Array Processing in Microseismic Monitoring - IEEE Xplore

Subsurface Exploration: Recent Advances in Geo-signal Processing, Interpretation, and Learning

James. H. McClellan, Leo Eisner, Entao Liu, Naveed Iqbal, Abdullatif A. Al-Shuhail, and Sanlinn I. Kaka

Array Processing in Microseismic Monitoring Detection, enhancement, and localization of induced seismicity

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urrent development of unconventional resources (such as shale gas, shale oil, and tight sands) requires hydraulic fracturing, which involves injecting fluid at high pressure into the subsurface reservoir. Such injections (or fluid production) cause stress changes in the reservoir. These stress changes often result in failure of the rocks with a concurrent release of seismic energy as seismic waves. The nature of seismic wave propagation in the subsurface media is complex. Based on the direction of propagation and the particle motion, body waves can be classified into P-waves (primary, compressional wave) and S-waves (secondary, shear wave). Passive seismic monitoring is based on recording these emitted waves and then using signal processing to extract characteristics such as amplitude, polarity, and arrival time, from which it is then feasible to estimate the location and character of the failure events.

Introduction

©istockphoto.com/Khadi Ganiev

Digital Object Identifier 10.1109/MSP.2017.2776798 Date of publication: 7 March 2018

1053-5888/18©2018IEEE

Signal processing of data from receiver arrays plays a key role in the two microseismic monitoring techniques in use today: downhole and surface monitoring, which are discussed in [26] and [11], respectively. Figure 1 shows a scenario with three active injection wells and the relative placement of downhole and surface arrays. The two types of monitoring arrays use vastly different numbers of receivers. Downhole monitoring arrays typically employ between six and 12 three-component (3C) receivers deployed in a vertical borehole, spanning a total aperture of 100–300 m; probably 90% of the current downhole monitoring acquisitions use only a single vertical monitoring well. Most downhole monitoring is carried out in existing wells if they are available; new, dedicated monitoring wells might be drilled in exceptional circumstances, but the additional cost might be five to ten times higher than the monitoring job itself. The downhole monitoring array(s) are situated close to the injection wells and at a similar depth to the reservoir, where microseismic events are expected to occur. As a result, the recorded waveforms have relatively high signal-to-noise ratio (SNR), and it is possible to pick the arrival times of the direct elastic (P or S) waves and determine polarization from 3C measurements.

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ceivers in each line. The star-like arrays radiating from the central injection site are designed for attenuating the surface waves radiated from the central pad where hydraulic fracturing creates a lot of seismic noise in the form of surface waves. Another 2-D array configuration Surface Sensor that has become popular is the so-called Array patch deployment, where subsets of receivers are deployed in small patches, e.g., 10 # 10, of densely spaced receivers with ten to 20 patches randomly distribut0 ed to form a large 2-D aperture [32]. The random patches provide more flexibility 500 to accommodate some real-world restrictions such as land permission and special 1,000 terrain. Because the intrapatch sensors are spatially quite dense, multichannel 1,500 noise-attenuation algorithms, such as f-k filtering, tau-p beam steering, f-x decon2,000 4,500 volution, median filtering, or trimmed mean filtering can be applied, to name 2,500 3,000 a few [33]. Thus, these small patches Monitoring Region are able to attenuate surface noise from 1,500 0 1,000 random directions, as well as from the 2,000 Northing (m) 3,000 4,000 central injection site. An equally suc5,000 Easting (m) cessful alternative to surface arrays are so-called buried arrays of geophones where receivers are deployed in shallow boreholes (50–200 m deep). Such deployment reduces surface noise by Downhole Sensor an order of magnitude while attenuatArray ing the signal usually only by a factor P S of two or three (lack of free surface boundary condition and impedance). Figure 1. An illustration of a surface array (star-like shape) and single downhole array for microseisThis means that each receiver in a shalmic monitoring of a reservoir in a layered velocity model. Red and white “beach ball” diagrams in the low borehole can effectively replace apvicinity of the horizontal sections of the wells illustrate possible positions of microseismic events. The proximately ten surface geophones. diagrams represent source mechanisms as explained in Figure 3. The receivers are illustrated using The event detected by a downhole green and red squares in the enlarged plots. Two sample traces are also given; waveforms received by surface receivers have more noise (lower SNR), while downhole waveforms show distinct arrivals of monitoring array is an observable P- and S-wave phases. P- or S-wave signal (or both) recorded on several receivers across the array, where the signal is significantly higher than noise. Such arrays Surface monitoring arrays might have as many as several use P- and S-wave arrival times to locate a microseismic event. thousand receivers (usually only vertical component) deployed For example, with known velocities v p and v s, the arrival on Earth’s surface or tens to hundreds of vertical component geophones deployed in shallow boreholes. The signals actime difference between the two waves yields an estimate of quired on surface arrays have much lower SNR at the indiradial distance to the event hypocenter. Triangulation of locavidual receivers due to two factors: 1) weaker received signals tion for either P- or S-waves, or a combination of both, leads because the source is farther away (geometrical spreading and to estimated depth and distance from the array, but the small absorption) and 2) higher noise because the surface receivers array aperture means that the depth accuracy degrades with are susceptible to various noise sources such as human actividistance; see [15]. A more significant issue is that a single verties and weather. Therefore, the stacking of many signals (by tical monitoring array cannot sense the azimuthal direction of coherent summation) is needed when trying to detect microthe event. Specifically, it is not possible to determine back aziseismic events. The surface receivers might be deployed on a muth from arrival times alone. As a result of this geometrical regular two-dimensional (2-D) grid or, more likely, in a star limitation, the azimuth of the arriving wavefronts must be meapattern as six to 12 lines with approximately hundreds of resured to determine microseismic event locations. The event back 100


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origin time of the event is unknown, and, azimuth may be determined directly from the Signal processing of therefore, one must carry out migrationP-wave because the particle polarization is data from receiver arrays based imaging in time, as well as space, parallel to the raypath direction for P-waves plays a key role in the two i.e., four-dimensional (4-D) imaging. A in an isotropic medium. The accuracy of this microseismic monitoring historical overview of the development of measurement as well as determination of techniques in use today: this method is given in [11] and originated back azimuth from higher SNR S-waves is from studies of natural seismicity. In some discussed in [14]. Monitoring from multiple downhole and surface cases, the migration-based approach is boreholes is becoming more common, but it monitoring. viable for downhole monitoring, e.g., [18], rarely solves the issue—only a small fraction while picking and triangulation can be used of the events can be observed on two or more (for stronger microseismic events) in the surface monitorwells. In fact, the most challenging limitation is the availability ing scenario. of additional downhole monitoring wells, since drilling a dediThe most significant challenge in surface microseismic cated monitoring well is expensive and wells previously used for monitoring is the difficulty of directly observing P- and S-wave production or exploration may not be suitable. Figure 2 illustrates signals. Surface monitoring relies on thresholding the stacked an example of a microseismic processing result from a downhole traces to detect microseismic events. Adapting the threshold monitoring array. The microseismic events are mapped as points value to SNR according to binary hypothesis testing allows us representing the source locations and mapping the injected to balance false positives versus missed detections. Assumpfluid penetration into the rock formation. tions about the correct noise model for surface monitoring cast The example is a microseismic data set acquired during some doubt on this approach, which requires an estimate of hydraulic fracturing of the Lower Silurian and Ordovician Forthe noise. In reality, some sedimentary basins are favorable mations in the Baltic Basin margin, Lubocino, North Poland for surface monitoring, as they do not severely attenuate and [35]. Two wells were drilled at this site: one vertical and one their near-surface conditions enlarge signal due to the impedhorizontal. The horizontal section of the stimulated well was ance contrast and free surface boundary condition [9]. Meandivided into multiple sections called stages, and each was while, some basins severely attenuate the signal resulting in hydraulically stimulated separately. The microseismic events unreliable detections [35]. show that stages remained mostly separated and did not interfere with one another. To increase the SNR by constructive superposition, stackFailure mode, source-mechanisms, and magnitudes ing the traces from a large number of receivers is a well-known Most signal processing for microseismicity is targeted mainmethod in active seismic, where it is used for migration-based ly at obtaining locations for the stress-induced events along imaging of subsurface structures. In active seismic, the source with a geometrical interpretation of these “dots in the box.” of a seismic signal generated by explosions, mechanical vibraHowever, the amplitude and polarity of the recorded waves tors, or airguns (for marine seismic) is controlled during the contain additional information about the source mechanisms data collection. However, in passive seismic monitoring, the of the events. These source mechanisms can represent

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Figure 2. (a) A map view and (b) an oblique view of microseismic events located in the calibrated anisotropic velocity model. Events are colored according to stages. The true perforation intervals are shown as corresponding diamonds (Figure used with permission from [35]).


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Figure 3. An illustration of the P-wave radiation pattern from a shear source. The (a) gray image shows a vertical fault with a horizontal motion of two blocks (San Andreas type, strike-slip). The white and red beach ball on top shows a corresponding representation of this source mechanism. The red color in the beach ball represents P-wave motion away from the source while white represents parts of the unit sphere where the P-wave motion is toward the source. This is also shown in the (b) 3-D plot where red denotes positive outward amplitudes of P-waves and blue negative inward amplitudes.

volumetric or shear-only changes. Volumetric changes, a mode I failure, can be expected as the injected fluids are incompressible and the hydraulic fracture is a volume-changing process, unlike most of the natural earthquake activity observed worldwide. Additionally, hydraulic fracturing in the

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Figure 4. Sample traces of microseismic data received on two spokes of the star-pattern sensor array. The sign change can be observed in the onfigure magnifiers, where the wave fronts were denoted by a black curve. The SNR of the P-wave arrival is lower, near the apex of the moveout due to the radiation pattern of the source.

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oil and gas industry often uses solid particles suspended in the fracturing fluid especially designed to be incompressible and keep the fracture open. As a result, a new volume is created by hydraulic fracturing, and the associated seismicity possibly may be the result of this volume change. The other type of source mechanisms, shear-only events, are similar to natural earthquakes and represent a mode II failure. They result from increased pore pressure along natural fractures as the ratio of shear-to-normal stress on these fracture changes due to fluid injection. For example, in a homogeneous isotropic medium, a shear failure creates both a P- and S-wave at the origin time of the seismic event. The radiated P-waves are polarized parallel to the source-receiver direction, while the shear waves are polarized perpendicular to the P-waves. Note that the P- and S-wave polarization differs in four quadrants (sign changes) as illustrated by the beach ball patterns in Figure 3(a). Then, in Figure 4, we show sample microseismic data received on two spokes of the star pattern sensor array, where, in the on-figure magnifiers, we can see the different signs of the wiggles due to the source mechanism. For a shear source, the ratio of the S-wave peak (maximum) amplitude to the P-wave peak amplitude is (v p /v s) 3 . In sedimentary rock formations the P-wave to S-wave velocity ratio (v p /v s) is usually close to two, resulting in significantly stronger S-waves. Thus, downhole monitoring arrays usually record much stronger S-waves. Analogous characterization of P-wave


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stacked in the patches as an input for semblance computation, and S-wave amplitudes of seismic waves can be made for tenbut this is difficult to achieve with a star-like array. sile sources (e.g., [7]). Note that information about relative A matched filter is perhaps the most common signal proamplitudes and polarities needs to be obtained from diverse cessing tool for effective signal detection because it maximizes spatial angles [38] to invert the source mechanism, adding the output SNR in the presence of additive noise. The discretecomplexity to the signal processing as will be discussed in the time impulse response of the matched filter is a time-reversed section “Source Mechanism-Based Detection, Localization, version of a known template signal, or wavelet, and the operaand Moment Tensor Estimation.” tion of matched filtering is equivalent to cross correlation. By A reservoir stimulation, such as hydraulic fracturing, is accorrelating the template with a received trace, the value of the companied with induced seismicity resulting from a reactivation correlation peak can be used as a likelihood of an already existing fracture or creation of indicator for the presence of the template in new fractures. Locations of microseismic The most significant the trace, and the peak location gives the events are used to map the geometry: the challenge in surface time offset in the trace. direction of fracture propagation, fracture In seismology, matched filtering analysis microseismic monitoring length, and height. The observed seismic(MFA) was originally applied in studies of ity contains additional information—the is the difficulty of directly repeating earthquakes, which exhibit high source mechanisms. The injection of the observing P- and S-wave resemblance in waveforms, focal mechafluid and creation of fractures that can store signals. nism, and location. In microseismic monitorlarge volumes of incompressible proppant ing, events induced by hydraulic fracturing particles suggest that seismicity induced by have similar features as repeating earthquakes, so MFA, which hydraulic fracturing may have a volumetric component. Thereuses a strong signal template to detect similar weaker events, is fore, it is important to determine if the induced seismic events a prevalent approach [12]. are shear or tensile. Another important parameter characterWhen the MFA requirement of having a template is not met izing microseismic events is size, which is usually measured due to high noise on a surface array or low magnitude of the by a magnitude or, better, by a seismic moment, representing a microseismicity, cross correlation is still a very useful operation total energy released by the microseismic event [8]. The corfor detecting and locating similar events across the channels of rect source mechanisms allow us to accurately interpret the dean array. Mathematically, MFA and cross correlation are nearly termined seismic moments, i.e., for shear events, moments are the same. However, in MFA, a known template waveform is proportional to sizes of fractured planes (assuming a constant correlated against a continuous data stream to detect occurstress drop), while for volumetric events, moments represent the rences of that waveform, whereas cross correlation is usually amount of volumetric change. Thus, a complete source mechaapplied to measure similarities across different channels. nism characterization is crucial for correct interpretation of the One can pick a signal segment in a channel and regard it interaction between microseismicity and hydraulic fracturing as the reference template to detect correlated signals on other and interpretation of microseismicity. channels using cross correlation. If the presence of a reference template is detected on many other channels, we could Microseismic signal detection and regard it as a good candidate of detected events. However, in enhancement in a sensor array practice, the pairwise cross correlation of many low SNR sigTwo important steps in microseismic monitoring are detecnals gives only low SNR cross correlation functions (CCFs). tion and characterization of microseismic events in data sets Among a variety of techniques developed for this issue, stacking that might contain a large number of weak events. Automated the CCF in phase over all of the channels and, if necessary, over detection, and enhancement is challenging for events with different components of a 3C sensor is a simple and effective complex waveforms, small magnitudes, and low SNR. In addisolution. In general, tion, the number of induced microseismic events exponentially increases with lower SNR. This property is summarized in the 3 N empirically observed Gutenberg–Richter law resulting from s [x] = 1 / / c i, j [x - t i], (1) 3N j = 1 i = 1 the fractal nature of fracture distribution [21]. Although recent studies indicate this law, commonly observed in natural earthquakes, does not strictly extend to induced seismicity because of the limited volume [13], [37], it is still observed that, for any event of a magnitude M w, there is at least a tenfold increase of events with magnitudes M w - 1. Therefore, any method that enables us to detect weaker events will significantly increase the number of detected events, which can then be used for characterizing fractures resulting from injected fluids. The geometry of a large sensor array can be optimized to enhance the low SNR signals from weaker events. For example, a monitoring array consisting of 2-D subarray patches can use signals

where c i, j [x] = (h r, j * x i, j) [x], and h r, j and x i, j are the template and received signal for the ith channel, reference channel r, and jth component. In addition, t i is the travel time from the reference event location to the ith receiver, which can be determined by the moveout of the parent event (i.e., a strong reference event). Equivalently, the stacking in (1) is along the moveout of the reference events [12]. If the location of the microseismic events significantly deviates from the parent event, it is not satisfactory to shift the CCFs according to the moveout of the parent events. In addition, the moveout of the parent event is usually determined


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Figure 5. (a) Fifteen of 182 original traces, (b) noisy traces, SNR = –2.53 dB, and (c) denoising results. P- and S-wave arrivals are indicated using red and blue arrows, respectively. (Figure used with permission from [25].)

by a human picking the arrival times, which works only for strong events that can be seen clearly in the seismograms. Another option of the shifting t i is to detect the relative time delay Dt ir = t i - t r using cross correlation between the ith channel and the reference channel r. Also note that the cross correlation techniques are subject to the condition that the master and detected events have not only a similar location but also the same mechanisms, i.e., radiation. If the mechanism changes, cross correlation may actually lead to a false location due to the phase shift between the sampling of the radiation pattern. The purpose of stacking along the presumed moveout is to enhance the SNR of the CCFs or raw traces. If the signal is buried in noise, the lag values corresponding to the highest CCF peaks, i.e., the detected relative delays, may be far from the true delays and result in poor stacking performance. One way to avoid the shifting inherent with CCFs is to use the autocorrelation function (ACF), which always reaches its maximum at zero lag and is not affected by the radiation pattern (sign changes in quadrants) due to the source mechanism. To this end, [25] introduced a denoising and detection scheme based on stacked autocorrelations: 1) Compute the autocorrelation, ri [x], of each trace, and then stack the ACFs for all channels, rs [x] = (1/N) Rri [x] . 2) Replace the zero-lag value of the stacked ACF with the average of its neighboring values, 104

(rs [- 1] + rs [1]) if x = 0 .(2) rs [x] otherwise

The justification for this change is that additive white noise has an ACF that is Lv 2 d [x], which is nonzero only at x = 0. Since the ACF rs [x] has a large peak at x = 0, which needs to be reduced by Lv 2, the average of the neighboring values provides a reasonable estimate of the correct zero-lag value of the signal-only ACF. 3) Define the denoising filter’s impulse response as a windowed version of the modified ACF, f [x] = rts [x] w d [x], where w d [x] is a triangular window. 4) Convolve f [x] with each noisy trace in the collection. The result of these convolutions provides the N denoised traces xt i [l] = (f ) x i) [l] for i = 1, 2, f, N. This approach effectively designs a filter f [x] that enhances the signal energy and suppresses uncorrelated noise. When the noise is not white, a prewhitening filter is needed, which would be designed from the noise ACF estimated in noise-only intervals of the traces. The ACF denoising example in Figure 5 shows traces generated with moveout time delays from a single seismic trace; the denoising result attenuates the additive white Gaussian noise with some degradation of the P-wave arrival. Another denoising technique exploits the fact that microseismic recordings tend to have narrow bandwidth and thus can be localized in a time–frequency (TF) representation. The microseismic event is denoised by obtaining a low-rank approximation of the TF matrix, which is accomplished in [24] by using the singular-value decomposition (SVD) of the TF matrix. An easily synthesizable and high-resolution TF transform, known as the synchrosqueezing transform (SST), is selected for this purpose. Other transforms with less computational complexity can be used with some compromise in the performance, e.g., the short-time Fourier transform. The advantage of this approach over cross correlation is that it does not involve convolution, ensuring that the noise from the noisy records does not mix with the filtered data. Moreover, SVD filtering does not require an explicit threshold, and the denoising is carried out adaptively via the rank of the signal subspace. The following steps are involved in denoising multichannel microseismic data, y i (t) . 1) Obtain the TF matrix for each trace, Yi, i = 1, f, N. 2) Carry out the SVD of each TF matrix as R si Yi = U i R i V iH = U i =

G V iH, i = 1, f, N, (3) R in

where R si and R ni are the singular values corresponding to the signal and noise subspaces, respectively. 3) Cross correlate each distinct pair of traces, align the CCFs, and stack; then transform to a TF matrix Yc . 4) Perform the SVD of the TF representation of the stacked cross correlation, which gives Rc Yc = U c R c V cH = U c =

G V H . (4) 0 c

5) Replace the singular values in (3) by enhanced singular values from (4) as


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6) Obtain the noise-suppressed traces yli (t) by time-domain reconstruction from the TF matrices, Yil . 7) Repeat the above steps to remove noise iteratively. A second way of enhancing microseismic events using rank reduction is tensor decomposition, or higher-order SVD, which takes into account all of the traces at once during the decomposition. A three-dimensional (3-D) tensor decomposition method presented for denoising in [23] exploits correlation among the traces. Mathematically, the noisy seismic data in the TF domain across all sensors can be represented as a 3-D tensor

Y = X + N, (6)

where X and N correspond to a low-rank signal and the noise component, respectively. The frontal slices of the tensor Y are the TF representations of the traces; see Figure 6. A conventional way to denoise the traces is to solve the following optimization problem:

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efficient in terms of precision and accuracy, as shown in [1]. The picking methods can be applied on individual components of a 3C receiver or, alternatively, on some combination of these components, which has the advantage of less computational cost and enhanced SNR (obtained by weighted summation). The components of a 3C data set can be combined by taking the absolute value of the product of the individual components or by stacking the absolute value of individual components [1]. The array-based cross correlation method presented in [22] uses an iterative method for refining initial arrival-time picks for microseismic data. For an input record with N raw traces, x i (t), i = 1, f, N, the proposed method can be summarized in the following steps. 1) Pick a first break of any trace as a reference first break, t r . The TF representation can be used to pick this reference-first break, manually if necessary. 2) Cross correlate all of the traces with each other (pairwise). 3) Pick relative time delays between the reference trace and all other traces using the maximum values of the unstacked and

# d, (7)

where · * and · F represent the nuclear norm and Frobenius norm, respectively, for a tensor. The nuclear norm for 3-D tensor N is defined as Y * = / i = 1 YS i *, specifically the sum of the nuclear norm of the frontal slices, which is the sum of all nonzero rank(Y) singular values Y * = / j = 1 v j . The following steps outline a low-rank approximation using tensor SVD. 1) Transform the tensor Y to the frequency domain along the t = fft (Y, [], 3) . third dimension, i.e., Y t ::i = 2) Perform the SVD on the frontal slices, i.e., Y t :: i V t :: i R t ::Hi, i = 1, f, N. U 3) Apply soft thresholding on the singular values vj as t l. s j = (v j - x) +, where (·) + = max {0, (·)}, which yields R 4) Convert each component tensor back to the time domain, i.e., t , [], 3), V = ifft (V t l , [], 3) . t , [], 3), Rl = ifft (R U = ifft (U 5) Reconstruct the denoised tensor as X l = U # t Rl # t V H, where # t denotes the tensor product, and then obtain the denoised traces by transforming the TF representations back to the time-series. A denoising result using this technique is shown in Figure 7.

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Time picking in sensor arrays To locate or additionally process a microseismic event often requires phase picking of P- or S-wave arrivals. The estimated hypocenter locations are highly influenced by erroneous decisions on arrival times or their misidentifications, which ultimately results in the wrong interpretation of results. Automated picking methods can be classified into singletrace methods, which include energy ratio methods and Akaike information criteria (see [1] for more details), and multitrace/ array-based methods, which include cross correlation approaches, e.g., [23]. The multitrace cross correlation methods are more

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Figure 7. (a) The original traces from the Incorporated Research Institutions for Seismology data center, (b) noisy traces, SNR = - 3 dB, and (c) denoising results. (Figure used with permission from [23].)


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unaligned CCFs. From the relative time delays, updated first breaks are calculated. 4) Align each CCF, and sum the aligned CCFs to produce a stacked CCF. 5) Modify the unstacked and unaligned CCFs by cross correlating with the stacked CCF. 6) Terminate when the sum of squares error is acceptable; otherwise, go to step 3. The aforementioned steps are carried out for S-arrivals and then for P-arrivals (after muting the S-arrivals). An example is shown in Figure 8. A different strategy for time picking is to admit that some fraction of the picks will be false and then use a classifier to find the true picks for the event. Such a classifier needs to learn the pattern of a seismic event from all arrival-time picks and apply a rule to cluster the picks into two groups: true event and false picks. The noisy picks are discarded, so the classifier performs a type of denoising, although, strictly speaking, this is not denoising of the signal. Since the true first-arrival times of any isolated seismic event result in a predictable moveout curve on a monitoring receiver array, a parametric model for valid moveouts can be used to build a classifier for true picks of an actual seismic event. In seismology, it is well known that, for homogeneous media, the moveout curve across a linear array is a hyperbola. To utilize this prior knowledge, a random sample consensus (RANSAC)based [17], [30] arrival-time event clustering method has been developed to classify the events and nonevents in the picks. In a RANSAC-based method, two steps, i.e., hypothesize and test, are implemented iteratively as follows: ■■ Hypothesize: A minimal sample subset (MinSet, denoted as X kM) is randomly selected from the data set, and the unique model parameters (i k) are computed for this chosen MinSet for kth iteration.

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Figure 8. (a) Noisy traces [the original waveform is the same as in Figure 5(a)], where SNR = –2.53 dB and (b) picked P- and S-arrivals together with original traces. (Figure used with permission from [22].) 106

a b/2 d/2 x P (x, y, t; i) = 6x y t@ >b/2 c e/2H >yH d/2 e/2 f t x + 6g h i@ >yH + j = 0. t

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The RANSAC framework finds the parameter vector i = [a, f, i] T in a ten-dimensional space. Since each hypothesis and test step is numerically inexpensive, we can run this alternating scheme for a large number of iterations so that a good minimal subset (containing all event picks) can be picked with high probability. The method has been tested on a data set of 50 s collected by the Long Beach nodal dense array in Southern California, which contains 5,200 sensors [40], [41]. Figure 9(a) shows the top view of the dense sensor array with the event location marked in red. In (b), the 3-D view is shown with all arrival time picks indicated by using open circles. Using the RANSAC-based classification approach, the true picks are successfully selected from all of the picks, and the optimal hyperbolic surface is delineated using a red mesh.

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Test: All elements in the entire data set (X D) are checked to determine which ones can be labeled as inliers, i.e., consistent with the hypothesized model in the sense that the distance from the model’s moveout curve is less than some prescribed value (d) . The set of all such inliers is called a consensus set (ConSet, denoted as X kC) . For a surface array, the proposed method must try to fit an underlying hyperbolic surface from the set of time picks {(x n, y n, t n)} for n = 1, f, N, where x n and y n indicate the spatial locations of the corresponding sensor. The surface can be defined using a quadratic equation in (x, y, t) that takes the following general form: ■■

As discussed in the “Introduction” section, microseismic monitoring from large arrays using migration-based detection and location techniques is subject to selecting a threshold that results in a constant rate of false positives, i.e., detection of random noise interpreted as real events. This threshold, which depends on SNR, is commonly applied to the stacked trace to identify a true event, assuming a consistent SNR across the array. However, an abnormal value of SNR in a stacked trace may result from a sudden change of noise on a few receivers, e.g., when a car drives by or when the well head of a monitoring borehole is hit. To differentiate between such nonstationary noise and a true signal, we can measure the coherency of the signal across the array along the expected moveout. A noise burst in part of the monitoring array would show low coherency across the array while a true signal should show high coherency. Thus semblance, which is a measure of coherency, is used as an additional differentiator between true signals and false positives.


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seismic emission tomography (SET) semblance function was proposed [10] to combat the complex radiation pattern, which may cause false detection and degrade the localization result. The approach uses maximum-likelihood (ML) in the frequency domain to detect microseismic events, as well as estimate the source mechanism parameters by maximizing the generalized semblance functional over source coordinates and source parameters. The ML result not only improves the detectability of microseismic events and reliable estimation of the source mechanism of events with SNR of less than one, it also helps in determining parameters of complex microseismic origins in the presence of various incoherent noise sources. As an added benefit, the method also overcomes the detection of false events in incorrect locations for more complex focal mechanisms, previously observed with SET during the presence of high SNR. To determine the source mechanism and seismic moment, we can use either full waveform inversion or ray amplitude inversion. In both cases, we must compute the spatial derivatives of the Green’s function matrix. The derivative matrix G represents the response of the medium, i.e., the velocity and density model between the receivers and the source, to the force couple M ij (1 # i, j # 3) in the moment tensor matrix M. The observed amplitudes of waveforms in particle displacement d can be related to the derivative of the Green’s function G by

There are two principal challenges to the use of semblance in passive seismic monitoring: 1) Very low signal amplitude below the noise level results in low semblance because the semblance of noise is low. 2) The signal radiated by a shear source, or even by a tensile source, is not spatially coherent and varies across the sphere with the take-off angle, because microseismic events have generally complex radiation patterns. The first challenge is generally difficult to overcome as the semblance of true events decreases with SNR and the exponentially growing total events count and information obtained from the monitoring. Initially, semblance in microseismic monitoring was used by [6] to test the limits of detectability of isotropic sources, such as underground explosions (perforations). However, later use [19] of semblance to detect microseismic events encountered the aforementioned second challenge— the radiation pattern of microseismic events. The radiation pattern of a typical shear event results in severe reduction of semblance and affects the value of semblance much more than propagation effects (geometrical spreading/attenuation) [34]. The use of signal envelopes [19] overcame this challenge, but this methodology lowers the SNR on stacked traces, especially for weaker events [36]. High semblance for real microseismic events can be preserved if the amplitudes used for computation are corrected by a source mechanism, i.e., the amplitudes are corrected by the radiation pattern of the inverted source mechanism before the semblance computation [34]. Practically, not only the magnitude of the event but also the radiation pattern could greatly affect the detection results. A method based on a statistically optimal functional that generalizes the

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Figure 9. (a) The top view of the surface sensor array with the located event indicated by a red star. (b) The 3-D view of the picks (°) from the 2-D sensor array with the fitted hyperbolic surface in red, which is used to determine the event location. IEEE Signal Processing Magazine

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data set, as in a single vertical monitoring well, cannot resolve the dipole component perpendicular to the plane of stations and the hypocenter. Thus, single-azimuth data are insufficient for resolving tensile openings associated with volumetric changes of microseismic events. Current studies of source mechanisms of microseismic events induced by hydraulic fracturing monitored from boreholes seem to observe both shear and nonshear mechanisms. Some studies conclude that all induced events are pure shear; see [26] and references therein. Other studies conclude that induced events are associated with both shear and volumetric changes; e.g., [28]. Algorithms for inverting source mechanisms simultaneously with locations were developed by [2], [5], [31], and [39], showing that correct source mechanisms can be obtained even for very low SNR events. However, these algorithms present a unique challenge to signal processing—they all require preservation of relative amplitudes among all channels of the monitoring array. For instance, in [31], localization and source mechanism inversion are presented in the framework of a sparsity-promoting linear inverse problem. By discretizing the monitoring region of interest and assuming a known source waveform, we can generate a dictionary

Data Acquisition • Downhole Array(s) [15], [25] • Surface 2-D Grid or Star-Pattern Array [11], [39] • Surface Patch Arrays [30] • Near-Surface Monitoring [9]

Velocity Model Building • Model Calibration [2]–[4], [6] • Anisotropy [19]

Events Detection/Denoising • Matched Filtering [12] • Autocorrelation-Based Filtering [24] • Rank Reduction [22], [23] • False-Alarm Rate [10] • Cross-Correlation [21] • RANSAC-Based False Picking Removal [39]–[41]

Events Localization • Semblance [6], [18], [32], [34] • Reverse Time Migration [16], [26]

Simultaneous Estimation • Stacking + Least Squares Inversion [2] • Migration Imaging [5] • Sparse Promoting Linear Inversion [29]

Moment Tensor Estimation • Least Squares Inversion [25], [27], [36]

Source Mechanics • Shear Source [27] • Tensile Source [7]

Figure 10. The signal processing techniques for microseismicity addressed in this article.

(derived from the six independent components of the 3 × 3 moment tensor matrix). The time variation of the source process is convolved with the medium response G. For induced seismicity in a far-field ray approximation, the time dependency can be approximated by a delta function, and the convolution reduces to multiplication. In that case, the least-squares moment tensor inversion of (9) is

W = [W [1] W [2] f [W [K]], (11)

based on the Green’s function (spatial impulse response), where K is the number of grid points in the region. Here, W [i] is actually a submatrix, which contains six columns, corresponding to six free parameters of the source mechanism 3 # 3 matrix. The received signal on a downhole or surface array can be written as a linear combination of these submatrices

m = (G T G) - 1 G T d. (10) d obs = Wx. (12)

This source mechanism inversion is valid if the location of the microseismic event is known and the temporal evolution can be approximated by a delta function. A major limitation of borehole-based source mechanism inversions was identified in [28], where it was pointed out that data from a single vertical array of receivers in a onedimensional (1-D) velocity model do not constrain a 3-D inversion of the volumetric component of a source mechanism. In [38], it was shown theoretically that a single-azimuth 108

An explicit form of the matrix W is likely to be huge, but, since the microseismic events are sporadic in time, the vector x is very sparse. A greedy algorithm [e.g., orthogonal matching pursuit (OMP), block sparse OMP, or basis pursuit] can be applied to recover x. The approach in [31] employs a moment-tensor inversion of P-wave (or S-wave) amplitudes taken along the moveout for every potential point in a 3-D subspace and then corrects the


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polarity of amplitudes with the inverted moment tensor before Velocity estimation stacking. The block W [i] corresponding to nonzeros in x gives An accurate velocity model is crucial for the correct location of the information about the locations of events. Using a convenmicroseismic events. Unlike applications such as radar, where tional least squares approach as in (12) for this submatrix W, wave propagation occurs in a homogeneous medium (free space), elastic models of the earth are needed to capture the we obtain an estimate of the source mechanism. In a monitorsignificant variations in velocities of both P- and S-waves that ing region containing a large number of grid points, the size result in large differences in ray propagation. of the dictionary W can be prohibitively huge. In addition, the Both surface and downhole monitoring arrays require vecoherency between spatially close submatrices is usually quite locity model calibrations. Surface arrays often use only a single high due to the continuity of the wave propagation, which also velocity model if the array is dense and has a large aperture, as makes accurate location resolution very challenging. explained in the “Introduction” section. It is well known that The time-reversal method (RTM) is an effective tool to the increased coverage of the receiver array results in greatimage the location and source mechanism of microseismic er robustness in the location of the microseismic events, i.e., events. Energy emitted by microseismic events and transmitted reduced sensitivity to the velocity model. through the media in the form of wave Although surface microseismic monitoring propagation can be refocused back to the In seismology, it is arrays with wide aperture result in robust source. Mathematically, the time-reversal well known that, for horizontal positioning, they tend to have concept is simply to solve the wave equahomogeneous media, the large vertical uncertainty in the estimated tion backward in time using the received moveout curve across a event locations [2], [6]. wave field at the sensor array [16]. For a linear array is a hyperbola. Downhole arrays require a velocity modgiven velocity model of reasonable quality el that models both P- and S-wave propaand a sufficient array aperture, the extrapogation, if not more complicated anisotropic models. Also, lated wavefield will concentrate to a focus point, which can downhole microseismic velocity modeling is particularly be considered as an approximation of the source location. By challenging as usually both depth and horizontal position are examining the energy radiation pattern at this focus point, the extremely sensitive to the velocity model. A majority of curfocal mechanism can be estimated as well. rent injection projects, especially hydraulic fracturing of shale, Clearly, the wavefield extrapolation I (x, t) in a 3-D velocity are done in relatively simple flat-layered sedimentary basins. model gives a 4-D data volume, 3-D in space and 1-D in time, Therefore, the usual starting velocity model is a layered model. to be searched for the focus Downhole microseismic models usually use the sonic logs, i.e., -1 r measurement of P- and S-wave velocities along a borehole or I (x, t) = F ' / D (x ri, ~) G (x ri, x, ~) 1, (13) i vertical seismic profiling, to build an initial isotropic velocity model. Very often, the velocity model is then adjusted to locate perforation shots to match their correct known locations [29]. where D (x ri, ~) is the data received on sensor ri at frequency r is the complex conjugate of the approximated Green’s The velocity model adjustment can be realized in a number of ~, G ways, but it usually involves fitting S–P-wave traveltime diffunction, and F -1 is simply the inverse Fourier transform. To ferences. The S–P-wave traveltime differences that cannot be obtain the source location and origin time, we need to find t 0 explained by an isotropic model are then fitted by a transverse when I (x, t) has its maximum amplitude or exhibits a reasonisotropy (TI) with vertical axis of symmetry velocity model [4] ably focused image for the seismic events in the 4-D cube. This or a more complex velocity model [3]. method is called arithmetic-mean RTM (AmRTM). One of the Downhole calibration further requires learning the oriadvantages of RTM-based methods is that we do not need to entation of 3C sensors as polarization measurements will be pick the wave arrivals. Usually, we solve only one wave equaused to locate the microseismic events. Orientation of the tion to simulate the wave propagation using all of the traces as monitoring geophones often is determined from back aziinput data, which implements the summation in (13) implicitly. muths of P-waves generated by the perforation shots located In general, the source signature of a microseismic event is in the treatment well, assuming isotropy and lateral homogefar from an impulse, so the focus point in AmRTM is usually a neity of the medium between wells. Therefore, the orientation smeared region rather than a distinct bright spot. This increasof the geophones in the monitoring well is determined relative es the difficulty and accuracy of the detection and localization. to the position of the treatment well at depths corresponding To this end, different imaging conditions have been proposed, to the perforations. The orientation (in a geographical coore.g., geometric-mean RTM (GmRTM) [27]: dinate system) of the monitoring array and of the observed microseismic event hypocenters can, however, be obtained 1 (x) = / % W ri (x, t), (14) t i only from the positions of the receivers and the perforations. Therefore, any error in the positioning of the monitoring array -1 r or uncertainty in the locations of the perforations is directly The GmRTM can be where W ri = F {D (x ri, ~) G (x ri, x, ~)}. propagated into errors when estimating positions in the fracregarded as a cross correlation, and we collapse the time axis ture system. for the ease of localization. IEEE Signal Processing Magazine

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Seismic anisotropy is the variation of a seismic property such as velocity with the direction along which it is measured. The anisotropy type in a medium depends on its symmetry system, e.g., cubic, hexagonal, etc. The symmetry system of a medium defines what happens to its properties upon geometrical manipulations such as inversion and rotation. TI is the most common type of seismic anisotropy encountered in sedimentary rocks. TI involves a property that is the same within a plane but different along a perpendicular symmetry axis. In most TI media, velocity is lowest when measured parallel to the symmetry axis and highest when measured perpendicular to the symmetry axis. The authors of [20] use direct P- and S-waves recorded in typical downhole microseismic geometries to infer seismic anisotropy in narrow angular apertures. Application of their method on synthetic and real data in a gas-shale field indicated that seismic anisotropy is important in building a physically sound velocity model. In most applications of anisotropic model inversion from real data sets, the data needs to be explained by temporarily changing anisotropy. This is interpreted as increased cracked density resulting from hydraulic fracturing.

Summary The phenomenon of microseismicity is an active and challenging problem area for signal processing. We have described many techniques for the situation where the microseismic events of interest result from injection of fluids in wells to recover oil or gas resources. Figure 10 summarizes the interrelationships among all of the methods discussed in this article. Another area of active research is monitoring micro-earthquakes in areas where large quakes are expected. Dense surface arrays (with 3C sensors) are being deployed for continuous monitoring, so the data collected are noisy and the data sets are huge. Opportunities abound for new techniques that can exploit high-speed computation to mine these large data sets for low SNR events.

Acknowledgments We are grateful for the support from the Center for Energy and Geo Processing at both King Fahd University of Petroleum and Minerals, Saudi Arabia, and the Georgia Institute of Technology. We also acknowledge support from the long-term conceptual development research organization RVO: 67985891.

Authors James H. McClellan ([email protected]) received his B.S. degree in electrical engineering from Louisiana State University in 1969 and his M.S. and Ph.D. degrees from Rice University, Houston, Texas, in 1972 and 1973, respectively. He was a researcher at Lincoln Laboratory, Massachusetts Institute of Technology from 1973 to 1975, where he later became a professor from 1975 to 1982. He was with Schlumberger Well Services, Austin, Texas from 1982 to 1987. Since 1987, he has been a professor in the School of Electrical and Computer Engineering at the Georgia Institute 110

of Technology, where he holds the John and Marilu McCarty Chair. In 2004, he was a corecipient of the IEEE Jack S. Kilby Signal Processing medal for work on finite impulse response filter design. He is a Life Fellow of the IEEE. Leo Eisner ([email protected]) obtained his M.Sc. degree in physics from Charles University (Faculty of Mathematics and Physics), Prague, Czech Republic, in 1994. He received his Ph.D. degree in geological and planetary sciences from the California Institute of Technology, Pasadena, in 2001. He was a senior research scientist with Schlumberger Research, Cambridge, United Kingdom, from 2001 to 2007 and spent six years with MicroSeismic, Inc, Houston, Texas, from 2008 to 2014. He was awarded the Purkyne Fellowship from the Institute of Rock Structure and Mechanics, Academy of Sciences, Prague, Czech Republic, from 2010 to 2014. He is the founder and, since 2015, the full-time president of the seismic service company Seismik s.r.o. He is a continuous education lecturer for the Society of Exploration Geophysics and European Association of Geoscientists and Engineers. His papers and extended abstracts cover a broad range of subjects, including the seismic ray method, finite-difference methods, seismological investigations of local and regional earthquakes, and microearthquakes induced by hydraulic fracturing. Entao Liu ([email protected]) received his B.S. degree from Shandong University, Jinan, China, in 2005 and his Ph.D. degree from the University of South Carolina in 2011, both in applied mathematics. Currently, he is a postdoctoral associate with the Center for Energy and Geo Processing at the Georgia Institute of Technology. His research interests include signal processing, seismic imaging, machine learning, numerical analysis, and inverse problems. Naveed Iqbal ([email protected]) received his B.S. and M.S. degrees in electrical engineering from the University of Engineering and Technology, Peshawar, Pakistan. He received his Ph.D. degree from King Fahd University of Petroleum and Minerals, Saudi Arabia, where he is now a postdoctoral fellow. His research interests include adaptive algorithms, compressive sensing, heuristic algorithms, and seismic signal processing. Abdullatif A. Al-Shuhail ([email protected]) received his B.S. degree from King Fahd University of Petroleum and Minerals (KFUPM), Saudi Arabia, in 1988 and his M.S. and Ph.D. degrees from Texas A&M University in 1993 and 1998, respectively, all in geophysics. He is an associate professor of geophysics at KFUPM. He founded and directed the NearSurface Seismic Investigation Consortium at KFUPM in 2006–2008. He holds three U.S. patents. He is a coauthor of Processing of Seismic Reflection Data Using MATLAB (Morgan & Claypool, 2011) and Seismic Data Interpretation Using Digital Image Processing (Wiley, 2017). His interests include near-surface effects on petroleum seismic data, seismic investigation of fractured reservoirs, and ground penetrating radar. Sanlinn I. Kaka ([email protected]) received his B.S. degree in geology and his diploma in applied geophysics from Rangoon University, Burma, in 1983 and 1985, respectively.


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He received his M.S. degree in geology from King Fahd University of Petroleum and Minerals, Saudi Arabia, in 1993 and his Ph.D. degree in earth sciences from Carleton University, Ottawa, Canada, in 2006. Currently, he is a faculty member and graduate coordinator in the Department of Geosciences at King Fahd University of Petroleum and Minerals. His research interests are in the areas of engineering seismology, reservoir characterization and monitoring, groundmotions relations, and near-surface geophysics. His recent research focuses on applications of microseismic monitoring systems and enhancement, detection, and localization of microseismic events, as well as understanding fracture growth and the role of pre-existing fractures during multistage hydraulic fracture stimulation of shale gas reservoirs.

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