CWP-755

Imaging direct- as well as scattered-events in

microseismic data using inverse scattering theory

Jyoti Behura & Roel SniederCenter for Wave Phenomena, Colorado School of Mines, Golden, Colorado

ABSTRACT

Similar to surface reflection data, microseismic data also contain multiply-scattered events. They are especially prevalent in borehole microseismic databecause of low attenuation. These scattered events, if not imaged accurately, canlead to the spurious microseismic hypocenters. Here, we introduce an imagingalgorithm that accurately images not only the primary arrivals but also the mul-tiply scattered events. The algorithm uses the exact Green’s function computedusing an iterative scheme based on inverse-scattering theory. Extraction of theGreen’s function, however, requires surface reflection data and a backgroundvelocity model. Imaging of surface microseismic data involves computation ofthe Green’s function between the image point and the surface receivers andthe application of an imaging condition to the data. Borehole-microseismic-data imaging, however, requires two additional steps – first, computation of theGreen’s function between the borehole receivers and the surface and second,computation of the Green’s function between the image point and the bore-hole receivers using seismic interferometry. Tests on synthetic data show thatour imaging algorithm not only locates the microseismic hypocenters accuratelybut also substantially reduces the number of spurious events.

1 MULTIPLE ISSUES

As seismic waves propagate through the subsurface,they undergo scattering because of the presence of het-erogeneities (in velocity and density). In reflection seis-mology, events undergoing more than one episode ofscattering are commonly referred to as multiples. Sincemultiples can result in spurious reflectors on images, thecommon practice is to predict and suppress them priorto imaging. However, since multiples also contain infor-mation about the subsurface heterogeneities, there is anincreased effort towards using them in imaging insteadof just discarding them.

Data recorded by passive sensors and duringactive microseismic monitoring also contain singly-and multiply-scattered events in addition to the di-rect arrival. Such data are commonly used to lo-cate the sources of these hydraulic-fracturing inducedmicroseismic events and thus compute an estimateof the stimulated reservoir volume and the evolutionand geometry of induced fractures. Kirchhoff migra-tion (Gajewski et al., 2007) and reverse-time imag-ing (McMechan, 1982; McMechan et al., 1983) are theimaging algorithms commonly employed to locate themicroseismic sources. Under Kirchhoff migration, the

image at any location is computed by first computingthe direct-arrival traveltime from the image point to thereceivers and then stacking the recorded data along thistraveltime-curve. In reverse-time imaging, the recordeddata is reversed in time and then injected into a smoothestimate of the subsurface velocity. If the velocity modelis accurate, the direct arrivals will focus at the correctmicroseismic hypocenters.

In the above imaging algorithms, the scattered ar-rivals, however, will also focus at times and locationsthat do not correspond to the true initiation time of themicroseismicity and the true hypocenters, respectively.They will result in numerous false positives particularlyfor large reflection coefficients. Many of the unconven-tional reservoirs with underlying/overlying sand-shalesequences can aggravate this issue. Scattering can beproblematic for borehole monitoring, in particular, be-cause of the large magnitudes of the multiples. Unfor-tunately, such false positives will not only lead to anoverestimation of the stimulated reservoir volume butalso result in a poor correlation of microseismicity withproduction. An example of this is clearly evident in thework of Roundtree & Miskimins (2011) where a sand-stone is hydraulically fractured in a controlled exper-

88 J. Behura & R. Snieder

iment. The microseismic data, when imaged, resultedin numerous hypocenters outside the sandstone block(Jennifer Miskimins, personal communication).

1.1 Exact Green’s function necessary

One possibility to addressing the above scattering issuein microseismic data is to predict and suppress the scat-tered events on data prior to imaging. Unfortunately,this requires the complete knowledge of the velocity anddensity model; no data-driven approaches exist for pre-dicting multiples in microseismic data. A comparison ofreverse-time imaging with smoothed versus true velocitymodel is shown in Behura et al. (2013). The alternativeapproach is to use all the data and image the scatteredarrivals (along with the direct arrivals) such that theyfocus at the correct hypocenters. This approach neces-sitates either the detailed and accurate knowledge ofthe velocity (and density) model or the knowledge ofthe Green’s function. It is extremely challenging to ob-tain detailed information of the subsurface velocity anddensity. Well-logs can provide such detailed models butonly locally. Seismic-inversion-derived subsurface mod-els most commonly depict only the low-wavenumberbackground.

1.2 Inverse-scattering theory to the rescue

Wapenaar et al. (2011) propose a methodology for re-constructing the 3D Green’s function between any “vir-tual source” in the subsurface and any location on thesurface using only surface reflection data and a back-ground velocity model. Their proposal is the 3D ex-tension of the 1D iterative algorithm of Rose (2002b,a)who shows that in layered media, it is possible to fo-cus all the energy at a particular time (or depth if thevelocity is known) by using a complicated source signa-ture. Rose’s algorithm was also implemented on 1D seis-mic data by Broggini & Snieder (2012) who again showthat a ’virtual source’ response can be generated fromsurface reflection data alone. The background velocitymodel is used to compute the direct arrivals betweenthe “virtual source” and the surface which are subse-quently fed into an iterative algorithm to compute theGreen’s function. Details of the 1D algorithm are givenin Rose (2002b,a); Broggini & Snieder (2012); the 3Dalgorithm can be found in Wapenaar et al. (2011) withthe derivation given in Wapenaar et al. (2013).

Here, we propose to use the above iterative algo-rithm to reconstruct Green’s function between the sub-surface image points and the surface and use them inimaging the direct as well as the scattered events in mi-croseismic data. We also introduce a methodology to im-age borehole microseismic data by combining the com-puted Green’s functions with seismic interferometry.

d G

Figure 1. Schematic of the imaging algorithm applied tosurface microseismic data. d represents the microseismic data

recorded at the surface receivers (triangles) and G is theGreen’s function between any image point (denoted by thestar) and the surface receivers obtained from the iterativealgorithm.

2 SURFACE DATA IMAGING

The data recorded at a receiver xr due to a source atsome location x is given by

d(ω;xr,x) = Sx(ω)G(ω;xr,x), (1)

where ω is the frequency, d is the data, Sx is the sourcesignature at x, and G is the Green’s function. Note thatSx is not necessarily compact in time but can be com-plicated and of long duration. The source signature cantherefore be computed by the application of an imagingcondition to the data. A detailed description of the var-ious imaging conditions used in microseismic imaging isgiven in Behura et al. (2013). Here, we use the 2D space-time cross-correlation imaging condition (Behura et al.,2013):

Sx(ω) =∑

kr

d(ω, kr)G∗(ω, kr), (2)

where kr is the wavenumber over the receiver coordi-nates and ∗ represents complex-conjugation. Note thatSx obtained from equation 2 is a function of time whichis different from the zero-time imaging condition com-monly used in reverse-time imaging of microseismicdata.

2.1 Sigsbee test

We test our imaging algorithm on the Sigsbee model(Figures 2) as it generates strong internal multiples. Allthe boundaries in the velocity model are absorbing.

The microseismic survey comprises of 367 receiversspread on the surface at an equal spacing of 75 ft. Twomicroseismic sources (Figure 2a) are used for generatingthe data; the initiation times of the left- and the right-source are 0.096 s and 3.36 s, respectively. Also, the leftsource has a higher amplitude than the right source.

Microseismic imaging 89

(a)

X (kft)

Z (

kft)

0 5 10 15 20 250

5

10

kft/s

6

8

10

12

14

(b)

X (kft)

Z (

kft)

0 5 10 15 20 250

5

10

kft/s

6

8

10

12

14

Figure 2. (a) The Sigsbee velocity model used in generating the microseismic data and the reflection seismic data. The twopentagons represent the microseismic hypocenters and the triangles represent the receivers. There are a total of 367 receiversspread on the surface at an equal spacing of 75 ft. (b) The smooth model used in imaging.

A fixed-spread receiver geometry is used for acquir-ing the surface reflection data; this spread coincides withthe receiver geometry of the microseismic survey. Shotlocations for the surface reflection data also coincidewith the fixed-receiver spread. Thus, the surface reflec-tion data comprises of 357 shot gathers, with each shotgather containing 367 traces.

Figure 3a shows the image of the two microseismicsources obtained using the imaging methodology intro-duced here. Behura et al. (2013) argue that the imageof microseismic data should be displayed as a functionof space as well as time because the sources can be ex-tended in both space and time. The images in Figure 3correspond to specific depth slices of the z−x− t imagecube. Note that both microseismic sources have beenimaged at the correct time and also the right location;even the relative amplitudes of the two sources are pre-served. More importantly, there are no spurious events

in the image. The reverse-time image (Figure 3b), on theother hand, contains numerous events most of which arespurious. The left source is faintly visible, albeit its am-plitude is much smaller than the spurious events; theright source is barely discernible. Some of these spu-rious events can be eliminated by smoothing the saltbody; this will, however, lead to mis-positioning of themicroseismic hypocenters (in time and space). There-fore, in the presence of multiples, reverse-time imagingcan yield numerous false positives in identification ofmicroseismic sources. For such data containing multi-ples, the inverse-scattering imaging method introducedhere should be the algorithm of choice.

3 BOREHOLE DATA IMAGING

Like surface microseismic data, borehole data can alsobe imaged using the Green’s function Gib between the

90 J. Behura & R. Snieder

(a)

X (kft)

t (s)

10 12 14 16 18 20 22 240

2

4

6

8

10

(b)

X (kft)

t (s)

10 12 14 16 18 20 22 240

2

4

6

8

10

Figure 3. Images of the microseismic sources shown in Figure 2a obtained using the inverse-scattering-theory (a) and reverse-

time imaging (b). The images correspond to a depth of 5700 ft. Two iterations were used in computing G using the iterativealgorithm.

Microseismic imaging 91

d

Gis

Gib

Gbs

Figure 4. Schematic of the borehole microseismic data imag-ing algorithm based on Green’s function retrieval using the

iterative scheme. The triangles represent borehole receivers

and the star is the microseismic hypocenter. d is the bore-hole microseismic data, Gis represents the Green’s function

between the image point and the surface, Gbs represents theGreen’s function between the borehole receivers and the sur-

face, and Gib is the Green’s function between the image pointand the borehole receivers. Gis and Gbs are computed from

the surface reflection data using the iterative scheme, while

Gib is retrieved from Gis and Gbs using seismic interferom-etry.

image point and the borehole receivers. Gib, however,cannot be directly computed using the iterative algo-rithm of Rose (2002b,a) because the borehole receiversare in the interior of the medium and because of theabsence of reflection data with both shots and receiversin the borehole.. To compute Gib, we use the followingalgorithm:

(i) compute Gbs, the Green’s function between theborehole receivers and the surface receivers using theiterative algorithm

(ii) similarly, compute Gis, the Green’s function be-tween the image point and the surface receivers usingthe iterative algorithm

(iii) obtain Gib from Gis and Gbs using seismic in-terferometry (Wapenaar & Fokkema, 2006) based ei-ther on cross-correlation, deconvolution, or multi-dimensional deconvolution (Wapenaar et al., 2008).

Thereafter, we obtain the microseismic image by appli-cation of the following imaging condition to the data:

Sx(ω) =∑

kr

dbh(ω, kr)G∗

ib(ω, kr), (3)

where dbh is the borehole microseismic data and Sx isthe source signature at x.

3.1 Layer-cake test

We test the above borehole-microseismic-data imagingalgorithm on a layer-cake velocity model (Figure 5a).

The velocity model is constructed by extrapolatinglaterally a well-log velocity profile from Pennsylvania(Trenton Black River Project – Appalachian Basin).

Similar to the Sigsbee example above, all theboundaries are absorbing. The microseismic data is gen-erated for a single source location shown in Figure 5aand recorded at the 22 borehole receivers (Figure 5a).The initiation time of the source is 0.2 s. The surface re-flection data is acquired on a fixed-receiver spread with461 receivers equally spaced at 25 m intervals. The shotpoints coincide with the receiver spread.

In order to perform imaging using our methodol-ogy, we compute Gis, Gbs, and Gib as described above.Two iterations were used in computing Gis and Gbs us-ing the iterative scheme. Thereafter, we apply imagingcondition 3 on the borehole microseismic data. The re-covered image for the true source depth level is shownin Figure 6a. Note that the focusing is better than thatfor reverse-time imaging (Figure 6b). In addition, thespurious events have been largely eliminated.

4 ROLE OF BACKGROUND VELOCITY

The background velocity model is used to com-pute the direct arrivals which are thereafter in-put into the iterative algorithm to calculate theGreen’s function Wapenaar et al. (2011). As suggestedin (Wapenaar et al., 2011), microseismic events visibleon the data can also be substituted for direct arrivals.However, since we neither know the hypocenters of suchevents and nor are there microseismic sources every-where, it is impractical to use visible events for directarrivals.

A viable solution would be to use arrivals from per-foration shots as direct arrivals because we already knowthe perforation locations. If the medium is laterally ho-mogeneous (commonly true for unconventional reser-voirs), one could use a well-log-derived velocity profile tocompute direct arrivals for other image points from theperforation-shot events using upward/downward wave-field continuation. Such an approach would alleviate theneed for a background velocity model.

As mentioned above, Green’s function retrievalusing the iterative algorithm of Rose (2002b,a);Wapenaar et al. (2011); Broggini & Snieder (2012) usessurface reflection data. Since the density information isalready contained in the reflection data, the events cor-responding to the scattered waves in the reconstructedGreen’s functions will have accurate amplitudes. Thisgreater accuracy should further help in reducing falsepositives in microseismic imaging and also yield moreaccurate source signatures.

92 J. Behura & R. Snieder

(a)

X (km)

Z (

km)

0 2 4 6 8 10 12

0

1

2

km/s

3

4

5

6

7

(b)

X (km)

Z (

km)

0 2 4 6 8 10 12

0

1

2

km/s

3

4

5

6

7

Figure 5. (a) The layer-cake velocity model used in generating borehole microseismic data and the surface reflection data. Thepentagon represents the hypocenter of the microseismic source and the triangles represent the borehole receivers. The boreholereceivers are emplaced as two separate arrays – one horizontal and the other vertical. Each array comprises of 11 receivers that

are evenly spaced at 20 m intervals. (b) The smooth velocity model used in imaging.

5 DISCUSSION

Microseismic imaging using conventional imaging algo-rithms uses only the recorded data and a backgroundvelocity model. The imaging technique described here,however, needs surface reflection data in addition.Nonetheless, it is becoming common practice to ac-quire both surface reflection data and microseismic datafor detailed characterization of unconventional plays.Moreover, the iterative algorithm requires an accurateknowledge of the source signature in the surface reflec-tion data. The source function is known in many cases(e.g. vibroseis acquisition) or can be recorded in oth-ers (e.g. air-gun source). Where, the source signature isunknown, deterministic methods such as Virtual RealSource (Behura, 2007) should be used to compute it.

The iterative algorithm of Rose (2002b,a);Wapenaar et al. (2011); Broggini & Snieder (2012)can successfully recover the Green’s function whenall the scattering is in the interior of the medium. Inthe presence of a free-surface, however, the algorithmfails to compute the exact Green’s function. Using

a modified algorithm, Singh et al. (2013) show thatthe exact Green’s function can be extracted even inthe presence of free-surface reflections. This modifiedalgorithm might be used for imaging microseismic datacontaining free-surface multiples.

The imaging algorithm introduced here is substan-tially more computationally intensive than conventionalalgorithms such as reverse-time imaging and Kirchhoffimaging. Computation of the direct arrivals is the pri-mary driver of the cost. There are two strategies forcomputing the direct arrivals between the image pointsand the surface receivers. First – the direct arrivals foreach image point can be computed on the fly while thecode is being executed. The number of forward com-putations will equal the number of image points. Thiswill require significant processor power but have min-imal disk input-output costs. Second – since there arefar fewer receivers than image points, one could computethe direct arrivals for all image points from each receiverlocation independently and then store them to the disk.Thus the number of forward computations will equal

Microseismic imaging 93

(a)

X (km)

t (s)

5 5.5 6 6.50

0.2

0.4

0.6

0.8

1

(b)

X (km)

t (s)

5 5.5 6 6.50

0.2

0.4

0.6

0.8

1

Figure 6. Images of the microseismic source shown in Figure 5a obtained using the inverse-scattering-theory based algorithm

(a) and reverse-time imaging (b). The images correspond to the true depth of the microseismic hypocenter (1800 m). The eventat t =0.3 s and x =6 km in (a) corresponds to the location of the vertical receiver array. The same event manifests as a linearmoveout in (b).

94 J. Behura & R. Snieder

the number of receivers. Because of reciprocity, one canthen read the direct arrivals from the disk for each im-age point; this, however, involves substantial disk input-output operations. Based on the number of receiversversus the number of image points, one can choose ei-ther of the above two strategies.

The iterative algorithm of Rose (2002b,a);Wapenaar et al. (2011); Broggini & Snieder (2012) isapplicable to only acoustic wave propagation. In thepresence of strong shear waves in microseismic data (es-pecially in borehole recordings), all imaging algorithmswill fail to properly characterize the microseismicity.Therefore, shear waves should be suppressed in the databefore imaging. Shear-wave suppression is more criticalfor borehole data and less so for surface acquisitionbecause of the strong near-surface attenuation.

6 CONCLUSIONS

Imaging of microseismic data in the presence of multi-ples will result in numerous false positives i.e. identi-fication of spurious microseismic hypocenters. In orderto image such data accurately, we have developed analgorithm that uses exact Green’s function derived us-ing an iterative scheme based on inverse-scattering the-ory. Both surface- and borehole-microseismic data canbe imaged using our approach. Tests on synthetic datashow that our approach can reduce false positives sig-nificantly as well as improve the focusing of the micro-seismic hypocenters.

ACKNOWLEDGMENTS

We thank Farnoush Forghani and Satyan Singh formany discussions. Support for this work was providedby the Consortium Project on Seismic Inverse Methodsfor Complex Structures at Center for Wave Phenomena.

References

Behura, J. 2007. Virtual Real Source. SEG Technical

Program Expanded Abstracts, 2693–2697.Behura, J., Forghani, F., & Bazargani, F. 2013. Im-proving microseismic imaging: role of acquisition, ve-locity model, and imaging condition. CWP Project

Review, 754, 77–86.Broggini, F., & Snieder, R. 2012. Connection of scat-tering principles: a visual and mathematical tour. Eu-ropean Journal of Physics, 33(3), 593.

Gajewski, D., Anikiev, D., Kashtan, B., Tessmer, E.,& Vanelle, C. 2007. Localization of seismic eventsby diffraction stacking. SEG Technical Program Ex-

panded Abstracts, 1287–1291.

McMechan, G. A. 1982. Determination of sourceparameters by wavefield extrapolation. Geophysical

Journal of the Royal Astronomical Society, 71, 613–628.

McMechan, G. A., Luetgert, J. H., & Mooney, W. D.1983. Imaging of earthquake sources in Long ValleyCaldera, California. Bulletin of the Seismological So-

ciety of America, 75, 1005–1020.Rose, J. H. 2002a. Time reversal, focusing and ex-

act inverse scattering. 1 edn. Springer-Verlag, Berlin.Pages 97–105.

Rose, J. H. 2002b. Single-sided autofocusing of soundin layered materials. Inverse Problems, 18, 19231934.

Roundtree, R., & Miskimins, J. 2011. ExperimentalValidation of Microseismic Emissions from a Con-trolled Hydraulic Fracture in a Synthetic LayeredMedium, SPE 140653. In: SPE Journal.

Singh, S., Snieder, R., & Behura, J. 2013. Reconstruc-tion of the exact Green’s function in the presence of

a free surface.Wapenaar, K., & Fokkema, J. 2006. Green’s func-tion representations for seismic interferometry. Geo-

physics, 71(4), SI33–SI46.Wapenaar, K., van der Neut, J., & Ruigrok, E. 2008.Passive seismic interferometry by multidimensionaldeconvolution. Geophysics, 73(6), A51–A56.

Wapenaar, K., Broggini, F., & Snieder, R. 2011. Aproposal for model–independent 3D wave field recon-struction from reflection data. SEG Technical Pro-

gram Expanded Abstracts, 30(1), 3788–3792.Wapenaar, K., Broggini, F., Slob, E., & Snieder, R.2013. Three-Dimensional Single-Sided MarchenkoInverse Scattering, Data-Driven Focusing, Green’sFunction Retrieval, and their Mutual Relations. Phys.Rev. Lett., 110(Feb), 084301.