Microseismic Event Estimation Via Full Waveform Inversion · PDF fileMicroseismic Event...

Microseismic Event Estimation Via Full Waveform Inversion

Susan E. Minkoff1, Jordan Kaderli1, Matt McChesney2, and George McMechan2

1Department of Mathematical Sciences, University of Texas at Dallas

2Department of Geosciences, University of Texas at DallasRichardson, TX 75080, USA

IMA Hot Topics WorkshopHydraulic Fracturing: From Modeling and Simulation to Reconstruction and

Characterization

May 13, 2015

Exploration Seismology

Exploration is the search for commercial deposits of useful minerals, includinghydrocarbons, geothermal resources, etc.

Source generates a disturbance (wave).

Wave reflects when it encounters a change in material properties.

Returning wave is recorded using seismometers at the earth’s surface.

We can analyze the recorded data to image the earth’s interior.

Source can be intentional or active (e.g. explosion) or unintentional or passive (e.g.earthquake).

Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 2 / 31

Hydraulic Fracturing

(a) Hydraulic Fracturing

Fracking is used to extract oil and gas from materials with low permeability such asshale.

High pressure liquid is injected into the well to create fracture openings that allowoil and gas to flow more freely.

Buildup of pressure and stress may result in a microseismic event (small earthquake),thus generating a passive source for imaging.


Hydraulic Fracturing Simulation and Elastic Response (the Big Picture)

Processing Workflow:

Using the Complex Fracture Research Code (CFRAC) (courtesy of Marc McClure,UT Austin, CPGE), model coupled flow and deformation to synthesize microseismicevents produced by hydraulic fracturing.

The code models hydraulic injection of a single phase fluid into an impermeableisotropic medium with discrete fractures.

Deformation is modeled in a 2D plane assuming quasistatic equilibrium.

Extract synthesized microseismic events from the flow/deformation code and injectthe microseisms into an 3D (visco)elastic wave modeling code (courtesy of GeorgeMcMechan, UTD, Geosciences).

Model the elastic wave response resulting from these microseismic sources.

Result could be used as forward model for inversion.


Numerical Example: Problem Setup

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

X (m)

Y (

m)

Fracture Geometry

Student Version of MATLAB

(b) Fracture Geometry: black line iswell; blue line is natural fracture; redlines are (potential) hydraulic frac-tures

0 1000 2000 3000 4000 5000 6000 7000 80000

1

2

3

4

5

6

7

8

Time (sec)

Well Stimulation Treatment Curves

Inje

ctio

n R

ate

(kg

/s)

0 1000 2000 3000 4000 5000 6000 7000 80000

10

20

30

40

50

60

70

80

Inje

ctio

n P

ress

ure

(M

Pa)


(c) Well Treatment Curve

Model contains a single natural fracture transecting an open wellbore.

Strike of natural fracture is 60◦.

Two potentially forming hydraulic fractures at ends of natural fracture (strike is 90◦).

Injection pressure held constant at 60 MPa.

Injection rate varies with time as failures occur along the fracture(s).

Note: additional injection rate variation after about 5000 s due to failure onhydraulic fracture.


Numerical Example: Microseismic Event Generation

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

X (m)

Y (

m)

Fracture Geometry with Microseismic Hypocenters


(d) Fracture Geometry with microseisms

0 1000 2000 3000 4000 5000 6000 7000 80000

1

2

3

4

5

6

7

8

Time (sec)

Well Stimulation Treatment Curves with Microseismic Events

Inje

ctio

n R

ate

(kg

/s)

0 1000 2000 3000 4000 5000 6000 7000 8000−2

−1

0

1

2

3

4

5

6

Mic

rose

ism

ic M

om

ent

Mag

nit

ud

e


(e) Well Treatment Curve with microseisms

Microseismic events defined to occur when sliding velocity reaches 0.005 m/s.

One event has occurred along the potentially forming hydraulic fracture.

Microseismic events correlate with changes in flow rate.

Microseismic event at 5250 s corresponds to failure on hydraulic fracture.


Numerical Example: Elastic Wave Modeling from Microseismic Event 13

Microseism 13

Well Natural Fractures Hydraulic Fractures Microseismic Hypocenters Geophone Locations

(f) Fracture Geometry withmicroseismic hypocenters

x−coordinate [m]

y−co

rdia

nate

[m]

vx snapshot 80 ms

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

Sei

smic

Am

plitu

de (

m/s

)

−1

−0.5

0

0.5

1

x 10−6


(g) X-component of particlevelocity modeled using micro-seismic event 13

x−coordinate [m]

y−co

rdia

nate

[m]

vy snapshot 80 ms

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

Sei

smic

Am

plitu

de (

m/s

)

−1

−0.5

0

0.5

1

x 10−6


(h) Particle velocity (y)

x−coordinate [m]

y−co

rdia

nate

[m]

vz snapshot 80 ms

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

Sei

smic

Am

plitu

de (

m/s

)

−6

−4

−2

0

2

4

6

x 10−7


(i) Particle velocity (z)

Microseismic source has dip of 90◦, strike of 90◦, and rake of 0◦.Small microseismic event occurred along potentially forming hydraulic fracture.


Numerical Example: Elastic Wave Modeling from Microseismic Event 14

Microseism 14

Well Natural Fractures Hydraulic Fractures Microseismic Hypocenters Geophone Locations

(j) Fracture Geometry withmicroseismic hypocenters

x−coordinate [m]

y−co

rdia

nate

[m]

vx snapshot 80 ms

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

Sei

smic

Am

plitu

de (

m/s

)

−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1


(k) X-component of particlevelocity modeled using micro-seismic event 14

x−coordinate [m]

y−co

rdia

nate

[m]

vy snapshot 80 ms

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

Sei

smic

Am

plitu

de (

m/s

)

−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1


(l) Particle velocity (y)

x−coordinate [m]

y−co

rdia

nate

[m]

vz snapshot 80 ms

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

Sei

smic

Am

plitu

de (

m/s

)

−0.06

−0.04

−0.02

0

0.02

0.04

0.06


(m) Particle velocity (z)

Microseismic source has dip of 90◦, strike of 60◦, and rake of 0◦.

Microseismic event occurred along natural fracture.

Note the directional polarity of the emitted wavefield.


Numerical Example: Receiver Data for Microseismic Event 13

X-component of particle velocity as recorded at the receiver locations.

Note the existence of both P and S-wave arrivals in the recorded seismograms.


Outline

Goal is to estimate the microseismic source using full waveform inversion.

I. Description of Problem and Approach

II. Overview of Full Waveform Inversion

III. Numerical Experiments for Source Location and Onset Time

IV. Discussion of Future Work


Traditional Methods for Microseismic Event Detection

Figure: Traditional Methods rely on traveltime picking of first arrivals.

(a) Event estimation usingclean data

(b) Event estimation usingnoisy data

Reference (courtesy of Pioneer Natural Resources):

1. Han L., J. Wong, and J. C. Bancroft, “Hypocenter location using hodogram analysis of noisy 3C

microseismograms”, CREWES Research Report - Vol. 21, University of Calgary, (2009), pp. 1-14.


Seismic Full Waveform Inversion

1

c2

∂2u

∂t2−∇2u = s

(c) Forward Problem

(d) Velocity Inversion (e) Source Inversion


Assumptions

We model wave propagation through a constant density medium using the acoustic waveequation:

m(x , z)∂2u(x , z , t)

∂t2−∇2u(x , z , t) = f (x , z)w(t)

where

m(x , z) is the known squared slowness, i.e. the reciprocal of the sound velocity squared,

f (x , z) is the spatial component of the source of acoustic energy,

w(t) is a Ricker wavelet, and

u(x , z , t) is the acoustic pressure.

In the typical inverse problem, we know f (x , z)w(t), and we want to determine the soundvelocity, i.e. we want to find m(x , z).

In our source inversion problem, we know m(x , z), and we want to find f (x , z)w(t).


Overview of Full Waveform Inversion1

1 Choose initial guess f0.

2 Given the correct sound velocity and the current source estimate fn, solve the waveequation un = F [fn].

3 Compute the residual un − dobs , where dobs is the recorded data.

4 Solve the adjoint equation backwards in time using the residual as the sourceF ∗(un − dobs).

5 Compute the gradient to find a descent direction for the least squares objectivefunction J(f ) = 1

2‖F (f )− dobs‖2.

6 Update the model fn+1 = fn − α ∗ gradient.

7 Increment n and loop back to Step 2.

1Note: all experiments shown were implemented using a modified version of PySIT, a seismic inversiontoolbox developed originally by the Imaging and Computing Group at MIT.


Comparison of gradient for velocity inversion vs. source inversion

In the typical velocity inversion problem, J(m) = 12

Ps,r

hR T

0(Ss,ru − ds,r )2dt

i.

In our source inversion problem, J(f ) = 12

Ps,r

hR T

0(Ss,ru − ds,r )2dt

i.

In the typical velocity inversion problem, δmJ =Ps

hR T

0(m̃ ∂2u

∂t2 , λ)dti.

In our source inversion problem, δf J =Ps

hR T

0(w , λ)dt

i.

We do not need to store the forward model data for all time steps.


Overview of Full Waveform Inversion

Step 1: Given the correct sound velocity and an initial guess for the source f0, solve thewave equation u0 = F [f0].

(f) Experimental Setup (g) Receiver Data for Initial Source

Note that F is the forward operator, i.e. the wave equation operator, and maps from thex-z domain to the t-x domain.



Step 2: Compute the residual un − dobs .

(h) Receiver Data for Initial Source (i) Recorded Data

(j) Residual



Step 3: Solve the adjoint equation backwards in time using the residual as the sourceF ∗(un − dobs).

(k) Residual

(l) Adjoint Field at time t =1.5

(m) Adjoint Field at time t = 0

Note that F ∗ (the adjoint operator) maps from the t-x domain to the x-z domain.Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 18 / 31


Step 4: Compute the gradient to find a descent direction for the least squares objectivefunction J(f ) = 1

2‖F (f )− dobs‖2.

(n) Gradient



Step 5: Update the model fn+1 = fn − α ∗ gradient.

(o) fn (p) −α ∗ gradient

(q) fn+1



Step 6: Increment n and loop back to Step 1:Given the correct sound velocity and the current source estimate fn, solve the waveequation un = F [fn].

(r) Receiver Data after 1 Iteration (s) Recorded Data


Numerical Experiments: inverting for spatial component of the source (f )

Note: for all the experiments shown,

Domain is size 181 x 141.

Velocity is assumed constant and known.

For this experiment

Time-dependent component of source is 20 Hz Ricker wavelet (known).


Inverting for spatial component of the source using noisy data

Initial source estimate is zero everywhere. Data has a 0.008 signal-to-noise ratio!!Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 23 / 31

Inverting for time-dependent part of the source (w)


Inverting for time-dependent part of the source using noisy data

Data has 0.083 signal-to-noise ratio!!


Joint inversion for both the time and space components of the source


Joint inversion for both the time and space components of the source

Problem: source is too spread out in space which has a corresponding impact on the timedependence. Need to focus the source.


Adding L1 Regularization

With regularization our new objective function for the spatial component of the source isJ(f ) = 1

2‖F (f )− dobs‖2

2 + λ‖f ‖1 where λ is a penalty parameter.

Anywhere in the domain where the source is zero (in our case, almost everywhere), thesecond term above is not differentiable. Several L1 minimization algorithms attempt tohandle this problem.

We focus on Iteratively Reweighted Least Squares (IRLS12): Away from fi = 0, gradientof the regularization term ∇‖f ‖1 contains components fi/|fi |.

Defining a diagonal matrix W with elements Wi,i = 1/|fi | we can handle thenon-differentiability at fi = 0 by

Wi,i =

1/|fi | |fi | ≥ ε1/ε |fi | < ε

or by

Wi,i = 1/q

(f 2i + ε2)

where ε is a tolerance, and ∇‖f ‖1 = Wf .1Daubechies, Devore, Fornasier, Gunturk, “Iteratively reweighted least squares minimization for sparse

recovery”. Communications on Pure and Applied Mathematics, v.63, no.1., 2010.2Aster, Borchers, and Thurber. Parameter Estimation and Inverse Problems. Elsevier, 2005.


Numerical Experiment: inverting for spatial component of the source (f )with L1 Regularization.

Domain is size 181 x 141.Velocity is assumed constant and known.Time-dependent component of source is 20 Hz Ricker wavelet (known).ε = 10−12.


Numerical Experiment: inverting for spatial component of the source (f )with L1 Regularization.


Conclusions and Future Work

Hydraulic fracturing of low permeability shale rock creates fractures.

Buildup of pressure and mechanical stress may lead to small releases of elasticenergy (earthquakes) which are called “microseismic events”.

These passive sources can be used to further refine our images of the earth’ssubsurface (e.g., estimates of the velocity).

To estimate these sources traditional methods have relied on picking “first arrivals”of seismic energy in the data.

Unfortunately, first arrival picking is very difficult in the presence of noise.

By using full waveform inversion, we have successfully found the spatial location ofthe microseismic event as well as the onset time even in the presence of substantialnoise and with poor initial guesses.

Joint inversion for both the space and time component of the source may requireadditional information from well logs, etc.

Our future work will include

Extending the work to more realistic problems, including more realisticrepresentations of the source. Coupling the “big picture” with the source inversionvia FWI.

Adding uncertainty quantification in the context of joint inversion for velocity andthe source.


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