}$ negative anomaly$^{[12]}$} 
\vspace*{4pt}\\ 

\parbox[t]{2cm}{\centering Inactive intra-oceanic or intra-OCT}  &
\parbox[t]{4.5cm}{\centering Detachment surfaces exposed in Alpine ophiolites} & 
\parbox[t]{7.7cm}{\centering Calcite-cemented breccias
(ophicalcites)$^{[13], [14]}$; gouge veins injected in cataclasite
suggest transient supra-hydrostatic $p_{f}^{[15]}$} 
\vspace*{4pt}\\ 

\morerows{1}{\parbox[t]{2cm}{\centering Active intra-oceanic}}  &
\parbox[t]{4.5cm}{\centering Mid-Atlantic ridge Atlantis massif,
mid-Atlantic ridge 13\textdegree--15\textdegree~N} & 
\parbox[t]{7.7cm}{\centering Fluid inclusions$^{[16], [17]}$; hydraulic breccias$^{[18]}$} 
\vspace*{4pt}\\

& \parbox[t]{4.5cm}{\centering South Pacific Woodlark-D'Entrecasteaux ridge Moresby detachment}\vspace*{2pt} &
\parbox[t]{7.7cm}{\centering Low $V_{P}$ and high porosity values in
the fault zone suggest supra-hydrostatic $p_{f}^{[19]}$; dilatant
crak-seal veins suggest episodic near-lithostatic $p_{f}$ and
hydrofracturing$^{[20],[21]}$; calcite veins parallel to foliation
suggest supra-lithostatic $p_{f}^{[22]}$} 
\botline
\end{tabular}
\tabnote{References: $^{[1]}$\citet{ReynoldsLister1987}, 
$^{[2]}$\citet{Smithetal1991}, $^{[3]}$\citet{Selverstoneetal2012},
$^{[4]}$\citet{Yuanetal2018}, $^{[5]}$\citet{Selverstoneetal1995}, 
$^{[6]}$\citet{Axenetal1995}, $^{[7]}$\citet{Axenetal2001},
$^{[8]}$\citet{BergerHerwegh2019}, $^{[9]}$\citet{Yuanetal2020}, 
$^{[10]}$\citet{Collettinietal2008}, $^{[11]}$\citet{Clemenzietal2015},
$^{[12]}$\citet{Morettietal2009}, $^{[13]}$\citet{FruhGreenetal1990},
$^{[14]}$\citet{Picazoetal2013}, $^{[15]}$\citet{Manatschal1999},
$^{[16]}$\citet{Escartinetal2003}, $^{[17]}$\citet{Castelainetal2014},
$^{[18]}$\citet{Picazoetal2012}, $^{[19]}$\citet{Floydetal2001},
$^{[20]}$\citet{Rolleretal2001}, $^{[21]}$\citet{Kopfetal2003}, 
$^{[22]}$\citet{FaminNakashima2005}.}
\tabnote{MCC: metamorphic core complex. LANF:
low-angle normal fault. OCT: ocean-continent transition.\unskip\break $\sigma_{v}$:
principal vertical stress axis.}
\end{table*}


The other mechanisms listed above may also facilitate large
displacement along low-angle normal faults. In particular, analog
modeling suggests that extension can take place above continuous
low-strength layers such as evaporites 
\citep{VendevilleJackson1992A,VendevilleJackson1992B}. Regarding the
reorientation of the stress axes in the vicinity of the fault,
\citet{Lecomteetal2011} propose to explain reactivation of misoriented
low-angle normal faults by calling for an elasto-plastic frictional
gouge instead of the classical frictional fault gouge. Plastic strain
can initiate the displacement despite the misorientation. Following the
initiation, stress axes near the fault zone rotate to a more favorable
orientation with respect to the fault surface, allowing further
displacement.

\subsection{Role of abnormally high $p_{f}$ in strike-slip\newline tectonics}

The activity of steeply dipping to vertical plate-boundary transform or
intra-plate strike-slip faults moderately to severely misoriented with
respect to the principal stress axes constitutes a challenge since the
discovery of nearlyperpendicular normal stresses acting along the San
Andreas fault \citep{MountSuppe1987,Zobacketal1987}. As such, the San
Andreas faults appears as a weak fault, and explanations for it have
been extensively looked for. The models and mechanical analyses of
\citet{Byerlee1990,Byerlee1993} and \citet{Rice1992} attempt to show
that supra-hydrostatic $p_{f}$ could account for the weakness of the
fault. Experimental measurement of clay permeabilities 
\citep[e.g.,][]{FaulknerRutter2001} provide a mechanism for the
maintenance of excess $p_{f}$ in strike-slip fault zones. However,
drilling across the fault zone during the SAFOD (San Andreas Fault
Observatory at Depth) program at ${\sim}$3~km depth did not reveal any
supra-hydrostatic $p_{f}$, prompting researchers to propose other
mechanisms that could explain the weakness: fault rocks with extremely
low friction coefficients such as talc \citep{MooreRymer2007} or clays 
\citep{Schleicheretal2009a,Schleicheretal2009b,Carpenteretal2011,Holdsworthetal2011},
stress axes reorientations to more favorable attitudes at short
distances from the fault 
\citep{ProvostHouston2001,HardebeckMichael2004,Healy2008}. It seems
clear that pressurized fluids do not weaken the San Andreas fault in
its upper part (between the surface and a ${\sim}$3~km depth), except
perhaps for micro-earthquake activity  \citep{Mittempergheretal2011}.
Hydro-mechanical modeling 
\citep[e.g.,][]{FultonSaffer2009,Beeleretal2013} suggests that
supra-hydrostatic $p_{f}$ could play a role in the weakening at depths
larger than the SAFOD drilling.\unskip\break Conversely, hydro-mechanical modeling
by \citet{Fultonetal2009} suggest that supra-hydrostatic $p_{f}$ cannot
be maintained along the San Andreas fault at shallow (${<}$3~km) depth,
and that other mechanisms such as shear-enhanced compaction or thermal
pressurization inside the fault zone have to be invoked.

Table~\ref{tab4} provides examples of transform or strike-slip faults
along which supra-hydrostatic $p_{f}$ could play or could have played a
role in the past or present fault activity. Direct evidence for
abnormally high $p_{f}$ can be found in shallow boreholes drilled
across the New Zealand Alpine fault, but no data from depths larger
than a few hundred meters are available. Indirect evidence consist
either in rare hydraulic fractures or in more frequently observed
geophysical (electrical conductivity or seismic velocity) anomalies. In
this last case, even if the anomalies can be interpreted as caused by
the presence of fluids at depth, they do not bring undisputable
evidence for pressurized fluids. The apparent scarcity of abnormally
high $p_{f}$ ascertained along transform or strike-slip fault zones may
be due to the lack or scarcity of efficient seals. Indeed, fault zones,
especially their damage zones if any, crossing the entire crust may
appear as conduits rather than barriers or seals.


\begin{table*}
\caption{Examples of geological or geophysical evidence for
displacement along transform faults or strike-slip faults
triggered or favored by supra-hydrostatic pore fluid pressures $p_{f}$
inside or near fault zones\label{tab4}}
\begin{tabular}{cc}
\thead
Area, name of structure & Evidence \\ 
\endthead
\parbox[t]{3cm}{\centering California, San Andreas fault} &
\parbox[t]{11cm}{\centering Very low resistivity, low $V_{P}$, and high a
$V_{P}/V_{S}$ ratio suggest supra-hydrostatic $p_{f}^{[1]}$; calcite and
anhydrite-filled mode I veins in SAFOD cores suggest that transient
increases of supra-hydrostatic (possibly supra-lithostatic) $p_{f}$
occurred during fault activity and may constitute a triggering
mechanism for some micro-earthquakes recorded at depth near SAFOD
drilling site$^{[2]}$; frictional sliding and stress-driven DMT
microstructures suggest that deformation in the active shear zones is
displacement-weakening, possibly due to local and transient high
$p_{f}$ build-ups along creeping segments$^{[3]}$; microstructural and
geochemical data from SAFOD samples indicate that transient co-seismic
fluid overpressure events overprint aseismic creep along the fault$^{[4]}$}
\vspace*{4pt}\\ 

\parbox[t]{3cm}{\centering Turkey, North Anatolian Fault} & 
\parbox[t]{11cm}{\centering Fluid inclusions in subhorizontal extension
veins suggest supra-hydrostatic $p_{f}^{[5]}$; continuous ascent of deep
crustal or mantle fluid ($\mathrm{CO}_{2}$, $\mathrm{CH}_{4}$ or
He) could result in near-lithostatic or supra-lithostatic $p_{f}^{[6]}$;
low electrical resistivity (measured by magnetotelluric methods) and
low $V_{P}$ (measured by 2-D seismic velocity tomography) suggest high
$p_{f}$ at 5--15~km depth$^{[7],[8],[9]}$} 
\vspace*{4pt}\\ 

\parbox[t]{3cm}{\centering New Zealand, Alpine Fault} & 
\parbox[t]{11cm}{\centering Slug tests in shallow (150~m deep) boreholes
suggest that the near-surface Alpine fault zone may be site of high
$p_{f}$ gradient$^{[10]}$; pressure measurement during drilling reveals a
slight (9\%) supra-hydrostatic $p_{f}$ in shallow
(${\sim}$900~m deep) borehole$^{[11]}$; tremors appear to be
located at 25--45~km depth, in a region of high P-wave
attenuation that could be the site of supra-hydrostatic $p_{f}^{[12]}$} 
\vspace*{4pt}\\

\parbox[t]{3cm}{\centering Japan, Atotsugawa fault} & 
\parbox[t]{11cm}{\centering High $p_{f}$ could account for creep
along some parts of the fault$^{[13]}$} 
\vspace*{4pt}\\ 

\parbox[t]{3cm}{\centering Japan, Nojima fault} & 
Discrete hydraulic fractures$^{[14]}$ 
\vspace*{4pt}\\ 

\parbox[t]{3cm}{\centering Central Alps, Adamello pluton} & 
\parbox[t]{11cm}{\centering Reactivation of the severely misoriented
inactive Gole Larghe fault$^{[15]}$} 
\vspace*{4pt}\\ 

\parbox[t]{3cm}{\centering Southeastern Brazil, Ribeira Shear Zone}\vspace*{2pt} & 
\parbox[t]{11cm}{\centering Fluid inclusions in foliation-parallel or
extensional quartz veins along the shear zone indicate $p_{f}$
fluctuations that are interpreted as the result of a fault-valve
behavior$^{[16]}$} 
\botline
\end{tabular}
\tabnote{References: $^{[1]}$\citet{EberhartPhillipsMichael1993},
$^{[2]}$\citet{Mittempergheretal2011}, $^{[3]}$\citet{Hadizadehetal2012},
$^{[4]}$\citet{Hadizadehetal2024}, $^{[5]}$\citet{Janssenetal1997},
$^{[6]}$\citet{Pfisteretal2000}, $^{[7]}$\citet{Karabulutetal2003},
$^{[8]}$\citet{Tanketal2005}, $^{[9]}$\citet{Karasetal2020},
$^{[10]}$\citet{Sutherlandetal2012}, $^{[11]}$\citet{Sutherlandetal2017},
$^{[12]}$\citet{Wallace2020}, $^{[13]}$\citet{Katoetal2007},
$^{[14]}$\citet{Boullier2011}, $^{[15]}$\citet{Mittempergheretal2009},
$^{[16]}$\citet{Faleirosetal2007}.}
\tabnote{SAFOD: San Andreas Fault Observatory at
Depth. DMT: diffusive mass transfert.}
\end{table*}



\subsection{Conclusions}

A review of the literature dealing with the role of abnormally high
$p_{f}$ along faults in the brittle crust allows to draw the following
key ideas.

(1) Undebatable evidence for supra-hydrostatic $p_{f}$ come from
pressure measurements in oil industry or scientific boreholes (DSDP,
OPD, IODP). Near-horizontal dilatant veins found along low-angle faults
also constitute a strong evidence, especially when fluid inclusions
preserved in these veins indicate supra-hydrostatic $p_{f}$ at the time
of fluid entrapment. Geophysical anomalies, either electrical
(conductivities) or seismological (seismic velocities), are interpreted
as caused by abnormally high $p_{f}$ at depth along fault zones.

(2) Evidence, whatever direct or indirect, for supra-hydrostatic
$p_{f}$ appear common along low-angle normal faults (detachments) or
reverse faults (including d\'{e}collements) 
(Tables~\ref{tab1}--\ref{tab3}). 
Fluids appear to be efficiently trapped
beneath flat-lying or gently dipping allochtons that can act as
impervious or low-permeability lids. Conversely, conclusive evidence
for supra-hydrostatic $p_{f}$ along transform or strike-slip faults are
scarcer than along low-angle normal or reverse faults
(Table~\ref{tab4}), possibly because such vertical or steeplydipping
fault zones lack tight and laterally continuous seals that could
prevent fluids from leaking upward to the surface.

(3) Along with fracturing and comminution linked with displacement
along faults, fluid circulation and associated fluid-rock interactions
quite often result in alteration of minerals, resulting in weaker
minerals such as clays, talc and other minerals whose frictional
properties are much weaker than primary minerals. This chemical effect
of fluids is clearly a serious competitor with the pressurization of
fluids to account for fault weakening.

(4) Mechanisms such as shear stress-enhanced compaction, thermal
pressurization, or stress reorientation near fault zones certainly play
roles in the reactivation of misoriented faults, but they are difficult
to be recognized in the geological record.


\section{Fluids and natural earthquakes}\label{sec4}

\subsection{Intra-plate earthquakes, earthquake\newline sequences,
background seismicity,\newline subduction earthquakes}

Table~\ref{tab5}  presents
examples of studies that attempt to relate major
intra-continental earthquakes, earthquake sequences, background
seismicity, subduction earthquakes and aftershock sequences to
abnormally high $p_{f}$. Some of these examples were already introduced
in the previous section, but without any specific mention to the
seismogenic activity of the relevant faults.

\begin{sidewaystable*}
\vspone
\caption{Examples of geophysical evidence for major
earthquakes and aftershocks triggered or favored by abnormally high
pore fluid pressures $p_{f}$ in or around fault zones\label{tab5}}
\fontsize{9.5}{11.5}\selectfont
\begin{tabular}{ccc}
\thead
Type of event & Area and/or events & Evidence \\ 
\endthead
\morerows{9}{\parbox[t]{2cm}{\centering Intraplate earthquakes,
earthquake sequences and background seismicity}}  & 
Central Alps & 
\parbox[t]{34pc}{\centering Unexpected background seismic activity
in the lower crust accounted for by supra-hydrostatic $p_{f}^{[1]}$} 
\vspace*{4pt}\\

& Himalaya MCT & 
\parbox[t]{34pc}{\centering Drop in $V_{P}$ and $V_{S}$ values,
increase of $V_{P}/V_{S}^{[2]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Himalaya background sesimicity} & 
\parbox[t]{34pc}{\centering Supra-hydrostatic $p_{f}$ at depth deduced
from correlated seasonal variation of stress and seismicity$^{[3]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Northern Apennines (1997--1998
Umbria-Marche-Colfiorito, 2000 Faenza and 2012 Emilia seismic
sequences)} & 
\parbox[t]{34pc}{\centering Supra-hydrostatic $p_{f}$ ($\lambda \geq
0.9$) inferred from the presence at depth of Triassic evaporite
impervious seals$^{[4]}$; supra-hydrostatic $p_{f}$ ($\lambda \geq
0.7$) suggested by stress inversion of focal mechanisms$^{[5]}$;
space--time evolution of seismic activity fits with diffusion laws,
$p_{f} \sim\sigma_{V}^{[6], [7]}$; $V_{P}/V_{S}$ changes along a fault
system suggest that $p_{f}$ fluctuations controlled the space--time
evolution of the Emilia sequence and the activation of the second main
shock$^{[8]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Central and southern Apennines (2009
Abruzzo-L'Aquila sequence, 2010--2014 Mt Pollino sequence)}  &
\parbox[t]{34pc}{\centering Supra-hydrostatic $\mathrm{CO}_{2}$~$p_{f}$
values in exploratory boreholes$^{[9], [10]}$; supra-hydrostatic
$p_{f}$ propagation along a fault system tracked by space--time
variations of $V_{P}/V_{S}$ anomalies during earthquake
migration$^{[11]}$; high $V_{P}/V_{S}$ and low $Q_{P}/Q_{S}$ indicative
of supra-hydrostatic $p_{f}^{[12]}$; temporal evolution of
$V_{P}/V_{S}$ suggests an increase through time of supra-hydrostatic
$p_{f}$ (up to ${\sim}$200~MPa at 10 km depth), eventually triggering
the 6 April 2009 $M_{W}$ 6.3 mainshock$^{[13]}$; increase of the
$V_{P}/V_{S}$ ratio and evolution of shear wave splitting before the
earthquake are interpreted as reflecting the progressive influx of
pressurized fluids near the hypocentral of the $M_{w}$ 6.3 L'Aquila
main shock$^{[14]}$; mantle-sourced $\mathrm{CO}_{2}$ accumulates under
near-lithostatic or supra-lithostatic $p_{f}$ in deep traps which may
control the Apennines seismic activity$^{[15], [16]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering East Iceland rift zone} & 
\parbox[t]{34pc}{\centering Stress inversion of focal mechanisms
suggests near-lithostatic $p_{f}$ values ($\lambda \sim 1$)$^{[17]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Back-arc side of NE Japan ($M > 6$
thrust-fault type events)}\vspace*{2pt} & 
\parbox[t]{34pc}{\centering Mohr--Coulomb analysis suggests that
severely misoriented faults are reactivated by supra-hydrostatic
$p_{f}$ through a fault-valve mechanism$^{[18]}$} \tabularbreakfive\\

& \parbox[t]{3cm}{\centering Kaapvaal craton (2017 $M_{W}$ 6.5 Bostwana
earthquake)} & 
\parbox[t]{34pc}{\centering Episodic seismic activity in an otherwise
stable craton explained by sporadic near-lithostatic $p_{f}$ ($\lambda
\sim 0.85$)$^{[19]}$}
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering New Madrid seismic zone (1811--1812
sequence)} & 
\parbox[t]{34pc}{\centering A test of the role of stress tensor shape
$\Phi$, fault friction coefficient $\mu$, $p_{f}$, and gradient of
$\sigma_{D}$ with depth by a Mohr--Coulomb-based parametric analysis
shows that reactivation of the faults requires supra-hydrostatic
$p_{f}$ ($\lambda = 0.68\ndash 0.81$), unless $\mu$ is less than
0.4$^{[20]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Japan, Nojima fault, 1995 $M_{W}$ 7.2 Kobe
earthquake} & 
\parbox[t]{34pc}{\centering Seismic velocity anomalies near the
hypocenter could reflect supra-hydrostatic $p_{f}$ that may have
contributed to the initiation of the Kobe earthquake$^{[21]}$} 
\vspace*{4pt}\\ 

& Cascadia &
\parbox[t]{34pc}{\centering Seismic tomography indicates abnormal
$V_{P}/V_{S}$ and Poisson ratio values interpreted as caused by
near-lithostatic $p_{f}^{[22], [23]}$} 
\vspace*{4pt}\\

& NE Japan &
\parbox[t]{34pc}{\centering Aftershock focal mechanisms of the 1968 M
8.2 Tokachi earthquake suggest a weak plate interface accounted for by
the post-seismic release of overpressured fluids following the main
rupture$^{[24]}$; seismic reflection imaging shows that the megathrust
corresponds to a reflector with negative polarity, which could be
explained by high $p_{f}$ having possibly triggered the the 2011 $M_{W}$
9 Tohoku event$^{[25]}$; mechanical analysis suggests stress
permutations in the forearc region caused by fluctuations in $p_{f}$
during the seismic cycle (fault-valve action)$^{[26]}$} 
\vspace*{4pt}\\

& SW Japan &
\parbox[t]{34pc}{\centering 3-D seismic reflection data show the
presence of a LVZ (${\sim}$2~km thick, ${\sim}$15~km
wide, and ${\sim}$120~km long) beneath the Nankai accretionary
prism, inside which inferred abnormally high $p_{f}$ may control
interplate coupling$^{[27]}$} 
\vspace*{4pt}\\

& Central America &
\parbox[t]{34pc}{\centering Extremely high $V_{P}/V_{S}$ ratios in the
entire subducting oceanic crust is interpreted as due to high $p_{f}$.
Varying velocity ratios in the overriding continental crust further
allow to map varying coupling domains$^{[28]}$} 
\vspace*{4pt}\\

& Chile\vspace*{2pt} &
\parbox[t]{34pc}{\centering The importance of the post-seismic fluid
discharge suggests overpressured $p_{f}$ beneath the subduction
interface before large interplate events$^{[29],[30]}$; 3-D seismic
tomography allows to map the distribution, along the plate interface,
of domains with abnormally high $p_{f}$ and domains with lower $p_{f}$
and to propose a correlation between these domains and the patches
which slip aseismically (high $p_{f}$) and those which are locked (low
$p_{f}$)$^{[31]}$} \tabularbreakfive\\

& \parbox[t]{3cm}{\centering New Zealand, Hikurangi subduction zone} &
\parbox[t]{34pc}{\centering A Mohr--Coulomb analysis suggests that the
recurrence of megathrust earthquakes may be triggered by fluctuation
of $p_{f}$ (from hydrostatic to lithostatic) in addition to stress
accumulation$^{[32]}$} 
\vspace*{4pt}\\ 

\morerows{3}{Aftershocks}  & 
\parbox[t]{3cm}{\centering 1992 Landers earthquake} &
\parbox[t]{34pc}{\centering Increase of $p_{f}$ because of post-seismic
fluid flow and Coulomb stress changes account for the chronology and
spatial migration of the Landers event aftershocks$^{[33]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Apennines (1997 Umbria-Marche, 2009
L'Aquila, 2012 Emilia earthquake sequence)} &
\parbox[t]{34pc}{\centering Space--time migration of aftershocks fits
with diffusion laws of fluids in porous media$^{[34], [35]}$; inversion
of earthquake nodal planes allows to map the 3-D $p_{f}$ distribution
at depth in the hypocentral region of the L'Aquila earthquake and
shows that time-space migration of aftershocks fits with diffusion laws
of $p_{f}^{[36]}$; aftershocks induced by a reduction in the fault
shear strength due to a pulse of $p_{f}^{[37]}$; aftershock decay
rate and $V_{P}/V_{S}$ changes along the fault system suggest that a
$p_{f}$ pulse controlled the space--time evolution of the 2012 Emilia
sequence$^{[38]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering 2011 Tohoku earthquake, NE Japan} &
\parbox[t]{34pc}{\centering Reactivation of misoriented fault planes of
the aftershock seismic faults is accounted for by varying
supra-hydrostatic $p_{f}^{[39]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering 2004 Sumatra earthquake}\vspace*{2pt} &
\parbox[t]{34pc}{\centering Aftershock migration along a splay fault
merging with the megathrust is explained by upward migration of fluids,
although supra-hydrostatic $p_{f}$ is not ascertained$^{[40]}$}  
\botline
\end{tabular}
\xxtabnote{References: $^{[1]}$\citet{Deichmann1992}, 
$^{[2]}$\citet{Mandaletal2022}, $^{[3]}$\citet{Bettinellietal2008},
$^{[4]}$\citet{Quattrocchi1999}, $^{[5]}$\citet{BoncioBracone2009},
$^{[6]}$\citet{Lombardietal2010}, $^{[7]}$\citet{Calderonietal2009},
$^{[8]}$\citet{Pezzoetal2018}, $^{[9]}$\citet{Collettinietal2009A},
$^{[10]}$\citet{Chiodinietal2004}, $^{[11]}$\citet{Chiarabbaetal2009a},
$^{[12]}$\citet{Chiarabbaetal2009b}), $^{[13]}$\citet{DiLuccioetal2010},
$^{[14]}$\citet{Lucenteetal2010}, $^{[15]}$\citet{Chiodinietal2011},
$^{[16]}$\citet{DiLuccioetal2022}, $^{[17]}$\citet{Plateauxetal2012},
$^{[18]}$\citet{Sibson2007,Sibson2009}, $^{[19]}$\citet{Gardonioetal2018}, 
$^{[20]}$\citet{LeclereCalais2019}, $^{[21]}$\citet{Zhaoetal1996},
$^{[22]}$\citet{Audetetal2009}, $^{[23]}$\citet{Peacocketal2011}, 
$^{[24]}$\citet{MageeZoback1993}, $^{[25]}$\citet{Kimuraetal2012},
$^{[26]}$\citet{Sibson2013}, $^{[27]}$\citet{Parketal2010}, 
$^{[28]}$\citet{AudetSchwartz2013}, $^{[29]}$\citet{HusenKissling2001},
$^{[30]}$\citet{Koerneretal2004}, $^{[31]}$\citet{Morenoetal2014}, 
$^{[32]}$\citet{SibsonRowland2003}, $^{[33]}$\citet{BoslNur2002}, 
$^{[34]}$\citet{Milleretal2004}, $^{[35]}$\citet{Antoniolietal2005}, 
$^{[36]}$\citet{Terakawaetal2010}, $^{[37]}$\citet{Malagninietal2012}, 
$^{[38]}$\citet{Pezzoetal2018}, $^{[39]}$\citet{LeclereFabbri2013}, 
$^{[40]}$\citet{Waldhauseretal2012}.}
\xxtabnote{MCT: Main
Central Thrust. $Q_{P}/Q_{S}$: attenuation ratios of $P$ and $S$ waves.
3-D: three-dimensional. LVZ: low seismic velocity zone. $\Phi$: stress
tensor shape; $\Phi= (\sigma_{2} -\sigma_{3})/(\sigma_{1}
-\sigma_{3})$.}
\end{sidewaystable*}

Except rare examples of direct measurements in boreholes, evidence for
supra-hydrostatic $p_{f}$ triggering or favoring intra-plate
earthquakes are mostly indirect. Body-wave velocity anomalies detected
by two-dimensional or three-dimensional tomography suggest that
pressurized fluids are present in hypocentral regions of many
earthquakes. Most authors agree that fluids are trapped at depth and
that their accumulation results in abnormally high $p_{f}$ values which
in turn weaken the faults.


Evidence for abnormally high $p_{f}$ that could either trigger or
favor the propagation of subduction zone~earthquakes mainly comes from
body wave velocity anomalies revealed by tomography (Table~\ref{tab5}). Other
indirect evidence come from mechanical analyses based on the
reactivation of misoriented fault planes \citep[e.g.,][]{Sibson2013}. The
analysis of \citet{Seno2009}, based on the construction of the differential
stress profiles across several subduction zones, shows that the pore
fluid pressure ratio $\lambda$ accounts for much of the
interplate coupling.


\subsection{Aftershocks}

\subsubsection{Present-day aftershocks} 

In many cases, aftershocks following large magnitude events typically
migrate both in space and time. This was first noticed by 
\citet{NurBooker1972} following the fortuitous or induced seismic
sequences at Denver and Rangely \citep{Healyetal1968,Raleighetal1976}.
Since then, precise hypocenter relocations show that the temporal and
spatial migration follows laws of diffusion of pressure fronts in
porous media, suggesting that pressurized fluids contribute to trigger
aftershocks (Table~\ref{tab5}). The theoretical analysis of
\citet{Miller2020}, based on the modeling of permeability fluctuations
with time during the seismic cycle, further shows that major events not
characterized by co-seismic or post-seismic releases of large amounts
of fluids are followed by very few aftershocks, whereas those
characterized by the release of significant amounts of co- or
post-seismic fluids will be followed by large aftershock populations.
Even if other mechanisms such as loading of faults by Coulomb stress
transfer can influence the triggering or the propagation of aftershocks
\citep{Nostroetal2005}, the role of supra-hydrostatic $p_{f}$ appears
significant in many cases.

\subsubsection{Aftershocks in the geological record}

Because of their small magnitudes, aftershocks related to past
earthquakes are uneasy to recognize in the geological record. However,
a specific type of aftershocks, called ``golden'' aftershocks, is
presumably recognized in Archean rocks (Yilgarn craton, western
Australia) where mechanical analyses based on Coulomb stress transfer
following major earthquakes suggest that transiently abnormally high
$p_{f}$ triggered ruptures on secondary faults after main events 
\citep{CoxRuming2004,Micklethwaite2008}. Indeed, the Yilgarn craton  
gold deposits hosted in secondary low-displacement hectometric faults
and shear zones do not show a random spatial \mbox{distribution,} but are
clustered in rock volumes near terminations of primary plurikilometric
strike-slip fault segments. Mechanical analyses of the stress transfer
following major earthquakes along any of the fault segments show that
specific rock volumes are stress-loaded ahead of the segment
terminations [so-called ``loaded'' lobes, inside which the stress
state acting on pre-existing fractures makes them close to failure;
\citealp{Kingetal1994}]. Pressurized fluid expelled from the main shock
hypocentral volume then percolates through the fracture network in the
loaded lobes, triggering eventual ruptures and allowing, by pressure
drop, deposition of gold-bearing mineralization. The repetition of main
shocks and aftershocks eventually results in deposits of
economical interest.

\subsection{Subducting slab intermediate-depth\newline earthquakes}

\subsubsection{Seismological evidence for supra-hydrostatic $p_{f}$ in
currently subducting slabs}

In subduction zones, intermediate-depth earthquakes, that is,
earthquakes with hypocentral depths between ${\sim}$50 and 300~km, are
no longer localized along the plate interface, but inside the
subducting slab. Various mechanisms have been proposed to account for
nucleation or propagation of this intermediate-depth seismicity
\citep{Frohlich2006,Houston2015}: (1) dehydration embrittlement, in
which locally abnormally high $p_{f}$ allows a transition from a
viscous regime of deformation to brittle faulting, (2) thermal
instabilities, or (self-localizing) thermal runaway, in which incipient
ductile shear zones develop as rheological instabilities along which
brittle failure can nucleate; (3) ``anticrack faulting'', triggered
by mineral phase change reactions. Among these mechanisms, which can
act in concert, the first one is of peculiar interest here. As
summarized in Table~\ref{tab6}, evidence or suspicion for
supra-hydrostatic $p_{f}$ come from three-dimensional seismic
tomography across subducting slabs currently in their post-seismic
stage or in their inter-seismic stage.


\begin{sidewaystable*}
\vspone
\caption{Examples of geological and geophysical evidence for
intermediate-depth seismicity in modern or fossil subduction
zones triggered or favored by supra-hydrostatic pore fluid pressures
$p_{f}$\label{tab6}}
\begin{tabular}{cccc}
\thead
Setting & Area & Name of structure & Evidence \\ 
\endthead
& NE Japan & \parbox[t]{4cm}{\centering Japan trench (subducting
Pacific slab)} &
\parbox[t]{11cm}{\centering Seismic tomography indicates abnormal
$V_{P}/V_{S}$ and Poisson ratio values interpreted as caused by
near-lithostatic $p_{f}^{[1]}$; seismic tomography shows slab
dehydration; released fluids become overpressured and account for
seismicity$^{[2]}$; 3D seismic tomography suggests evidence for
near-lithostatic $p_{f}$ in the hypocentre of a $M_{W}$ 7.1 intraslab
earthquake at a 66~km depth$^{[3]}$; $V_{P}$ and $V_{S}$ variations in the
subducting slab indicates development of high $p_{f}^{[4],[5]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Central Andean subduction} &
\parbox[t]{4cm}{\centering Chile trench (subducting Nazca plate)} &
\parbox[t]{11cm}{\centering High $p_{f}$ could have contributed to the
nucleation or to the propagation of a $M_{W}$ 7.8 earthquake in
northern Chile at a 115~km depth$^{[6]}$; high $V_{P}/V_{S}$ ratios in
the subducting Nazca plate and thermodynamic modeling of dehydration
reactions suggest high $p_{f}$ at depths ${>}$50~km$^{[7]}$}  
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Lesser Antilles} & 
\parbox[t]{4cm}{\centering Subducting Atlantic plate} &
\parbox[t]{11cm}{\centering Hypocenters between 120 and 160~km are
distributed where seismic tomography indicates low $V_{P}$ values and
high $V_{P}/V_{S}$ ratios, suggesting high $p_{f}^{[8]}$} 
\vspace*{4pt}\\

& \parbox[t]{3cm}{\centering Middle America trench} &
\parbox[t]{4cm}{\centering Middle America trench (subducting Cocos
plate)}\vspace*{2pt} &
\parbox[t]{11cm}{\centering Nucleation of a $M_{W}$
7.1 earthquake at a 57~km depth in the subducting Cocos plate
tentatively explained by high $p_{f}$ resulting from the brucite $+$
antigorite $=$ olivine $+$~$\mathrm{H}_{2}\mathrm{O}$ reaction$^{[9]}$} 
\tabularbreaksix\\ 

\morerows{5}{\parbox[t]{2cm}{\centering Fossil subduction zones}}  &
\morerows{1}{Central Alps}  & 
\parbox[t]{4cm}{\centering Dent Blanche basal thrust} & 
\parbox[t]{11cm}{\centering Cross-cutting relationships between foliated
cataclasites, mylonites and quartz-clinozoisite veins ($0.95 <
\lambda < 1$)$^{[10]}$} 
\vspace*{4pt}\\

& & \parbox[t]{4cm}{\centering Valpelline Shear Zone between
Valpelline and Arolla units, Dent Blanche} & 
\parbox[t]{11cm}{\centering Metamorphic tensile veins ($\lambda \sim
0.7$)$^{[11]}$}  \vspace*{4pt}\\

& \morerows{1}{Western Alps}  & Monviso & 
\parbox[t]{11cm}{\centering HP crack-seal veins in eclogite-facies metagabbros and oscillatory
growth zoning of minerals as products of precipitation suggest
fluctuations of $p_{f}^{[12]}$; eclogite-facies vugs suggest lithostatic
$p_{f}^{[13]}$; four distinct large negative
$\delta^{7}\mathrm{Li}$ excursions in garnet mantles result
from kinetic fractionation of Li isotopes through bulk diffusion during
at least four overpressured fluid pulses$^{[14]}$} 
\vspace*{4pt}\\

& & Lanzo & 
\parbox[t]{11cm}{\centering Hydrofracturing of omphacitites by
$\mathrm{CH}_{4}$--$\mathrm{H}_{2}$-rich fluids at 30--80~km depth$^{[15]}$} 
\vspace*{4pt}\\

& California & 
\parbox[t]{4cm}{\centering Franciscan Complex} &
\parbox[t]{11cm}{\centering Rhythmic chemical zoning in HP garnets
result from growth-dissolution cycles driven by pressure pulses
($p_{f} = 100\ndash 350$~MPa)$^{[16]}$} 
\vspace*{4pt}\\

& Zambia & 
\parbox[t]{4cm}{\centering Relics of subducted lower oceanic crust,
late Precambrian Zambezi belt}\vspace*{2pt} & 
\parbox[t]{11cm}{\centering Hydraulic fracturing$^{[17]}$}  
\botline
\end{tabular}
\xxtabnote{References: $^{[1]}$\citet{Nakajimaetal2001}, 
$^{[2]}$\citet{MishraZhao2004}, $^{[3]}$\citet{Nakajimaetal2011},
$^{[4]}$\citet{Shiinaetal2013}, $^{[5]}$\citet{Shiinaetal2017}, 
$^{[6]}$\citet{Kugeetal2010}, $^{[7]}$\citet{Blochetal2018},
$^{[8]}$\citet{Paulattoetal2017}, $^{[9]}$\citet{GutierrezAguilaretal2022},
$^{[10]}$\citet{Angiboustetal2015}, $^{[11]}$\citet{Menantetal2018},
$^{[12]}$\citet{Spandleretal2011}, $^{[13]}$\citet{AngiboustRaimondo2022},
$^{[14]}$\citet{Hooveretal2022}, $^{[15]}$\citet{Giuntolietal2024},
$^{[16]}$\citet{Vieteetal2018}, $^{[17]}$\citet{JohnSchenk2006}.}
\xxtabnote{HP: high pressure metamorphic conditions.}
\end{sidewaystable*}

\subsubsection{Evidence for excess $p_{f}$ at intermediate depths in
the geological record}

Table~\ref{tab6} further provides examples of structures (crack-seal
veins, mineral overgrowths) reported from high-pressure metamorphic
terranes which can be interpreted as resulting from overpressured
fluids during intermediate-depth seismic activity. Brittle dilatant
veins crossing ductilely deformed high-pressure rocks are one
convincing piece of evidence for abnormally high $p_{f}$. Similarly,
finely zoned rims around garnets in eclogitic rocks can be interpreted
as repeated growths of thin garnet layers following cyclical arrivals
of co-seismic fluids. In these cases, the sharpness of the boundaries
between the domains with distinct element concentrations are sharp,
whereas they should be irregular or diffuse in the case of
intracystalline high-temperature solid diffusion, confirming the fluid
pulse hypothesis. Through a detailed analysis of such zoned garnet
overgrowths, \citet{Vieteetal2018} estimate that at least four
overpressured fluid pulses occurred in less than 300,000 years.

\subsection{Seismic swarms}

Whatever they are related to volcanic systems or not, many seismic
swarms appear to be triggered or favored by pressurized fluids
(Table~\ref{tab7}). The most convincing argument for the role of
$p_{f}$ lies in the fact that, like for aftershock sequences, the
spatial and temporal migration of hypocentres follows diffusion laws of
pressure front propagation in porous media. Several authors however
propose that other mechanisms can also play a role, in combination with
$p_{f}$ wave propagation. A frequently invoked additional mechanism is
Coulomb stress transfer 
\citep{Aoyamaetal2002,Hainzl2004,Yukutakeetal2011,Fischeretal2014}. In
particular, studying a swarm developed near the Hakone volcano, central
Japan, \citet{Yukutakeetal2011} were able to show that the hypocenters
of a first earthquake sequence were aligned along fault-like planar
surfaces, while those of a subsequent sequence were located in
compressive lobes associated with the planar surfaces, demonstrating
the sequence fluid-triggered events followed by Coulomb stress
transfer-triggered events. Besides, \citet{Aoyamaetal2002} call for
stress corrosion as an additional mechanism in the triggering of
seismic swarms.


\begin{table*}
\caption{Examples of geophysical evidence for
seismic swarms or seismic swarm-like sequences triggered or
favored by abnormally high pore fluid pressures $p_{f}$ in or around
fault zones\label{tab7}\vspace*{-3pt}}
\tabcolsep=4pt
\begin{tabular}{cc}
\thead
Area and/or events & Evidence \\ 
\endthead
\parbox[t]{4cm}{\centering Central and northern Japan (Matsushiro,
Tohoku, Hida mountains, Hakone volcano)} &
\parbox[t]{11.2cm}{\centering Space--time evolution of seismicity fits with
$p_{f}$ diffusion laws$^{[1], [2], [3]}$; pressurized fluid diffusion
accounts for space--time evolution of seismicity along with Coulomb
stress transfert and stress corrosion$^{[4]}$; pressurized fluid diffusion
and Coulomb stress transfert account for space--time evolution of
seismicity$^{[5]}$} 
\vspace*{4pt}\\ 

\parbox[t]{4cm}{\centering Dobi graben seismic sequence, Afar rift, Djibouti} &
\parbox[t]{11.2cm}{\centering Space--time evolution of seismicity fits with
$p_{f}$ diffusion laws$^{[6]}$} 
\vspace*{4pt}\\ 

\parbox[t]{4cm}{\centering East African Rift, Uganda, Rwenzori region} &
\parbox[t]{11.2cm}{\centering Spatial overlap in the middle crust between
intense volatile and $\mathrm{CO}_{2}$ circulation and swarm
hypocentral regions$^{[7]}$} 
\vspace*{4pt}\\ 

\parbox[t]{4cm}{\centering Central Europe (West Bohemia/Vogtland),} & 
\parbox[t]{11.2cm}{\centering Space--time evolution of seismicity fits with
$p_{f}$ diffusion laws$^{[8], [9]}$, but static and dynamic Coulomb stress
changes also play a role$^{[10], [11], [12]}$; at about 9~km depth,
$\lambda \sim 0.98$ ($p_{f} = 244$~MPa, that is 5~MPa below
$\sigma_{v}$)$^{[13]}$} 
\vspace*{4pt}\\ 

\parbox[t]{4cm}{\centering Western Europe (Vosges mountains)} &
\parbox[t]{11.2cm}{\centering Space--time evolution of seismicity fits with
$p_{f}$ diffusion laws$^{[14]}$} 
\vspace*{4pt}\\ 

\parbox[t]{4cm}{\centering Western Alps (Ubaye region and vicinity)} & 
\parbox[t]{11.2cm}{\centering Space--time evolution of seismicity fits with
$p_{f}$ diffusion laws$^{[15], [16] [17]}$; supra-hydrostatic $p_{f}$
are necessary for reactivation of misoriented faults ($\lambda =
0.41\ndash 0.51$)$^{[18]}$; time-space evolution of seismicity and
development of excess $p_{f}$ (between 35 and 55~MPa) explained by
creep compaction$^{[19]}$; space--time evolution of seismicity fits
with $p_{f}$ diffusion laws, but co-seismic stress transfer explains
the seismicity close to the mainshock source$^{[20]}$} 
\vspace*{4pt}\\ 

\parbox[t]{4cm}{\centering Corinth rift} &
\parbox[t]{11.2cm}{\centering Space--time evolution of seismicity fits with
$p_{f}$ diffusion laws$^{[21], [22]}$} 
\vspace*{4pt}\\ 

\parbox[t]{4cm}{\centering Southern Italy, Mt Pollino region} &
\parbox[t]{11.2cm}{\centering Space--time evolution of seismicity fits with
$p_{f}$ diffusion laws$^{[23]}$} 
\vspace*{4pt}\\ 

\parbox[t]{4cm}{\centering Southern California (including Long Valley caldera)}\vspace*{2pt} &
\parbox[t]{11.2cm}{\centering Space--time evolution of seismicity fits with
$p_{f}$ diffusion laws$^{[24], [25]}$, possibly combined with episodic aseismic
slip$^{[26]}$} 
\botline
\end{tabular}
\tabnote{References: $^{[1]}$\citet{Nur1974}, $^{[2]}$\citet{Cappaetal2009},
$^{[3]}$\citet{Yoshidaetal2016}, $^{[4]}$\citet{Aoyamaetal2002}, 
$^{[5]}$\citet{Yukutakeetal2011}, $^{[6]}$\citet{Noiretal1997}, 
$^{[7]}$\citet{Lindenfeldetal2012}, $^{[8]}$\citet{Parotidisetal2003},
$^{[9]}$\citet{Hainzl2004}, $^{[10]}$\citet{HainzlFischer2002},
$^{[11]}$\citet{FischerHoralek2005}, $^{[12]}$\citet{Fischeretal2014},
$^{[13]}$\citet{Vavrycuk2002}, $^{[14]}$\citet{Audinetal2002},
$^{[15]}$\citet{Jenattonetal2007}, $^{[16]}$\citet{Godanoetal2013},
$^{[17]}$\citet{Baquesetal2021}, $^{[18]}$\citet{Leclereetal2012},
$^{[19]}$\citet{Leclereetal2013}, $^{[20]}$\citet{DeBarrosetal2019},
$^{[21]}$\citet{Duvergeretal2015}, $^{[22]}$\citet{DeBarrosetal2020},
$^{[23]}$\citet{DeMatteisetal2021}, $^{[24]}$\citet{Prejeanetal2003},
$^{[25]}$\citet{Shellyetal2016}, $^{[26]}$\citet{VidaleShearer2006}.}
\vspace*{-9pt}
\end{table*}

\subsection{Fluid overpressures and slow earthquakes}

Slow earthquakes, a collective name including slow-slip events, low- or
very-low-frequency earthquakes, low-frequency tremors, non-volcanic  
tremors, and episodic tremor-and-slip events, are in many cases
suspected to be triggered or favored by supra-hydrostatic $p_{f}$.
Table~\ref{tab8} is a non-exhaustive compilation of studies that relate
slow earthquakes (in the broad sense) with evidence for
supra-hydrostatic $p_{f}$. With the exception of one study pertaining
to the San Andreas fault, all other studies deal with slow earthquakes
in subduction zones. Direct evidence come from measurements in ODP or
IODP boreholes equipped with pressure or fluid flow sensors 
\citep{Brownetal2005,Arakietal2017}. Indirect evidence are provided by
geophysical methods (seismic tomography or magneto-tellurics) that show
that domains characterized by seismic velocity anomalies or by low
resistivities, which are explained by the presence of possibly
overpressured fluids, overlap zones of nucleation of slow events.
Besides, laboratory experiments carried out on oceanic crust rocks
(gabbros, serpentinites) and numerical modeling further support the
interplay between supra-hydrostatic $p_{f}$ and slow earthquakes 
\citep{Peacock2009,Katayamaetal2012,KitajimaSaffer2012,Beeleretal2013,
SafferWallace2015,BernaudinGueydan2018,Conditetal2020,DalZilioGerya2022,
Eberhardetal2022}.

\begin{sidewaystable*}
\vspone
\caption{Examples of geological or geophysical evidence for present-day
or past slow earthquakes triggered or favored by abnormally high pore
fluid pressures $p_{f}$  in or around fault zones\label{tab8}}
\begin{tabular}{ccc}
\thead
Setting & Area, structure, unit & Evidence \\ 
\endthead
\morerows{4}{\parbox[t]{3cm}{\centering Present-day events along plate
interfaces, subduction zones}}  & 
\parbox[t]{3.5cm}{\centering Cascadia} & 
\parbox[t]{13cm}{\centering Seismic imaging and seismic wave analyses
suggest that $p_{f}$ is near-lithostatic in a LVL inside which SSEs or
ETSs nucleate$^{[1], [2], [3], [4]}$; supra-hydrostatic $p_{f}$ inferred
in anisotropically permeable foliation parallel to the plate interface
explains NVT distribution$^{[5]}$; 3-D seismic tomography and
magneto-tellurics show that LFEs nucleate in a landward dipping region
characterized by a high Poisson ratio and by a high electrical
conductivity; the region is interpreted as saturated by fluids trapped
at near-lithostatic $p_{f}^{[6]}$; variations in seismic velocities in
the LVL after ETSs likely reflect $p_{f}$ fluctuations$^{[7]}$} 
\vspace*{4pt}\\
& \parbox[t]{3.5cm}{\centering Middle America trench} & 
\parbox[t]{13cm}{\centering Episodic fluid flow pulses measured in ODP
boreholes correlate with seismic tremor in the frontal part of the
plate interface and could reflect expulsion of transiently
overpressured fluids$^{[8]}$; SSEs nucleate in an ultra-slow velocity
layer inside which fluids may be overpressured$^{[9]}$; LFE occurrence
during a SSE is interpreted to result from a $p_{f}$ fluctuation having
migrated updip along the subduction interface$^{[10]}$} 
\vspace*{4pt}\\
& \parbox[t]{3.5cm}{\centering NE Japan (Japan trench)} & 
\parbox[t]{13cm}{\centering In the upper part of the downgoing Pacific,
between 60 and 80 km depth, a zone of high $V_{P}/V_{S}$ is accounted
for by high $p_{f}^{[11]}$} 
\vspace*{4pt}\\
& \parbox[t]{3.5cm}{\centering SW Japan (Nankai subduction zone)}\vspace*{2pt} & 
\parbox[t]{13cm}{\centering NVDT possibly linked with high
$p_{f}^{[12]}$; LFT suppressed where $p_{f}$ is low$^{[13]}$; slow slip
is located in a high reflectivity and high Poisson ratio portion of the
subducting oceanic crust$^{[14]}$; NVT are located in a portion of the
subducting oceanic crust characterized by $V_{P}$ and $V_{S}$ anomalies
related to high $p_{f}^{[15], [16]}$; SSE occur in a portion of the
subducting slab characterized by seismic velocity anomalies likely
caused by high $p_{f}^{[17]}$; slow seismic slip in the shallow parts
of the subduction interface is characterized by waves rich in
high-frequency components, suggesting $p_{f}$-controlled tensile
fractures$^{[18]}$; $p_{f}$ fluctuations measured in IODP boreholes
correlate with SSEs in the shallow parts of the subduction
interface$^{[19], [20]}$} \tabularbreakeight\\
& \parbox[t]{3.5cm}{\centering New Zealand (Hikurangi margin)} & 
\parbox[t]{13cm}{\centering Deep SSEs occur in a zone characterized by
a high $P$ wave attenuation and by a high $V_{P}/V_{S}$ ratio, suggesting
high $p_{f}^{[21]}$; anomalously-shallow slow slip events occur in a
low $V_{P}$ zone where $p_{f}$ is supposed to be supra-hydrostatic
($\lambda^* = 0.87$)$^{[22]}$; 3-D $V_{P}$ and $V_{P}/V_{S}$ tomography
from 8 to 70~km depth along the subduction interface, where both large
shallow SSEs and small deep SSEs were recorded, is interpreted as
subducted sediment with high $p_{f}^{[23]}$; OBS data show that
tectonic stresses in the subducting slab change throughout SSE cycles,
possibly as a consequence of $p_{f}$ fluctuations in the vicinity of
the plate interface$^{[24],[25]}$; repeating SSEs occur in a zone
below which high $V_{P}/V_{S}$ values suggest high $p_{f}^{[26]}$} 
\vspace*{4pt}\\ 
\parbox[t]{3cm}{\centering Present-day events along plate boundary transform faults} & 
\parbox[t]{3.5cm}{\centering San Andreas fault} &
\parbox[t]{13cm}{\centering NVT activity near Parfield following large
earthquakes seem to be enhanced by static shear stress and Coulomb
stress increases, but $p_{f}$ fluctuations at depth (15--30~km) may also
play a role$^{[27]}$; NVT near Parkfield likely reflect shear failure on
a critically stressed fault in the presence of near-lithostatic
$p_{f}^{[28]}$} 
\vspace*{4pt}\\ 
\morerows{7}{\parbox[t]{3cm}{\centering Evidence in the geological
record along subduction zone plate interfaces}}  & 
\parbox[t]{3.5cm}{\centering Namibia (Damara belt)} &
\parbox[t]{13cm}{\centering Hydrothermal quartz veins preserved in
ductilely deformed rocks attest for hydrofracturing caused by high
$p_{f}$ during LFEs and VLFEs in the plastic aseismic regime below the
seismogenic zone$^{[29]}$} 
\vspace*{4pt}\\
& \parbox[t]{3.5cm}{\centering Cyclades (Cycladic blueschist unit, Syros)} & 
\parbox[t]{13cm}{\centering Brittle deformation structures (shear
fractures and veins) in eclogite lenses embedded in ductilely deformed
blueschist are interpreted to result from SSEs triggered by high
$p_{f}^{[30]}$} 
\vspace*{4pt}\\
& \parbox[t]{3.5cm}{\centering SW Japan (Triassic Tomuru blueschists)} & 
\parbox[t]{13cm}{\centering Quartz-filled crack-seal shear and
extension veins in subduction m\'{e}lange formed by frictional sliding
and tensile fracturing at near-lithostatic $p_{f}$ at short reccurrence
times (a few years, determined from kinetic modeling of quartz
precipitation) are tentatively accounted for by episodic strain release
during ETSs$^{[31]}$} 
\vspace*{4pt}\\
& \parbox[t]{3.5cm}{\centering New Zealand (Dun ophiolite, Livingstone Fault)}\vspace*{2pt} &
\parbox[t]{13cm}{\centering Field and microstructural observations
suggest that chemical reactions involving serpentinite can promote rock
hardening and generate in situ fluid over-pressure patches and brittle
failure in the source region of deep tremor along the slab-mantle
interface$^{[32]}$} \tabularbreakeight\\
 & \parbox[t]{3.5cm}{\centering Alaska (Kodiak accretionary complex)} & 
\parbox[t]{14cm}{\centering Quartz vein microstructures and estimation
of duration of local silica diffusion indicate that near-lithostatic
$p_{f}$ can produce crack seal bands in less than 10 days, which is
similar to the duration of slow earthquakes$^{[33]}$} 
\vspace*{4pt}\\
 & \parbox[t]{3.5cm}{\centering Northern Apennines (continental metasediments)} & 
\parbox[t]{14cm}{\centering Syn-mylonitization quartz-carpholite
dilational shear veins formed under HP metamorphic conditions as a
result of high $p_{f}$ are interpreted as a record of deep ETS
events$^{[34]}$} 
\vspace*{4pt}\\
 & \parbox[t]{3.5cm}{\centering Central Alps (Arosa zone)} & 
\parbox[t]{14cm}{\centering Crack-seal veins formed under blueschist
facies conditions concurrently with viscous flow as a result of
near-lithostatic $p_{f}$; the low estimated values of differential
stresses suggest that the veins formed during slow slip and tremor
events$^{[35]}$} 
\vspace*{4pt}\\
 & \parbox[t]{3.5cm}{\centering California (Franciscan complex eastern belt)}\vspace*{2pt} & 
\parbox[t]{14cm}{\centering Opening increments of ${\sim}$1~mm in
blueschist-facies metasediments are interpreted as the result of
transient near-lithostatic $p_{f}$ during LFEs$^{[36]}$}  
\botline
\end{tabular}
\xxtabnote{References: $^{[1]}$\citet{Abersetal2009}, 
$^{[2]}$\citet{Audetetal2009}, $^{[3]}$\citet{Tauzinetal2017}, 
$^{[4]}$\citet{AudetSchaeffer2018}, $^{[5]}$\citet{Delphetal2018},
$^{[6]}$\citet{Calvertetal2020}, $^{[7]}$\citet{Gosselinetal2020},
$^{[8]}$\citet{Brownetal2005}, $^{[9]}$\citet{Songetal2009},
$^{[10]}$\citet{Franketal2015}, $^{[11]}$\citet{Shellyetal2006b}, 
$^{[12]}$\citet{Obara2002}, $^{[13]}$\citet{SenoYamasaki2003},
$^{[14]}$\citet{Kodairaetal2004}, $^{[15]}$\citet{Shellyetal2006a}, 
$^{[16]}$\citet{Matsubaraetal2008}, $^{[17]}$\citet{Katoetal2010}, 
$^{[18]}$\citet{Sugiokaetal2012}, $^{[19]}$\citet{Arakietal2017},
$^{[20]}$\citet{Ariyoshietal2021}, $^{[21]}$\citet{WallaceEberhart-Phillips2013},
$^{[22]}$\citet{Bassettetal2014}, $^{[23]}$\citet{EberhartPhillipsBannister2015}, 
$^{[24]}$\citet{ShaddoxSchwartz2019}, $^{[25]}$\citet{Warren-Smithetal2019},
$^{[26]}$\citet{Yarceetal2021}, $^{[27]}$\citet{NadeauGuilhem2009}, 
$^{[28]}$\citet{Thomasetal2009}, $^{[29]}$\citet{Fagerengetal2018},
$^{[30]}$\citet{Behretal2018}, $^{[31]}$\citet{Ujiieetal2018}, 
$^{[32]}$\citet{Tarlingetal2019}, $^{[33]}$\citet{FisherBrantley2014},
$^{[34]}$\citet{GiuntoliViola2021}, $^{[35]}$\citet{ConditFrench2022},
$^{[36]}$\citet{SchmidtPlatt2022}.}
\xxtabnote{LVL: low-velocity
layer. SSE: slow-slip event. ETS: episodic tremor and slip. NVT:
non-volcanic tremor. 3-D: three-dimensional. LFE: low-frequency
earthquake. NVDT: non-volcanic deep tremor. ODP: Ocean Drilling
Program. LFT: low-frequency tremor. OBS: ocean-bottom seismometer.
VLFE: very low frequency earthquake. HP: high pressure.}
\end{sidewaystable*}

\subsubsection{Evidence in the geological record}

Tracking slow earthquake phenomena in the geological record is not
easy, since rocks only exhibit frozen structures, for which strain
rates are difficult to estimate. However, several studies contend that
past slow slip events left tracks in surface-exhumed fault rocks
(Table~\ref{tab8}). Most of such studies pertain to ancient subduction
interface-related slow events triggered or facilitated by
near-lithostatic $p_{f}$. These studies are based on scenarii that are
compatible with cyclic fracturing and fluid arrival in the fractured
zones. One key issue in the slow-earthquake interpretation is the
estimated duration of events. Based on silica diffusion from wall rock
to quartz crak-seal veins found along a shear zone adjacent to a
paleo-d\'{e}collement in the Kodiak accretionary complex, 
\citet{FisherBrantley2014}
could estimate the time necessary to precipitate quartz for
one crak-seal band as less than 10 days, which could correspond to the
duration of some slow events in subduction zones. Similarly, based on a
kinematic model~of the growth of microscopic quartz bands following\unskip\break
cyclical pore fluid ingression in crack-seal veins from the Shimanto
accretionary prism, \citet{Ujiieetal2018} could estimate the minimum
duration of precipitation between two successive fluid pulses as less
than~5 years. Such a duration is too low for \mbox{standard} earthquake
rupture, but could correspond to episodic tremor and slip. Overall, the
recognition of slow earthquakes in the geological record is still
speculative, but quantification of duration of various inter-seismic or  
co-seismic phenomena such as mineral precipitation could validate the
inferred geological signature of slow events.

\subsection{Fluids and man-made earthquakes}

Several man-made earthquakes show that fluids can trigger seismic
ruptures. One emblematic piece of evidence for this triggering role is
the earthquake activity that occurred in Colorado following waste water
disposal at depth \citep{Healyetal1968}. Experimental water injection
at depth at Rangely [Colorado, \citealp{Raleighetal1976}] confirmed
than fluids could trigger earthquakes. Since then, the artifical
triggering of earthquakes has been ascertained in a large variety of
human activities: hydrocarbon extraction 
\citep{WiprutZoback2000,Amosetal2014,Bourneetal2014,VanWeesetal2014},
dam reservoir impoundment 
\citep{Rastogietal1997,Gupta2002,McGarretal2002,Zhangetal2019}, 
industrial waste water repository \citep{Horton2012,Yecketal2016},
carbon dioxide storage projects \citep{ZobackGorelick2012}, and water
injection in deep boreholes to produce geothermal energy 
\citep{DeichmannGiardini2009,Terakawaetal2012,McGarretal2015}.
Fluid-injection-experiments at the KTB borehole in Germany have shown
that even small pressure variations (${<}$1~MPa) could trigger numerous
microearthquakes at a depth of 9~km \citep{ZobackHarjes1997}. In most
case studies, the $p_{f}$ build-up in the vicinity of critically loaded
faults is responsible for failure. However, abnormally high $p_{f}$ may
also act indirectly by triggering aseismic slip which in turn leads to
an earthquake \citep{Weietal2015}. Lastly, stress perturbations by
Coulomb stress transfer can also contribute to man-induced seismic
ruptures \citep{DeMatteisetal2024}.\looseness=-1


\subsection{Conclusions}


The interactions between fluids and seismic ruptures in the brittle
crust or in subducting slabs are more and more recognized or suspected
(Tables~\ref{tab5}--\ref{tab8}). The role of overpressured fluids in
the triggering or propagation of small-magnitude events such as
aftershocks, swarms and, to a lesser extent, slow earthquakes, seems to
be well established. Regarding large-magnitude events, the role of
excess pore fluid pressures  is more difficult to ascertain. However, a
large body of evidence suggests that seismic ruptures, especially those
along plate interfaces in subduction zones, take place in crustal
volumes where seismic tomography indicates body wave 
\mbox{velocity} anomalies
that are interpreted as the consequence of the presence of
overpressured fluids. The present review of literature further shows
that abnormally high pore fluid pressures may not be the only
mechanism. Indeed, stress perturbations can act in concert with
abnormally high $p_{f}$ and the inferred decrease of
$\sigma_{n}$.


\section{Conclusions}

A review of the literature shows that fluids physically interact
everywhere and at all scales with deformation in the brittle crust and
in subducting slabs. Since they are more permeable than most intact
rocks, fractures, faults and shear zones in the brittle or
brittle-ductile crust and in the subducting slabs appear as efficient
paths for fluid circulation. Provided that impervious seals develop
transiently or permanently, fluids can accumulate and their pressure
can increase. Where faults are critically stressed, only a minor
overpressure value (a few MPa above the hydrostatic pressure) can
trigger or favor rupture or displacement. Where faults are not
critically stressed, for instance where they are severely misoriented
with respect to the active stress tensor, larger excess $p_{f}$ values
are needed for reactivation. Fluid overpressures can be estimated by
using chemical data or fluid inclusion data in exhumed rocks. Estimated
values are as follows: 25--135 MPa at seismogenic depths [\textit{ca}. 5
to 10~km, Shimanto paleo-accretionary prism,
\citealp{Raimbourgetal2022}, Kodiak paleo-accretionary prism,
\citealp{Vrolijk1987}], 50--150~MPa at 8--9~km [Apennines,
\citealp{Mullis1988}], 110~MPa at \textit{ca}. 20~km [Central Alps,
\citealp{BergerHerwegh2019}], 200--350~MPa at 8--10~km or deeper [Val
d'Or district, Canada, \citealp{Robertetal1995}], 100--350~MPa at
30--70~km in an exhumed subducted lithosphere \citep{Vieteetal2018}.

The influence of abnormally high $p_{f}$ is of utmost importance in the
triggering or in the propagation of seismic ruptures. The $p_{f}$
effect appears to be~common in small to moderate magnitude ($M
< 5\sim 6$) events such as aftershocks or swarm
sequences. The role of high $p_{f}$ is less obvious for large magnitude
($M > 6$ or higher) events. However, the precursor
mechanisms preceding large magnitude events may be partly controlled by
$p_{f}$ build-up.  Future~\mbox{researches} 
will concentrate on this aspect of
the seismic cycle. In particular, a critical issue is to try to
determine whether a $p_{f}$ increase is the triggering (causal)
mechanism for a seismic rupture propagation or is a consequence of a
\mbox{propagating} \mbox{rupture} triggered by a mechanism that would not be related
to $p_{f}$. In their spatio-temporal monitoring of
$V_{P}$ and $V_{S}$ variations
during the 1997 Umbria-Marche sequence, central Italy (Table~\ref{tab5}),
\citet{Chiarabbaetal2009a} suggest that the $p_{f}$ propagation
precedes the seismic ruptures. A similar conclusion is reached by 
\citet{Yoshidaetal2023} in their study of a swarm sequence resulting in
a $M_{w}$ 6.2 event in NE Japan. Besides, the \textit{in-situ}
experiments of \citet{Guglielmietal2015} and  \citet{Cappaetal2022}
show that a $p_{f}$ increase triggers aseismic slip that eventually
turns into a seismic displacement. From their field study of
intermediate-depth earthquakes frozen in an ancient oceanic crust, 
\citet{JohnSchenk2006} conclude that seismic rupture was not preceded
but rather accompanied and followed by fluid ingression in the
hypocentral volume (Table~\ref{tab6}). Further experimental or
\textit{in situ} works along with detailed geological or geophysical
analyses are obviously needed before the complex interrelationships
between $p_{f}$ variation and inception or propagation of brittle
fracture or slip along faults can be fully understood.

High $p_{f}$ values also play a role in the triggering or maintenance
of slow slip earthquakes and related phenomena along several subduction
interfaces or along transform faults. Since these transient phenomena
can in turn influence or control large-magnitude seismic ruptures, a
careful analysis or monitoring of $p_{f}$ build-up is an important
direction of future research. The precursory results of 
\citet{Brownetal2005,Mikadaetal2006,FultonBrodsky2016} or 
\citet{Ariyoshietal2021} are examples of such a promising monitoring.

\section*{Declaration of interests}
The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

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