stochastic modeling of fluid induced seismicity · analysis of fluid-induced seismicity summary of...
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Alexander GARCIAARISTIZABAL
Stochastic modeling of fluidinduced Seismicity
Istituto Nazionale di Geofisica e VulcanologiaSezione di Bologna (Italy)
Workshop on “Anthropogenic Hazards”, June 1112, 2018Mining school, Oulu University, Finland
Outline
1 Introduction and general concepts
2 Stochastic modeling of Fluidinduced seismicity I: Injection phases
3 Stochastic modeling of Fluidinduced seismicity II: postinjection phases
4Points to take home
1 Introduction and general concepts
Induced seismicity, in general, refers to seismic events that are induced by stress perturbations resulting from anthropogenic activity
Fluidinduced seismicity
Induced seismicity, in general, refers to seismic events that are induced by stress perturbations resulting from anthropogenic activity
Fluidinduced seismicity
Hydraulic fracturing for recovery of hydrocarbons from low.perm. layers
Wastewater disposal
Oil and gas field depletion
Enhanced geothermal systems (EGS)
Fluid injection for secondary oil recovery
Fluidinduced seismicityGeneral physical constraints
According to the characteristics of the fluid pressure perturbation respect to the stress field in the rock, the generated fluidinduced seismicity can be
associated with different physical processes (e.g., Shapiro et al., 2007):
Fluidinduced seismicityGeneral physical constraints
According to the characteristics of the fluid pressure perturbation respect to the stress field in the rock, the generated fluidinduced seismicity can be
associated with different physical processes (e.g., Shapiro et al., 2007):
Fluid injections resulting in Pp < σ3
The behavior of seismicity triggering in space and time is mainly controlled by a process of relaxation of stress and pore
pressure perturbations initially created atthe injection source.
Fluidinduced seismicityGeneral physical constraints
According to the characteristics of the fluid pressure perturbation respect to the stress field in the rock, the generated fluidinduced seismicity can be
associated with different physical processes (e.g., Shapiro et al., 2007):
Fluid injections resulting in Pp > σ3
Fluid injections resulting in Pp < σ3
In this case the properties of the induced seismicity are controlled by the parameters of the process of hydraulic fracture growth
The behavior of seismicity triggering in space and time is mainly controlled by a process of relaxation of stress and pore
pressure perturbations initially created atthe injection source.
Analyzing FluidInduced Seismicity
Analyzing FluidInduced Seismicity
Analyzing FluidInduced Seismicity
Analyzing FluidInduced Seismicity
Analyzing FluidInduced Seismicity
Analyzing FluidInduced Seismicity
2/3. Stochastic modeling of event occurrences in time
Injectionperiod
“Freeresponse” period
e.g., Cooper basin, Australia (EGS)
2/3 Stochastic modeling of event occurrences in time
Injectionperiod
“Freeresponse”period
Injectionperiod
“Freeresponse”period
Cooper basinFracture
propagation 1
2 Stochastic modeling of Fluidinduced seismicity I: Injection phases
Modeling seismicity rates during fluid injections
3/20
By its ‘nature’, fluidinduced seismicity is generally a nonstationary process
dt
Stochastic modeling modeling the distribution of InterEvent Times (→ IET)
Basic Tool
Main problemDistribution characterizing inter
event times (IET)
Analysis of fluid-induced seismicity
Summary of stochastic models frequently used for analyzing time-varying fluid-induced seismicity in the time domain:
✔ The Reasenberg & Jones model (1989, 1990, 1994)
✔ The modified Epidemic-type aftershock model, ETAS (Bachmann et al. 2011)
✔ The Σ-based (seismogenic index) model of Shapiro et al., 2010.
Analysis of fluid-induced seismicity
Summary of stochastic models frequently used for analyzing time-varying fluid-induced seismicity in the time domain:
It is a simple model for estimating the rate of earthquakes greater than or equal to magnitude M, at a time t following a mainshock eventof a given magnitude M
MS
● a and b are the parameters of the Gutenberg & Richter distribution; ● c and p arethe coefficients of the modified Omori law describing the decay
rate of the aftershock activity following the ‘mainshock’.
✔ The Reasenberg & Jones model (1989, 1990, 1994)
✔ The modified Epidemic-type aftershock model, ETAS (Bachmann et al. 2011)
✔ The Σ-based (seismogenic index) model of Shapiro et al., 2010.
Analysis of fluid-induced seismicity
✔ The Reasenberg & Jones model (1989, 1990, 1994)
✔ The modified Epidemic-type aftershock model, ETAS (Bachmann et al. 2011)
✔ The Σ-based (seismogenic index) model of Shapiro et al., 2010.
→ The rate of aftershocks greater than or equal to a magnitude M
min at a time t days following an
event of magnitude Mi is given by (Ogata 1989):
Summary of stochastic models frequently used for analyzing time-varying fluid-induced seismicity in the time domain:
Analysis of fluid-induced seismicity
→ The rate of aftershocks greater than or equal to a magnitude M
min at a time t days following an
event of magnitude Mi is given by (Ogata 1989):
→ the total rate of earthquakes >= a threshold magnitude is a superposition of the individual aftershock sequences, superimposedon top of a longer-term background rate of seismicity (λ
0).
✔ The Reasenberg & Jones model (1989, 1990, 1994)
✔ The modified Epidemic-type aftershock model, ETAS (Bachmann et al. 2011)
✔ The Σ-based (seismogenic index) model of Shapiro et al., 2010.
Summary of stochastic models frequently used for analyzing time-varying fluid-induced seismicity in the time domain:
Analysis of fluid-induced seismicity
✔ The Reasenberg & Jones model (1989, 1990, 1994)
✔ The modified Epidemic-type aftershock model, ETAS (Bachmann et al. 2011)
✔ The Σ-based (seismogenic index) model of Shapiro et al., 2010.
Bachmann et al. (2011) propose a simple model to correlate the total background rate in a time period t to the injection flow rate F
r(t):
→ the total rate of earthquakes >= a threshold magnitude is a superposition of the individual aftershock sequences, superimposedon top of a longer-term background rate of seismicity (λ
0).
Summary of stochastic models frequently used for analyzing time-varying fluid-induced seismicity in the time domain:
Analysis of fluid-induced seismicity
The expected number of events in a time period t greater than or equal to a given magnitude M is determined from:
● QC is the cumulative fluid injection volume;
● Σ is the seismogenic index that is dependent on the tectonic setting, and is calculated empirically.
✔ The Reasenberg & Jones model (1989, 1990, 1994)
✔ The modified Epidemic-type aftershock model, ETAS (Bachmann et al. 2011)
✔ The Σ-based (seismogenic index) model of Shapiro et al., 2010.
Summary of stochastic models frequently used for analyzing time-varying fluid-induced seismicity in the time domain:
Analysis of fluid-induced seismicity
We discuss here a 'hybrid' (I-FR) modeling approach:
→ The injection/free-response (I-FR) modeling approach
✔ Analysis of injection periods in the time domain
✔ Analysis of free-response periods in the time domain
10/40
Summary of stochastic models frequently used for analyzing time-varying fluid-induced seismicity in the time domain:
✔ The Reasenberg & Jones model (1989, 1990, 1994)
✔ The modified Epidemic-type aftershock model, ETAS (Bachmann et al. 2011)
✔ The Σ-based (seismogenic index) model of Shapiro et al., 2010.
Modeling seismicity rates during fluid injections
We model the IET distribution adopting a ‘Covariate approach’:
Method
Modeling seismicity rates during fluid injections
We model the IET distribution adopting a ‘Covariate approach’:
Method
Modeling seismicity rates during fluid injections
We model the IET distribution adopting a ‘Covariate approach’:
Method
Basic assumptions:
✔ We assume that it is possible to identify a probability distribution describing the IET;
Modeling seismicity rates during fluid injections
We model the IET distribution adopting a ‘Covariate approach’:
Method
Basic assumptions:
✔ We assume that it is possible to identify a probability distribution describing the IET;
✔ We assume that all the event occurrences in the seismic catalog are associated to the fluid injection process. It implies that:
i. Event interactions are weak or do not exist (may be valid in lowmagnitude events);
ii.Eventual regional/background seismicity has been removed
Modeling seismicity rates during fluid injections
We model the IET distribution adopting a ‘Covariate approach’:
Method
Basic assumptions:
✔ We assume that it is possible to identify a probability distribution describing the IET;
✔ We assume that all the event occurrences in the seismic catalog are associated to the fluid injection process. It implies that:
i. Event interactions are weak or do not exist (may be valid in lowmagnitude events);
ii.Eventual regional/background seismicity has been removed
✔ We assume that it is possible to identify a relationship between the Probability model parameter(s) and the industrial activity
Modeling seismicity rates during fluid injections
We model the IET distribution adopting a ‘Covariate approach’:
Method
Identify and select a probability
distribution as a basic ‘functional
template’
A
Modeling seismicity rates during fluid injections
4/20
We model the IET distribution adopting a ‘Covariate approach’:
Method
Identify and select a probability
distribution as a basic ‘functional
template’
Assess the most adequate functional form relating the parameters of the
probability distribution and
covariates of interest
A
B
Modeling seismicity rates during fluid injections
4/20
We model the IET distribution adopting a ‘Covariate approach’:
Method
Identify and select a probability
distribution as a basic ‘functional
template’
Assess the most adequate functional form relating the parameters of the
probability distribution and
covariates of interest
Implement a robust procedure for
model selection
A
B
C
5/20
Method
A. Identify and select a probability distribution as a basic ‘functional
template’
Stochastic modeling ofevent occurrences in time:
Injection Period
Homogeneous Poisson process →
Nonhomogeneous Poisson process →
t IET →
5/20
Method
A. Identify and select a probability distribution as a basic ‘functional
template’
We test two possible probability distributions:
WeibullWeibull ExponentialExponential(With covariates)(With covariates)
5/20
Method
We test two template probability distributions:
WeibullWeibull ExponentialExponential
A. Identify and select a probability distribution as a basic ‘functional
template’
Exponential IET
Exponential IETWith covariates
(With covariates)(With covariates)
6/20
Method
B. Assess the most adequate functional form relating the
prob. model parameters and covariates of
interest
1. Identification of covariate(s) of interest
2. Write model parameter(s) as a function of the covariates of interest
6/20
Method
B. Assess the most adequate functional form relating the
prob. model parameters and covariates of
interest
1. Identification of covariate(s) of interest
2. Write model parameter(s) as a function of the covariates of interest
Cooper Basin(Australia)
6/20
Method
B. Assess the most adequate functional form relating the
prob. model parameters and covariates of
interest
1. Identification of covariate(s) of interest
2. Write model parameter(s) as a function of the covariates of interest
6/20
Method
B. Assess the most adequate functional form relating the
prob. model parameters and covariates of
interest
1. Identification of covariate(s) of interest
2. Write model parameter(s) as a function of the covariates of interest
1. Linear relationship between the seismicity rate and IR (“usual” model)
where:
6/20
Method
B. Assess the most adequate functional form relating the
prob. model parameters and covariates of
interest
1. Identification of covariate(s) of interest
2. Write model parameter(s) as a function of the covariates of interest
1. Linear relationship between the seismicity rate and IR (“usual” model)
2. A generalization using polynomial functions of the form:
where:
6/20
Method
B. Assess the most adequate functional form relating the
prob. model parameters and covariates of
interest
1. Identification of covariate(s) of interest
2. Write model parameter(s) as a function of the covariates of interest
Inference problem
Method
C. Implement a robust procedure
for model selection
Example of Possible criteria:
● Akaike’s information Criterion (AIC)● Schwarz’s Bayesian information Criterion (BIC)● Bayes factors (Bkl)● ...
7/20
Method
We compute Bayes Factors, Bkl, for comparing model Mk to model Ml for observed data x.
For models a priori equally probable:
C. Implement a robust procedure
for model selection
Jeffreys (1961); Raftery (1996)
Example of Possible criteria:
● Akaike’s information Criterion (AIC)● Schwarz’s Bayesian information Criterion (BIC)● Bayes factors (Bkl)● ...
Data analysis
Episode:
“The Geysers Prati 9 and Prati 29 cluster”
IS-EPOS platform
8/20
1. The Geysers (US):
Data analysis
Episode:
“The Geysers Prati 9 and Prati 29 cluster”
IS-EPOS platform
● 6.7 years of data
● ~1254 events with M≥1.4● ~1.04×107 m3 of fluids injected
General info:
8/20
1. The Geysers (US):
Data analysisThe Geysers (US)
9/20
Testing the performance
Learningdataset
Forecasting& testing
Data analysis
Process description:
10/20
Testing the performance
The Geysers (US)
11/20
Testing the performance
log(Injection rate, [l/s]) Time (Days after 10/12/2007)
Forecastingwindow
Moving window approach
Data analysis
The Geysers (US)
11/20
Testing the performance
log(Injection rate, [l/s]) Time (Days after 10/12/2007)
Data analysis
The Geysers (US)
11/20
Testing the performanceData analysis
3 Stochastic modeling of Fluidinduced seismicity II: freeresponse (or postinjection phases)
Stochastic modeling of event occurrences in time:
“Freeresponse” phase
“Freeresponse”phase
'Freeresponse” (or postinjection) phases
Stochastic modeling of event occurrences in time: 'Freeresponse” phases
Considering the trigger models (VereJones and Davies 1966), it is assumed that the conditional probability of a shock occurring at a time t after a given triggering event is proportional to a decay function (t)λ .
Stochastic modeling of event occurrences in time: 'Freeresponse” phases
Considering the trigger models (VereJones and Davies 1966), it is assumed that the conditional probability of a shock occurring at a time t after a given triggering event is proportional to a decay function (t)λ .
An exponential decay,
An inverse powerlaw decay
Modified Omori law (Utsu 1961),
ETAS model,
Regarding the nature of (t), different functions can be considered:λ
{
Results
Hydraulic stimulation in Enhanced Geothermal
System
● ~50 days of data
● ~15431 events with M≥0.8
● ~2.0×104 m3 of fluids injected
General info:
3/5
Cooper basin (Australia):
Data analysis
Regarding the postinjection phases...
Decay function Modeled using the Modified
Omori (MOL) law model
Parameterization proposed by Holschneider et al., 2012)
2/5
Regarding the postinjection phases... Modeled using the Modified Omori (MOL) law model
4/5
Regarding the postinjection phases...
Parameter values Modeled using the Modified Omori (MOL) law model
5/5
Regarding the postinjection phases...
Parameter values Modeled using the Modified Omori (MOL) law model
5/5
OJO: REVISAR – BARRA DE ERROR FIP1 NO COERENTE
Regarding the postinjection phases...
Parameter values Modeled using the Modified Omori (MOL) law model
5/5
OJO: REVISAR – BARRA DE ERROR FIP1 NO COERENTE
4 Points to take home
Stochastic modeling of event occurrences in time: Summary
Injection period “Freeresponse”period
Injection period “Freeresponse”period
Recurrence analysisHPP / NHPP
Model parameteris a function of the
Injection rate
Stochastic modeling of event occurrences in time: Summary
Injection period “Freeresponse”period
Recurrence analysisHPP / NHPP
Model parameteris a function of the
Injection rate
Modeling the rate of events after a time t using an adequate decay function (t)λ
p parameter of MOL higher than in
“natural” seismic sequences
Stochastic modeling of event occurrences in time: Summary
Injection period “Freeresponse”period
Recurrence analysisHPP / NHPP
Model parameteris a function of the
Injection rate
Modeling the rate of events after a time t using an adequate decay function (t)λ
Predictive model
IS Seismic hazard assessment:Temporal analysis
p parameter of MOL higher than in
“natural” seismic sequences
Stochastic modeling of event occurrences in time: Summary
Conclusive remarks
17/20
ConclusionsWhat we have learned?
17/20
A covariate approach, in which the parameters of a template probability distribution are allowed to change according to
injectionrelated parameters is a flexible tool for modeling non
stationary, fluidinduced seismicity
rates
3.2 bbl/min
15 bbl/min
0.25 bbl/min
Injection periods
What we have learned?
18/20
A template exponential distribution of IET, with a linear function relating the logarithm of the
distribution’s μ parameter and the logarithm of the injection rate, is the model that better describes the
observations.
Conclusions Injection periods
What we have learned?
18/20
A template exponential distribution of IET, with a linear function relating the logarithm of the
distribution’s μ parameter and the logarithm of the injection rate, is the model that better describes the
observations.
This result suggests that the μ parameter of the
exponential distribution of IET and the injection rate have a powerlaw
relationship
α1
The Geysers −1.04 to −0.78
Cooper Basin −1.22 to −0.73
Conclusions Injection periods
What we have learned?
19/20
Time (Days after 10/12/2007)Time (Days after 10/12/2007)
models calibrated using the most recent past data produce forecasts that are more coherent with the observations
Moving window approach Full window approach
Conclusions Injection periods
19/20
p parameter of MOL is higher than in “natural” seismic sequences:
It implies that seismicity rates decay faster
Conclusions Postinjection periods
This work was performed in the framework of the European SHEER (SHale gas Exploration and Exploitation induced Risks) project, funded from the European Union Horizon 2020 Research and Innovation Programme,
under grant agreement 640896. The Cooper Basin data is available through a database of fluid-induced seismicity episodes created in the SHEER project. The Geysers dataset is available via IS-EPOS platform of
the EPOS (European Plate Observing System) project.
Thanks