Human subsurface activities induce significant hazard by (re-)activating slip on faults, which are
ubiquitous in geological reservoirs. Laboratory and field (decametric-scale) fluid injection
experiments provide insights into the response of faults subjected to fluid pressure
perturbations, but assessing the long-term stability of fault slip remains challenging. Numerical
models offer means to investigate a range of fluid injection scenarios and fault zone
complexities and require frictional parameters (and their uncertainties) constrained by
experiments as an input. In this contribution, we propose a robust approach to extract relevant
microphysical parameters that govern the deformation behaviour of laboratory samples. We apply
this Bayesian approach to the fluid injection experiment of
Induced seismicity is of primary concern in human subsurface activities, including geothermal energy
production, wastewater and
Laboratory experiments provide the means to investigate the mechanisms for (unstable) fault slip at
high resolution under well-controlled conditions
As an alternative approach, decametric-scale fluid injection tests allow one to probe the response
of a tectonic fault to fluid pressure perturbations under in situ conditions
In the present study, we reinterpret the laboratory and decametric-scale fluid injection
experiments reported by
To describe the observed laboratory observations of
Firstly, the CNS model considers a representative elementary volume of fault gouge of thickness
The rate of granular flow is itself a function of stress and porosity and can be written as
In the present study, we treat the laboratory sample as a single degree-of-freedom (spring block)
system, with uniform porosity and an internal state of stress. This implies that the fluid pressure is
considered to be uniform and constant throughout the sample, with no coupling between volumetric
deformation and fluid pressure. This assumption is valid for samples with sufficiently high
permeability, such that the characteristic timescale of fluid diffusion is smaller than the timescale of deformation. In other words, the sample is assumed to be in equilibrium with the externally
applied fluid pressure (“drained”) at all times. In the laboratory experiments of
In the simplified CNS framework laid out above, the dynamics of the system are fully governed by
Since the proposed inversion protocol does not involve numerically solving a forward model, a single
evaluation of either Eqs. (
We apply the above procedure to the laboratory fluid injection experiment performed by
Overview of laboratory measurements of
Lower triangle (blue graphs and those below them): corner plot of the posterior distributions of the inverted
parameters
We first fit Eq. (
Panel
We continue by fitting the (logarithm of) measured slip rate based on Eq. (
Results of the inversion procedure.
Finally, for verification, we numerically solve the forward model given by Eqs. (1a) and (1b)
with the parameters obtained in the inversion procedure (Fig.
Encouraged by the results of the proposed inversion method for the laboratory experiment, we
continue to apply the same procedure to the field injection test of
Corner plot of the posterior distributions of the inverted parameters
While these other values seem entirely reasonable, the inferred value of
Since the CNS model fault strength (and therefore the fault slip rate) is directly controlled by the
dilatancy parameter
Traditionally, laboratory experiments are interpreted within the framework of rate-and-state
friction (RSF), commonly presented as
Aside from the fault-parallel slip, the fault opening potentially provides a second prominent
constraint. In the classical RSF framework, volumetric deformation is not explicitly accounted
for. Traditionally, the state parameter
While the CNS microphysical parameters can be directly estimated from laboratory experiments, their
incorporation into numerical models of tectonic faults may be subject to moderation based on
geological or physical considerations. In laboratory experiments conducted at room ambient
conditions and comparatively high deformation rates (of the order of micrometres per second up to millimetres per second), the gouge
porosity remains close to the critical-state porosity. Likewise, in the laboratory experiment of
The property that
Combining now the observations made in Sect.
In this work, we analysed the fluid injection experiments conducted by
The excellent agreement between the CNS model and the laboratory data allows us to interpret the
dynamics of the fault in terms of volumetric deformation (porosity changes). By doing so, we
circumvent the velocity dependence of the rate-and-state friction parameters
A Python script that reproduces the results and figures in this paper, along with the laboratory and field injection data, is available at
MPAvdE conceptualised the study and performed the analyses. MMS and FC provided the laboratory and field data. JPA supervised MPAvdE. All authors discussed and prepared the contents of the paper.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Thermo–hydro–mechanical–chemical (THMC) processes in natural and induced seismicity”. It is a result of the 7th International Conference on Coupled THMC Processes, Utrecht, Netherlands, 3–5 July 2019.
The authors thank the topical editor André Niemeijer and two anonymous reviewers for their
encouraging and constructive comments on the paper. Martijn P. A. van den Ende, Frédéric Cappa, and
Jean-Paul Ampuero are supported by French government through the UCA
This research has been supported by the Agence Nationale de la Recherche (grant no. ANR-15-IDEX-01).
This paper was edited by André R. Niemeijer and reviewed by two anonymous referees.