Microseismic interferometry

Abstract

The past decade witnessed rapid development of the theory of seismic interferometry followed by numerous applications of interferometric approaches in seismic exploration and exploitation. This body of work, partially collected in the "Seismic Interferometry" supplement of Geophysics (2006), SEG's 2008 reprint volume edited by Wapenaar et al., and the "Interferometry Applications" special section of The Leading Edge (2011), conclusively demonstrates that a stack of crosscorrelations of traces recorded by two receivers over sources appropriately distributed in a three-dimensional heterogeneous Earth can retrieve a signal that would be observed at one receiver if another acted as a source of seismic waves. This assertion is applicable to both active-source data (many instructive geometries of this kind are examined by Schuster, 2009) and passive records of ambient noise; examples of the latter, summarized by Snieder and Wapenaar (2010), range from ultrasonics (Weaver and Lobkis, 2001) to global seismology (Shapiro et al., 2005).

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Passive seismic and microseismic—Part 2
1478 The Leading Edge December 2012
SPECIAL SECTION: P a s s ive seismic and microseismic—Part 2
Microseismic interferometry
The past decade witnessed rapid development of the
theory of seismic interferometry followed by numerous
applications of interferometric approaches in seismic
exploration and exploitation. is body of work, partially
collected in the “Seismic Interferometry” supplement of
G (2006), SEG’s 2008 reprint volume edited by
Wapenaar et al., and the “Interferometry Applications” special
section of e Leading Edge (2011), conclusively demonstrates
that a stack of crosscorrelations of traces recorded by two
receivers over sources appropriately distributed in a three-
dimensional heterogeneous Earth can retrieve a signal that
would be observed at one receiver if another acted as a source
of seismic waves. is assertion is applicable to both active-
source data (many instructive geometries of this kind are
examined by Schuster, 2009) and passive records of ambient
noise; examples of the latter, summarized by Snieder and
Wapenaar (2010), range from ultrasonics (Weaver and
Lobkis, 2001) to global seismology (Shapiro et al., 2005).
Passive seismic interferometry, sometimes called stochas-
tic interferometry, is especially well suited for downhole mi-
croseismic applications. Indeed, microseismic monitoring of
hydraulic stimulations of low-permeability reservoirs typically
lasts for days, supplying abundant data for turning geophones
into virtual sources (in the terminology of Bakulin and Cal-
vert, 2004) and analyzing the obtained outputs. To the best
of our knowledge, this opportunity was first recognized by
Miyazawa et al. (2008), who reconstructed the body P- and
S-waves propagating along a wellbore from steam-injection
noise recorded by three-component (3C) receivers. Essential-
ly, we follow their footsteps but with two modifications that
VLADIMIR GRECHKA, Marathon Oil Company
YANG ZHAO, University of California, Berkeley
appear to be important in practice. First, we seem to be able
to retrieve meaningful, clean, and straightforwardly interpre-
table signals from crosscorrelations of minutes of passive data
as opposed to a month-long record employed by Miyazawa
et al. (2008). Second, we do not explicitly remove locatable
microseismic events from the crosscorrelation process and,
instead, let normalization and stacking smooth out the as-
sociated amplitude anomalies.
In what follows, we describe the results of interferometry
applied to three downhole microseismic data sets acquired
in the hydrocarbon-bearing Niobrara, Eagle Ford, and Bak-
ken formations. Although the available 3C data make it theo-
retically possible to recover full elastic Green’s tensors for any
receiver pair, we restrict the scope of this article to a single,
along-the-well component of our 3C records. Depending
on the survey geometry, crosscorrelations of this component
yield either P- or S-waves traveling between the receivers,
which allow us to estimate the associated velocities that can
be used to build models for microseismic data processing.
Computations
We begin with outlining our computational procedure that
was performed in the time, t, domain. Let Ws,r(t) be the nor-
malized, along-the-well component of 3C seismic trace that
belongs to the shot gather s and is recorded by the receiver r.
Our usage of the term “receiver” is conventional because we
know where receiver r is located and what it records; the term
“shot gather,” however, needs to be explained. Because pas-
sive data, such as those displayed in Figure 1, contain waves
arriving from unknown natural sources to our receivers in
a selected time interval T, we define a shot gather as data
recorded by the receiver string during that time interval. Ac-
cording to the adopted definition, Figure 1 shows 1-s long (T
= 1 s) shot gather.
We take two traces ws,r1(t) and ws,r2(t) of shot gather s re-
corded at r1 and r2 and crosscorrelate them. We then stack the
obtained crosscorrelations over a subset of the available shot
gathers. e spectrum of the result,
(1)
where o denotes the time lag, is proportional to the sum of
spectra of the causal and acausal band-limited Green’s func-
tions between r1 and r2 if the physical sources (for instance,
contributing to the gather in Figure 1) have random and
uncorrelated spatial locations and amplitudes (Weaver and
Lobkis, 2001).
A few operational comments are now in order.
1) We normalize traces ws,r prior to crosscorrelating them to
suppress contributions of strong bursts of energy (e.g., mi-
croseismic events) whose signal-to-noise ratios can reach
Figure 1. Randomly chosen 1-s long microseismic shot gather recorded
by a string of 10 downhole receivers. is gather represents typical
input data for the case studies discussed in the paper.
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December 2012 The Leading Edge 1479
Passive seismic and microseismic—Part 2
over 100. Although we find this type of normalization
convenient because it eliminates the need to establish a
threshold for ambient noise and filter the input data ac-
cordingly, such an equalization of amplitudes is not abso-
lutely critical. e reason for its unimportance appears to
be a significant violation of the assumption of randomness
of natural seismic sources (Weaver and Lobkis, 2006), the
violation that prevents one from retrieving the correct am-
plitudes of waves comprising W (Equation 1). If the true
amplitudes of waves are unrecoverable in our conditions
and obtaining the correct kinematics remains the only re-
alistically achievable goal, amplitudes of input traces can
be severely distorted without compromising the traveltime
information (see Figures 9 and 10).
2) e time interval T defining the length of a shot gather
is a free parameter that needs to be selected. After experi-
menting with intervals ranging from 0.5 to 15 s, we found
that a particular value of T has little influence on the final
result, that is, on traveltimes of the expected arrivals, as
long as T is several times greater than the length of the
maximum crosscorrelation time lag o.
3) We apply zero-phase band-pass filters to the produced
stacks W of crosscorrelations to enhance their visual ap-
pearance. e frequency bandwidths f of our filters, listed
in the figure captions, are sufficient to preserve useful in-
formation in each displayed interferometric output.
Zero-offset VSP
Our first data set was acquired in a vertical well drilled to
monitor hydraulic stimulation of the Niobrara Formation
(Colorado, USA). In this geometry, retrieving VSP (vertical
seismic profiling) data from microseismic noise is possible.
An example of such zero-offset VSP is presented in Figure
2a, in which only 1 minute of raw record, whose portion
is displayed in Figure 1, sufficed to produce a meaningful
output. As Figure 2a demonstrates, turning the shallowest
receiver into a source recovers a causal downgoing wave. Be-
cause we crosscorrelate the vertical along-the-well receiver
components, it ought to be a P-wave. Its nature as the body
P-wave propagating in rocks surrounding the borehole be-
comes clear once we compare its traveltimes with those (red
dots in Figure 2a) derived from a sonic log (Figure 2b) in a
nearby vertical well. Sources of noise generating the P-wave
in Figure 2a have to be located above the receivers and likely
relate to human activity on the well pad.
Let us note that another, arbitrarily chosen minute of data
would not yield exactly the output shown in Figure 2a be-
cause natural sources are distributed nonuniformly in space
Figure 2. (a) Zero-offset VSP retrieved from 1 minute of microseismic data ( T= 15 s, f = [10, 50] Hz) recorded above the Niobrara Formation.
e red dots in (a) indicate the times obtained by integrating the P-wave sonic log in (b).
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1480 The Leading Edge December 2012
Passive seismic and microseismic—Part 2
Figure 3. Well trajectory (gray) and locations of receivers (triangles).
e dip of the lateral section covered by the receivers is 3°. e arrow
points in the direction of propagation of the P-wave reconstructed in
Figure 4.
Figure 4. Wave retrieved from crosscorrelations of 16 minutes of data
( T = 15 s, f = [20, 150] Hz) that propagates in the direction of the
arrow along the receiver string shown in Figure 3. e slope of the
dashed straight line implies the average apparent velocity of 4.5 km/s.
and nonperiodic in time. eir spatial nonuniformity is evi-
denced by the absence of upgoing waves in Figure 2a and the
lack of their temporal periodicity—by our inability to find
two sets of different shot gathers resulting in the same stack.
Still, all examined stacks exhibit P-waves similar to the one
in Figure 2a and make the differences in their propagation
times a useful measure of the uncertainty in reconstructing
kinematics of VSP-type data from microseismic noise.
Direct measurement of the horizontal velocity
Our success in recovering the VSP in Figure 2a suggests the
possibility of repeating the same process for receivers placed
in a horizontal well. is sort of interferometric reconstruc-
tion was attempted with microseismic data acquired in the
Eagle Ford (Texas, USA) by an array of eight receivers lo-
cated in an approximately horizontal section of a deviated
borehole (Figure 3). A stack of crosscorrelations of 16 min-
utes of data retrieves an arrival displayed in Figure 4. is
is an acausal wave propagating along the well from its toe
toward its heel as indicated by the arrow in Figure 3. To ex-
cite this wave, noise sources should be in or around the Eagle
Ford Formation southeast from the receivers. e existence
of such sources seems plausible because our receivers moni-
tored hydraulic treatments of a well located southeast from
the receivers and recorded several hundreds of locatable mi-
croseismic events (not shown).
Approximating the moveout of the dominant phase in
Figure 4 with a straight line yields the average apparent veloc-
ity of 4.5 km/s. is approximately horizontal velocity is to be
compared with the sonic log in Figure 5 that exhibits the ver-
tical velocity of about 4.1 km/s in the depth interval covered
by the receivers. If we disregard the difference in frequencies
of microseismic and sonic data and attribute the difference
in the vertical and horizontal velocities to anisotropy under
the assumption that a vertically transversely isotropic (VTI)
model is appropriate for the Eagle Ford shales, our two ve-
locities result in a omsen (1986) anisotropy coefficient ¡ of
approximately 0.1. While¡is notoriously difficult to measure
from the P-wave surface reflection data, here we estimated it
from passively recorded microseismic at no additional data-
acquisition cost. Clearly, the recovered value of ¡ can be used
in a velocity model constructed to locate the microseismicity.
Shear-wave crosswell survey
Our third example comes from a dual-well microseismic
survey (Figure 6) conducted in the Bakken (North Dakota,
USA). When we crosscorrelate the vertical components of
receivers in well 1 with those in well 2 and stack the crosscor-
relations, we expect to retrieve the shear (SV) waves propa-
gating from one well to another. Turning receivers in well 2
into sources yields the stacks of crosscorrelations presented
in Figure 7. To create the causal arrivals observed in Figure
7, natural sources have to be located to the west from well 2
(Figure 6). is time, we lack a hypothesis explaining their
physical origin because hydraulically stimulated wells moni-
tored from wells 1 and 2 were located to the east from well
1 (not shown).
e absence of knowledge of the sources of natural noise
does not prevent us from picking the traveltimes of the main
phase on seismograms in Figure 7 (red dots) and on seismo-
grams of other receivers in well 2 that also were turned into
sources. ose time picks yield a traveltime crossplot pre-
sented in Figure 8a. is crossplot, exhibiting a sharp time
increase and, hence, a pronounced velocity reduction at a
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December 2012 The Leading Edge 1481
Passive seismic and microseismic—Part 2
Figure 6. Geometry of dual-well microseismic monitoring in the
Bakken. e locations of receivers in two nearly vertical wells are
marked with the triangles.
Figure 5. Sonic log in a vertical well indicating the P-wave velocity of
about 4.1 km/s in the depth interval covered by the receivers (triangles)
in Figure 3.
Figure 7. Stacks of crosscorrelations of the vertical components of
receivers at depths 3102, 3200, 3245, and 3281 m in well 2 with the
vertical components of receivers in well 1 ( T = 0.5 s, f =[10, 100]
Hz). e duration of the observation is 300 × 0.5 s = 150 s. e red
dots are the automatic time picks of the main retrieved phase.
depth of about 3200 m in well 1, could constitute an input
to the crosswell traveltime tomography. Instead of perform-
ing a full-scale tomographic inversion, we extract the zero-
offset times (that is, the times between receivers in wells 1 and
2 that have the same depths) marked with the white line in
Figure 8a and, knowing the distances between the receivers in
the two wells, convert the obtained times into the average ve-
locities. e resulting depth velocity profile is shown with the
thick blocky line in Figure 8b. Overall, it matches the shear-
wave sonic log (thin line), proving that interferometry has
extracted the shear-wave crosswell data from natural noise.
e greatest velocity discrepancy between the sonic and
the reconstructed velocity profile, observed for the upper and
lower Bakken shales (Figure 8b), relates to the resolution of
the retrieved crosswell data. As seismograms in Figure 7 indi-
cate, the spectra of the crosswell data peak at approximately
40 Hz, yielding the dominant shear wavelength of about
75 m. At such a wavelength, the Bakken shale layers, whose
thicknesses are 8 and 15 m (Figure 8b), cannot be resolved
individually and contribute only to a smooth velocity decline
exhibited by the recovered blocky profile.
Concluding remarks and remaining issues
Interferometric processing of three passive data sets dis-
cussed in the paper demonstrates that noise, which would be
usually discarded, contains information useful for velocity-
model building. is information comes in the ability to
retrieve various crosswell and VSP-type data. Importantly,
based on our experience, natural sources of noise appear to
possess wide spatial apertures, allowing the successful recon-
struction of waves that travel directly between the downhole
receivers. While we can only speculate on the physical rea-
sons for those wide apertures, multiple scattering in the het-
erogeneous subsurface is likely to be one of them.
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1482 The Leading Edge December 2012
Passive seismic and microseismic—Part 2
Figure 8. (a) Traveltime picks of the dominant phases, such as those
in Figure 7, and (b) shear-wave sonic log (thin line) along with the
reconstructed S-wave vertical velocity (thick blocky line). e white
line in (a) indicates traveltimes extracted to calculate the blocky
velocity profile in (b). e triangles in (a) mark the locations of
receivers in wells 1 and 2 (Figure 6).
Figure 9. Sign of data displayed in Figure 1.
Figure 10. Comparison of traces given by Equations 1 and 2.
e black traces, computed with Equation 1, are identical to those
displayed in Figure 2a. e red traces were computed with Equation 2
for the same input data.
We expect the number of applications of interferometry in
microseismic to grow once practitioners recognize its value and
begin using the method. For instance, in addition to the pre-
sented crosswell example, the P- and SH-wave crosswell data,
similar to the SV-waves displayed in Figure 7, could be recov-
ered from crosscorrelations of the horizontal components of
the original records, producing a full 3C crosswell data set that
can be processed using the available tomographic techniques.
Another area of potential applications opens up if receivers are
left in place, enabling one to collect and analyze time-lapse
data without the need for employing active seismic sources.
Although many different applications can be envisaged,
they all will have to deal with the challenging issue of nonran-
domness of natural sources that entails the apparent inability
to extract true amplitudes from interferometric reconstruc-
tions. However, if we embrace this limitation as reality and
aim at obtaining the correct kinematics, we get a surprisingly
robust methodology that depends on the wave amplitudes
only weakly. To illustrate this point, we follow the idea of
Larose et al. (2004), who suggested that removing the ampli-
tude information from input data by replacing the traces with
their signs (Figure 9) or Equation 1 with
(2)
is not harmful for the traveltimes. Figure 10 shows that this
is, indeed, the case and computations performed with Equa-
tions 1 and 2 can be deemed identical for practical purposes.
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December 2012 The Leading Edge 1483
Passive seismic and microseismic—Part 2
e results obtained so far leave us with a straightforward
agenda: understand what microseismic interferometry can
provide, try to recover it, and learn from the experience.
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Acknowledgments: We are grateful to our Marathon colleagues Don
Caldwell, Shihong Chi, Yulia Khadeeva, Michael Pelissier, Jeffrey
Rutledge, and Lev Vernik for encouragement and helping with
data-handling issues. We thank Marathon Oil Company for the
permission to publish the article and guest editor Julie Shemeta for
useful editorial suggestions.
Corresponding author: vgrechka@marathonoil.com
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