stochastic modeling of fluid induced seismicity · analysis of fluid-induced seismicity summary of...

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