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Multiplet-clustering Analysis Reveals Structural Details within Seismic

Cloud at the Soultz Geothermal Field, France

Hirokazu Moriy, Hiroaki Niitsuma and Roy Baria

Abstract Multiplet-clustering analysis is a method for precise determination of microseismic event locations and is used to identify subsurface fractures and fracture networks. A multiplet is a group of microseismic events with very similar waveforms, despite different origin times, and is likely the expression of stress release on the same structure. The relative source locations of similar events can be determined with high resolution and accuracy by using the moving-window cross-spectrum analysis technique. Deduced seismic clusters, called multiplet clusters, are indicative of seismically activated structures, and the orientations of these structures can be estimated using the seismic clusters even though the absolute locations of the multiplet clusters cannot themselves be determined. We examine methods of determining the relative locations of multiplet clusters and introduce the concept of clustering analysis. The clustering analysis method is used to estimate the relative location of multiplet clusters by detecting phase differences between similar stacked events. We describe the procedure for multiplet-clustering analysis, estimate relative locations of multiplet clusters, and apply the method to induced microseismic data from the Soultz Hot Dry Rock field, France. We show that a fracture network can be delineated through multiplet-clustering analysis, whereas it is difficult to identify detailed structures on the basis of source locations estimated by the joint hypocenter determination method.

Introduction

Microseismic events can be induced by pressurizing a subsurface formation, and then used to identify hydraulically activated fractures and fluid flow direction in geothermal, oil, and gas fields. The mapping of induced microseismic events is invaluable for evaluating subsurface structures and determining their spatial distribution. High-resolution mapping of induced microseismic events, initiated during hydraulic fracturing tests in geothermal and oil fields, is required to (i) estimate source location; (ii) spatially distinguish individual fractures; and (iii) recognize their interconnectivity, since microseismic event locations can indicate fluid flow (pathways), as well as regions of pore-pressure propagation. Such information is indispensable for reservoir evaluation of Hot Dry Rock (HDR) or enhanced geothermal systems (EGS), where it is necessary to design well loci to intersect hydraulically activated fractures for efficient extraction of heated fluids.

Several advanced mapping techniques have been developed that accurately and reliably determine microseismic source locations. For example, Jones and Stewart (1997) proposed a collapsing method that moves source locations toward a center of gravity, according to a statistical criterion, for identification of structures otherwise blurred by random location error. The collapsing method is effective for emphasizing structural features in a seismic cloud and has been used to delineate structures in the Soultz Hot Dry Rock geothermal reservoir (France) and in caldera rings at Rabaul, Papua New Guinea (Jones and Stewart, 1997).

Phillips et al. (1997) and Phillips (2000) proposed a repicking method, which produces the relative time difference of phases within a group of similar microseismic events, followed by master event relative source locations (Phillips et al., 1997; Phillips, 2000). For this analysis, waveforms are lined up after low pass filtering, with P- and S-wave arrival times are manually repicked from a similar portion of the waveform. The technique can be used to identify wave arrival times and improve the accuracy of relative source location

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determinations. Phillips (2000) applied this analysis to microseismic clouds created by hydraulic stimulation in the Soultz HDR reservoir and delineated two distinct intersecting planar structures.

The double-difference method (Waldhauser and Ellsworth, 2000) is known as a precise relative mapping method. The method minimizes error related to an unmodeled velocity structure without the use of station correction, and is effective for determining relative source locations with high resolution within clusters that may be separated by large distances. Waldhauser and Ellsworth (2000) applied the double-difference method to seismic events associated with the Northern Hayward Fault, California, and revealed a lineation of seismic events along the fault.

We present a method for mapping microseismic multiplets. A microseismic multiplet is a group of seismic events with very similar waveforms, but having different origin times. Poupinet et al. (1984) analyzed pairs of similar earthquakes related to the Calaveras Fault, California, and estimated relative source locations with high accuracy. Poupinet et al. (1984, 1985) suggested that location accuracy is improved 10 times by using a cross-spectrum analysis, compared with conventional methods. Fréchet et al. (1989) applied a cross-spectrum analysis to similar induced microseismic events at La Mayet de Montague HDR geothermal site (France), to identify fluid-filled fracture pathways. Fréchet et al. showed that relocation, using a multiplet approach, is effective for delineating hydraulically activated structures produced by fluid injection. Multiplet research has revealed that structural planes determined from source locations of hydraulically induced multiplets represent pre-existing fracture planes, and that these fracture planes imply a critical condition for shear slip (Moriya et al., 1994; Gaucher et al., 1998; Lees, 1998; Li et al., 1998; Tezuka and Niitsuma, 2000; Moriya et al., 2002). The mapping and analysis of multiplets is an important technique for determining the geometry of a fault or revealing fault dynamics (Schwartz and Coppersmith, 1984; Fremont and Malone, 1987; Deichmann and Garcia-Fernandez, 1992; Vidale et al., 1994; Dodge et al., 1995; Nadeau, et al., 1995; Dodge and Beroza, 1996; Gillard et al., 1996; Schaff et al., 1998; Rubin et al., 1999).

Each of the above mapping techniques has advantages for deducing subsurface structure. For instance, the collapsing method is best used for large numbers of events and for detecting structures more than 100 m in size in entire seismic cloud. Clustering analysis is effective for estimating fractures within a size range of several tens to a hundred meters. The double-difference method has the merit of being able to relocate widely distributed, but connected, seismic events. The advantage of using multiplet analysis is that we can evaluate individual fractures, especially those with similar physical characteristics, because the correlation of their waveforms is based on their similarity (Rowe et al., 2002a). It is possible to evaluate fine detail structures at a scale of a few meters after first deducing the structures by using the collapsing method and clustering analysis.

An estimated source location is derived from the relative location within each multiplet group and the location of the multiplet cluster. The absolute location of the multiplet cluster is usually determined as its center of gravity and is the same before and after relocation. This imposes restrictions on the evaluation of a fracture system, since we cannot deduce the locations of the multiplet clusters in absolute terms.

The development of mapping methods for estimating the location of multiplet clusters is indispensable. If we introduce “clustering analysis” (a relocation technique based on precise manual repicking of absolute arrival times) into “multiplet analysis” (a relocation method based on precise detection of relative arrival times using the cross-spectral method), then we can estimate multiplet cluster locations and estimate spatial distribution of different fractures. The merit of the combined method is that precise relative arrival time measurements and relative locations can be determined within each group of similar events by using a cross-spectrum analysis (multiplet analysis), and that more accurate positions within the multiplet clusters can be also determined on the basis of manual repicking (clustering analysis).

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Our goal is to develop a mapping method that combined “multiplet analysis” with “clustering analysis.” In this paper, we explain a mapping algorithm for determining multiplet cluster locations, and demonstrate its effectiveness. The algorithm is then applied to the entire seismic cloud at the Soultz HDR field, and we compare our results with those derived by using the joint hypocenter determination (JHD) method and conventional multiplet analysis.

Induced Microseismic Multiplet

Similar microseismic events can be detected during hydraulic fracture testing, through lost circulation during well drilling, and so on. A group of similar microseismic events is called a multiplet (Poupinet et al., 1984). Figure 1 shows waveforms of a multiplet at the Soultz HDR field. The multiplet is most likely the expression of stress release on the same fracture plane; the similar waveforms suggest the same source mechanism (Poupinet et al., 1984). High-resolution mapping of a multiplet by cross-spectrum analysis, derived from the source location, makes detailed identification of small-scale fractures possible. Groups of similar seismic events have been observed in many different settings. Multiplets have been found to be important for understanding the physical properties of a fault and wave propagation paths and for deducing fault dynamics and quality factors (Schwartz and Coppersmith, 1984; Vidale et al., 1994; Nadeau et al., 1995; Dodge and Beroza, 1996; Schaff et al., 1998; Niitsuma et al., 1999; Rubin et al., 1999).

In multiplet analysis, we first have to search for similar microseismic events. The definition of “similarity” is useful if it is quantitative. Here, we use a coherency function, which is a measure of similarity (as a function of frequency) between 2 time series. Figure 1 shows an example of waveforms collected by using the coherency function, calculated by using a time window on the P- and S-waves. Averaged coherency within a frequency range reflects overall similarity between events. In our case, the event group adopted as a multiplet is one in which coherencies exceed a defined criterion for all combinations of events. Use of the coherency function makes it possible to automatically search for similar events.

Multiplet analysis deals with similar microseismic events. By considering the origin of similar events, source locations may provide information on the spatial distribution and orientation of seismically activated fractures. Since multiplet events have similar waveforms, small changes in travel time can be recognized by cross-correlation analysis or cross-spectrum analysis (Poupinet et al., 1984; Moriya et al., 1994; Rowe et al.,2002a, 2002b).

Relative differences in arrival time can be found in the frequency domain using the phase of the cross spectrum. The relative arrival time differences between waveforms for two similar events at all recording stations yields their relative source locations. Time delay estimation using the cross spectrum was performed for all possible event pairs within each multiplet, and the combined results were expressed as a linear equation to determine resulting event separations. Figures 2(a) and 2(b) show the initial JHD locations, and the results of a multiplet analysis of 25 multiplets, respectively. Source dimensions within each multiplet can be seen in Figure 2(b) to be significantly reduced, and the hypocenters have separated into spatially distinct clusters consistent with the multiplet divisions (indicated using different symbols). Each cluster therefore represents an individual fracture, as defined as defined by a group of similar events. The root mean square (RMS) error of events reflected by JHD is about 2 ms, whereas the error for the relative location is around 0.1 ms in the case of the multiplet analysis. The application of cross-spectrum analysis improves the location accuracy of identified structures. The absolute locations of multiplet clusters shown in Figure 2(b) have the same centers of gravity before and after relocation, which means that the positions of the multiplet clusters depend upon the distribution of the original source locations. This implies that a seismic event with a location error will affect the estimated absolute location of the multiplet cluster, which in turn creates difficulties when

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we attempt to estimate fracture location based on locations of the multiplet clusters. It was previously pointed out that the adjustment of cluster centroids relative to one another is needed to obtain accurate images of source locations (Rowe et al., 2002a,b). Clearly, it is necessary to develop a reliable method for estimating the absolute locations of multiplet clusters as well as their locations relative to one another.

Algorithm and Procedure for Multiplet-Clustering Analysis

The examination of multiplet waveforms has revealed that some multiplets have similar

waveforms, even though they may belong to different groups or have less similarity than other events within the same group. Therefore, the concept of clustering analysis is applicable to the estimation of relative locations of multiplet clusters. “Multiplet-clustering analysis,” as discussed here, is a method to estimate relative positions of the multiplet clusters after estimation of relative source locations within individual multiplets and is best described with an example of the analysis method using a seismic cluster identified by Phillips (2000) at Soultz field.

The original waveform data were recorded by 4-component detectors, having sensors arranged in a tetrahedron with one component vertical and the other three non-horizontal. These components were converted to 3-component signals X, Y and Z (vertical), orthogonal to one another (Jones and Asanuma, 1997). A coherency function was calculated by using the horizontal component signals at the station having a high S/N. In our automated search for similar waveforms, any group of seismic events with an average coherency above 0.68 within the frequency band from 100 to 200 Hz is regarded as a multiplet. A low threshold of coherency is chosen so that an automated search would be able to identify a maximum number of similar events. Although waveforms with low similarity may be identified as a multiplet group, we can later remove these waveforms from the dataset by closer examination of individual collected waveforms. After the grouping, the relative source locations are estimated using the method of cross-spectrum analysis (Moriya et al., 2002)

Following the determination of relative source locations within individual multiplets, it is necessary to estimate the relative locations of the multiplet centroids with respect to one another (e.g., Rowe et al., 2002a). Our approach to this task we term “multiplet-clustering analysis.”

The concept of multiplet-clustering analysis is illustrated in Figure 3. As a preprocessing step, we apply a low pass filter to the raw signals to emphasize the similarity of waveforms and decrease high-frequency components, since it is sometimes difficult to recognize similarity in the raw signals because of the coda waves and superimposed uncorrelated background noise. The transfer function of the filter must have a linear phase characteristic to prevent distortion of the signals. A finite impulse response (FIR) low pass filter with a cut-off frequency of 150 Hz is applied, although the signal energy is mostly in the frequency range of 100 to 250 Hz (Fig. 1). Care should be taken in selecting the cut-off frequency of the filter. In our experience, we tended to collect a larger number of similar waveforms when we selected a low cut-off frequency. The cut-off frequency must be selected after careful examination of the filtered waveforms and the number of events in each multiplet, because the scale of structure delineation may be affected.

After low pass filtering, we next make a stacked waveform as a representative waveform for each multiplet, similar to the method of Rowe et al. (2002a). Figures 4(a) and (b) show examples of waveforms used for stacking and their respective stacked waveforms. In these examples, 11 waveforms with similar horizontal components are stacked after cross-correlation analysis to the reference event. To make the stacked waveform, we choose an event with a high signal-to-noise (S/N) ratio as the master waveform, and then identify arrival times of slave events relative to the master event. In Figure 4, the topmost waveform is the master event for the 11 events. To estimate the relative location of multiplet clusters, relative arrival time differences are determined for P- and S-waves in the stacked waveforms.

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We prepare two kinds of stacked waveforms for each event by using horizontal and vertical signals to separately pick arrival times for P- and S-waves, respectively. The Z component signal is used for P-wave detection, and either the X or Y component signal is used for S-wave detection, depending on the signal to noise ratio. Figures 5(a) and (b) show aligned, stacked waveforms for 14 multiplets. In our example, relative arrival time differences are determined with respect to 1 master stacked waveform with a high signal-to-noise ratio. By examining the same portion of a waveform (e.g., by comparing peak position with the reference waveform) and shifting the slave waveform along the time axis (until the master and slave waveforms overlapped), we are able to determine the time lag, i.e., the shift of the slave waveform, and make adjustments relative to the master waveform. Manual phase picking is an effective method for estimating relative arrival time differences between similar waveforms, even though the signal onset may be unclear because of background noise. In a clustering analysis, Phillips (2000) used low pass filtered waveforms directly, instead of stacked waveforms, to determine arrival time differences and to estimate the source locations of the individual events. We highlight the first positive peak (arrow, Fig. 5), and shifted the slave waveforms to adjust each of the waveforms to the reference waveform. The repicked arrival times for the stacked waveforms are used to determine the positions of the multiplet centroids, and they compose the input data for the calculations. The locations are determined by using iteratively reweighted least squares method on the estimated residuals. After determining the centroids of the clusters, the individual multiplet events can be plotted relative to the centroids.

The source locations determined by clustering and manual repicking of the same events (Phillips, 2000) are shown in Figure 6(a). Phillips’ clustering and manual repicking analysis first identified the two intersecting, near-orthogonal structures delineated by these hypocenters. The same structure was also revealed by the automated, computer cross-correlation repicking algorithm of Rowe et al (2002a,b), when applied to over 300 of the events also repicked by Phillips. In Figure 6 we compare the hypocenters for a subset of 228 events from the 355 events analyzed by Phillips (2000) and Rowe et al. (2000b), comparing these hypocenters with our own relocations of multiplets having more than four similar events. This subset represents the events which met our criteria of coherency, as well as having both P- and S-waves identifiable at station e4601, whose signal to noise ratio is lower than that of other stations. In our search for similar events within Phillips’ (2000) cluster, we set the coherency threshold level at 0.68 for signal within a frequency band from 100 to 200 Hz. 233 events (corresponding to 64%) were identified as multiplets from the initial 355 events; these were classified into 57 doublets and multiplets.

Figure 6(a) shows Phillips’ relocations for this subset, and Figure 6(b) shows the same subset of the Rowe et al. (2000b) relocations. In Figure 6(c) we present the result from the multiplet-clustering analysis. A comparison of three methods indicates that the multiplet-clustering analysis can identify large-scale structures, which are seen as multiplet clusters, as well as fine detailed structures, which are derived from each multiplet.

Induced Microseismic Events at the Soultz HDR Field Soultz HDR Field

We applied multiplet-clustering analysis to microseismic events at the Soultz HDR field, France (Fig. 7; Baria et al., 1995; Baria et al., 1999). The European HDR project at Soultz-sous-Forêts was founded by France, Germany and the European Commission (EC) in 1987. The site is located on a local horst structure in the Rhine Graben, where Hercynian age granites are covered by a 1.4 km thick sedimentary section (Baria et al., 1999). Well GPK-1 was drilled to 3,590 m depth (open hole below 2,850 m depth), and since 1987 it has been used for a number of detailed experiments. A major hydraulic fracturing experiment was performed in September and October 1993. In the September test, 25,000 m3 of fresh water were injected between 2850-3350 m at progressively higher rates to 40 l/s and pressures of up to 10 MPa over

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a 17 day period. In October, a further 20,000 m3 of water were injected at up to 50 l/s into the entire open hole section. Through the test, it was demonstrated that the fracture network in the basement rock was well developed, with enhanced permeability and a substantial increase in transmissivity (Baria et al., 1999; Evans, 2000). The second deep well, GPK-2, was drilled in 1995 to a depth of 3,876 m. At reservoir depth, this well lies ~450 m south of GPK-1, and has a bottom hole temperature of 168°C. In 1995, GPK-2 was stimulated using brine followed by fresh water, and circulation tests performed to confirm the hydraulic connectivity between the two wells. In 1996, the open hole section of GPK-2 was again stimulated, with a total of 28,000 m3 of fluid injected at a maximum wellhead pressure of 13 MPa, and flow rates of up to 78 l/s (Gerard et al., 1997), to improve its injectivity. After these experiments, well GPK-2 was extended to about 5,000 m depth, and a hydraulic fracturing test was carried out in 2000.

Induced microseismic events from fracturing tests in 1993 were monitored by using 3 downhole 4-component detectors installed in wells 4550, 4616, and 4601, and 1 hydrophone installed in well EPS1. The 4-component detectors consisted of 4 accelerometers, mounted in a housing, which were set in sand at the bottom of the borehole and at 1500, 1420, and 1600 m depth. The hydrophone was set at a depth of 2850 m in well EPS1.

With the downhole seismic detectors installed in basement rock, high quality signals could be recorded and the transfer function from the source to each detector was simple. The frequency band of the acquisition system was from 10 Hz to 1 kHz, and the signals were digitized at a sampling frequency of 5 kHz (Baria et al., 1999). Source locations of more than 10,000 induced seismic events (Fig. 8; Baria et al., 1995), from the 1993 test, were determined by JHD (Baria et al., 1999), using a homogeneous velocity structure. The reservoir structure has also been evaluated by precise mapping methods (e.g., doublet/multiplet analysis, collapsing method, and clustering analysis; Jones and Stewart, 1997; Gaucher et al., 1998; Moriya et al., 2000; Phillips, 2000; Rowe et al., 2002b). For this study, we evaluated multiplets of the downhole seismic signals recorded for 10,182 events induced by the 1993 hydraulic fracturing test.

As a first step, a total of 5490 events (58.3% of the events) were identified as multiplets (containing more than 3 similar waveforms), with coherency ranging from 0.80 to 0.99. In our result, most collected waveforms (33%) had a coherency above 0.90, and the P- and S-waves were easily recognized. Figure 9 shows the JHD locations of the microseismic events that were identified as multiplets.

From 550 multiplets, we address those containing five or more events, yielding 142 multiplets containing a total of 1052 events. A minimum of 5 events per multiplet is needed to constrain the assumed planar structures producing the multiplet events.

The relative source locations within each multiplet were estimated by using cross-spectrum analysis to obtain relative P- and S-wave arrival times. The Fast Fourier Transform (FFT) time window-length for the cross-spectrum analysis was set at 5.12 ms. Cross spectra were calculated for 10 different time windows, shifted by 0.4-ms steps along the time axis, and averaged as complex vectors to obtain the cross-spectrum estimates. The slopes of the phases within the frequency band were calculated by fitting a line (by the method of unweighted least squares), with the time delay estimated as the relative arrival time delay. For both P- and S- arrival times, we set up an overdetermined system of first differences which we solved under an L2 norm for a consistent set of arrival time differences, applying an a posteriori zero mean constraint (e.g. Tezuka and Niitsuma, 2000). Source locations, relative to a reference source location, were determined within each multiplet by assuming that the velocity structure was homogeneous along the wave propagation path. The RMS errors for the relocation were about 0.1 ms. Figure 10 shows source locations of multiplets after conventional multiplet analysis. Locations of multiplet centroids were fixed with respect to their centers of gravity both before and after relocation; this is dependent on the original source distributions, as defined by the initial JHD locations.

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Application of Multiplet-Clustering Analysis To the Larger Catalogue Following the procedure outlined earlier for our test data set, we identified 142

multiplets within the full catalogue of over 10,000 induced microearthquakes. Stacked waveforms from our 142 surviving multiplets were visually classified into 7

subgroups by examination of their similarity, and a master stacked waveform was chosen as a reference waveform for each of the seven groups, based on high S/N. Arrival time differences for the stacks were determined relative to the master event by manual picking.

A total of 7 relative arrival time differences, for P- and S-waves at wells 4616, 4550, 4601, and for P-waves at the hydrophone in EPS1, were used to determine the locations of the multiplet clusters. We used a homogeneous velocity structure having P- and S-wave velocities of 5850 m/s and 3340 m/s, respectively (e.g. Jupe et al.,1994). Multiplet centroids were relocated using an iteratively reweighted least-squares approach.

Figure 11 shows source locations of multiplet events after multiplet-clustering analysis. Following multiplet-clustering analysis, small planar clusters corresponding to each multiplet were identified, within 3 larger seismic clouds denoted by “A”, “B” and “C.”

A multiplet plane is defined as the plane best fitting the distribution of the source locations within the multiplet distribution and is calculated by using a principal component analysis on the coordinates of the source locations (Flynn, 1965; Fehler et al., 1987). Through principal component analysis, the source distribution is approximated by an ellipsoid, with the plane defined by the first and second eigenvectors. The ratios of the first and second eigenvalues exceeded 0.83, so we considered the multiplet geometries to well represent a planar distribution of source locations (Moriya et al., 2002).

Depth slices of source locations before (Figures 12a qand 13a) and aftger (Figures 12b and 13b) multiplet-clustering analysis are compared. Figures 12b and 13b contain the same numbers of events.

Two separate clouds, corresponding to “A” and “B,” were identified at a depth interval of 2850 to 2950 m, as shown in Figure 12(b). Here, we do not describe in detail the significance of the structures, although the 2 clouds are considered to be fracture zones that intersect the borehole, which is consistent with the well-logging results.

Discussion

We discuss the feasibility of multiplet-clustering analysis and compare mapping results obtained by JHD, multiplet analysis, clustering analysis, and multiplet-clustering analysis. It is not appropriate to directly compare the accuracy of the locations by using the residuals obtained from the 3 different methods, since JHD was performed on the entire catalog but relocation using multiplets was applied to a far smaller dataset. However, it is reasonable to say on the basis of the RMS residuals that the relative locations within the multiplet clusters were better estimated by multiplet-clustering analysis than by the JHD method. The RMS by JHD was 1.92 ms, whereas 0.1 ms for the relative location within the multiplets. Location uncertainties were about 10 m for JHD and 0.5 m by multiplet analysis, when we assume a P-wave velocity of 5 km/s. Comparison between JHD and multiplet analysisindicates that the error in relative location was smaller than that by the JHD method, and that the multiplet analysis is effective for the identification of fine-scale structures. The improvement in relative location accuracy has been confirmed, at other fields, by other researchers (e.g., Poupinet et al., 1984).

Table 1 shows the RMS of the residuals at each well and the standard deviations that resulted from the multiplet-clustering analysis. The average of the RMS values of the residuals was 0.27 ms, and the average of the standard deviations of the residuals was 0.29ms, in the multiplet-clustering analysis. These errors does not involve the errors for intra-multiplet relaive location.

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Phillips (2000) reported that the residual variance was 0.49 ms, and that the residual standard deviation by station and phase ranged from 0.06 ms to 1.05 ms in his deep cluster (in cloud C), using a single-event location algorithm. He obtained a median 1σ major axis error magnitude in his analysis was < 4 m (for the case of a low pass filter with cut-off frequency of 50 Hz). Thus, the results from the multiplet-clusering analysis appear comparable to single event location results when relative arrival time inaccuracies have been reduced by careful, manual waveform alignment. The average of the RMS of residuals was 0.21 ms, and the average of the standard deviations of residuals was 0.23 ms in the multiplet-clustering analysis, if we use only the multiplet cluster locations in cloud “C” (shown in Figs. 2 and 6).

To visually verify the uncertainty of the multiplet cluster locations, we calculated synthetic source locations perturbed by errors in the estimation of relative arrival time differences from manual phase picking. Figure 14 shows cluster locations that involve synthetic errors, according to a normal distribution, where the standard deviations (1σ) correspond to the residuals from phase picking at each station (Table 1). A total of 100 synthetic locations were generated for all multiplet clusters. The synthetic sources were plotted around the center of gravity of each multiplet cluster. The elliptical distribution of synthetic sources was governed by the network geometry, whereas its size arose from the timing errors introduced by the perturbation of picks. The size of the error source distribution was around 7.5 m along the major axis of the (approximated) ellipsoid. If we assume that the location error is subject to a normal distribution, with a mean value of 0.27 ms and a standard deviation of 0.29 ms, then the 95% confidence error interval (2.8σ) is 1.08 ms, with a confidence coefficient of 95%. As a result, we suggest that location uncertainty can be expected to be less than 5.4 m, with 95% confidence.

Consequently, multiplet-clustering analysis can estimate a larger structure from the distribution of multiplet clusters as well as evaluate the location and orientation of detailed features within larger features estimated by JHD and clustering analysis. For example, within the 2 large structures that were recognized (Fig. 12), the multiplet-clustering technique was able to illuminate microstructures having strikes oriented at an angle of about 10 to 20 degrees to the direction of maximum horizontal stress.

Conclusion

We used multiplet-clustering analysis to estimate the locations of multiplet clusters and to identify fracture systems with higher resolution and accuracy. The microseismic multiplets observed at the Soultz HDR field in 1993 were analyzed to evaluate the feasibility of the proposed method. Twenty-five groups of multiplets were analyzed and results obtained by JHD, multiplet analysis, and multiplet-clustering analysis methods were compared. By examining residuals of cluster locations, it was shown that the uncertainty of determining cluster locations was smaller by multiplet-clustering analysis than that by JHD, and that structures can be distinguished in the 1993 Soultz microseismic data. Interpretation of the multiplet-clustering analysis for Soultz HDR data has resulted in the identification of 3 large structures. In addition to identification of these large structures, multiplet-clustering was useful for evaluating the location and orientation of detailed lineations and fracture patterns within those structures that are not apparent using JHD alone. Acknowledgments We thank Dr. C. A. Rowe (Los Alamos National Laboratory., USA) and Dr. W. S. Phillips (Los Alamos National Laboratory, USA) for providing us important source location data and for permission to use the data. We also thank Dr. K. Evans (ETH, Switzerland) for detailed technical discussions and helpful comments, and also Dr. G. Bignall (Tohoku University) for

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his suggestions. We thank Dr. D. Schaff and an anonymous reviewer for their comments and suggestions. This work was carried out as a part of the MTC/MURPHY International Collaborative Project (International Joint Research Grant) supported by NEDO and MESSC; and by a grant from the Industrial Technology Research Grant Program in 2000, supported by NEDO. References Baria, R., J. Garnish, J. Baumgärdner, A. Gérard, and J. Reinhard (1995). Recent developments in the European HDR research programme at Soultz-sous-Forêts (France), Proc. World Geothermal Congress, Florence, Italy, 2631-2637. Baria, R., J. Baumgärdner, and A. Gérard (1999). European HDR research programme at Soultz-sous-Forêts (France) 1987–1996, Geothermics, 28, 655-669. Deichmann, N., and M. Garcia-Fernandez (1992). Rupture geometry from high-precision relative hypocenter locations of microearthquake cluster, Geophys. J. Int., 110, 501-517. Dodge, D. A., and G. C. Beroza (1996). Detailed observations of California foreshock sequences: Implications for the earthquake initiation process, J. Geophys. Res., 101, 22371-22392. Dodge, D., G. C. Beroza, and W. L. Ellsworth (1995). Foreshock sequence of the 1992 Landers, California, earthquake and its implications for earthquake nucleation, J. Geophys. Res., 100, 9865-9880. Evans, K. F. (2000). The effect of the 1993 stimulation of well GPK1 at Soultz on the surrounding rock mass: Evidence for the existence of a connected network of permeable fractures, Proc. World Geothermal Congress 2000, 3695-3700. Everndon, J. F. (1969). Identification of earthquakes and explosions by use of teleseismic data, J. Geophys. Res., 74, 3828-3856. Fehler, M., L. House, and H. Kaieda (1987). Determining planes along which earthquakes occur: Method and application to earthquakes accompanying hydraulic fracturing, J. Geophys. Res., 92, 9407-9414. Flynn, E. A. (1965) Signal analysis using rectilinearity and direction of particle motion, Proc. IEEE, 53, 1725-1743. Fréchet, J., L. Martel, L. Nikolla, and G. Poupinet (1989). Application of the cross-spectral moving-window technique (CSMWT) to the seismic monitoring of forced fluid migration in a rock mass, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 26, 221-233. Fremont, M.-J., and S. D. Malone (1987). High precision relative locations of earthquakes at Mount St. Helens, Washington, J. Geophys. Res., 92, 10223-10236. Gaucher, E., F. H. Cornet, and P. Bernard (1998). Induced seismicity analysis for structure identification and stress field determination, Paper SPE 47324, Proc. SPE/ISRM, Trondheim, Norway. Gillard, D. A., M. Rubin, and P. Okubo (1996). High concentrated seismicity caused by deformation of Kilauea’s deep magma system, Nature, 384, 343-346.

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Jones, R. H., and H. Asanuma (1997), Analysis of the four-component sensor configuration, MTC/NEDO Internal Report, 2. Jones, R. H., and R. Stewart (1997). A method for determining significant structures in a cloud of earthquakes, J. Geophys. Res., 102, 8245-8254. Jupe, A., R. H. Jones, J. Willis-Richards, B. Dyer, J. Nicholls, and P. Jacques (1994). Report on HDR Phase 4 – Soultz Experimental Programme 1993/1994, CSM Associates Ltd., IR02/12. Lees, J. M. (1998). Multiplet analysis at Coso geothermal, Bull. Seismol. Soc. Am. 88, 1127-1143. Li, Y. P., C. H. Cheng, and M. N. Toksoz (1998). Seismic monitoring of the growth of a hydraulic fracture zone at Fenton Hill, New Mexico, Geophysics, 63, 120-131. Moriya, H., K. Nagano, and H. Niitsuma (1994). Precise source location of AE doublets by spectral matrix analysis of triaxial hodogram, Geophysics, 59, 36-45. Moriya, H., K. Nakazato, H. Niitsuma, and R. Baria (2000). Study of microseismic doublet/multiplet for evaluation of fracture system in Soultz HDR field, Proc. World Geothermal Congress 2000, 3807-3812. Moriya, H., K. Nakazato, H. Niitsuma, and R. Baria (2002). Detailed fracture system of the Soultz-sous-Forêts HDR field evaluated using microseismic multiplet analysis, Pure Appl. Geophys., 159, 517-541. Nadeau, R. M., W. Foxall, and T. V. McEvilly (1995). Clustering and periodic recurrence of microseismicities on the San Andreas fault at Parkfield, California. Science, 267, 503-507. Niitsuma H., M. Fehler, R. Jones, S. Wilson, J. Albright, A. Green, R. Baria, K. Hayashi, H. Kaieda, K. Tezuka, A. Jupe, T. Wallroth, F. Cornet, H. Asanuma, H. Moriya, K. Nagano, W. Phillips, J. Rutledge, L. House, A. Beauce, D. Alde, and R. Aster (1999). Current status of seismic and borehole measurements for HDR/HWR development, Geothermics, 28, 475-490. Phillips, W. S. (2000). Precise microearthquake locations and fluid flow in the geothermal reservoir at Soultz-sous-Forêts, France, Bull. Seismol. Soc. Am., 90, 1, 212-228. Phillips, W. S., L. House, and M. Fehler (1997). Detailed joint structure in a geothermal reservoir from studies of induced microearthquake clusters, J. Geophys. Res., 102, 11745-11763. Poupinet, G., W. L. Ellsworth, and J. Fréchet (1984). Monitoring velocity variations in crust using earthquake doublets: An application to the Calaveras fault, California, J. Geophys, Res., 89, 5719-5731. Poupinet, G., J. Fréhet, W. L. Ellsworth, M. J. Frémont, and F. Glangeau (1985). Doublet analysis: Improved accuracy for earthquake prediction studies, Earthquake Pred. Res., 3, 147-159,.

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Graduate School of Engineering, Tohoku University 01 Aramaki Aza Aoba, Aoba-ku, Sendai, 980-8579 Japan (H.M., H. N.) EEIG Heat Mining, 67250 Kutzenhausen, France (R. B.)

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Table 1

4616 4550 4601 EPS1 P S P S P S P Mean value of residual

of root mean square (ms)

0.20 0.33 0.28 0.31 0.23 0.17 0.30

Standard Deviation

(ms) 0.25 0.31 0.27 0.28 0.33 0.27 0.27

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Figure captions

Table 1. Residuals and standard deviation for the for recording locations, for relative locations in the multiplet-clustering analysis. Figure 1. Example multiplet waveforms recorded at station 4616 during stimulation at the Soultz Hot Dry Rock field, France. This multiplet includes events that spanned a time of 13 hours. Rotated, horizontal X component is shown. Figure 2. Source locations of multiplets estimated by (a) the joint hypocenter determination (JHD) method and (b) conventional multiplet analysis ; the same microseismic events were analyzed by the 2 different methods. The centers of gravity of the multiplet clusters remain fixed . Figure 3. Concept of multiplet-clustering analysis. After low pass filtering, waveforms are stacked to create a representative waveform. Relative phase arrival time differences between stacked waveforms are obtained to estimate relative locations of multiplet centroids. Figure 4. Stacked waveform (top) for one multiplet, and their contributing waveforms, at wells 4550 (a) and 4616 (b), are shown for the horizontal component signals. Figure 5. Stacked waveforms before (left) and after (right) visually aligning on their first peaks, shown for station 4616: (a) P- and (b) S-wave portions. The arrow denotes picking position of the peak for alignment and determination of relative phase arival. Figure 6. Source locations of multiplets determined by 3 different approaches: (a) Phillips’s clustering analysis, and (b) high-precision automatic repicking by Rowe et al. (2002b) and (c) multiplet-clustering analysis. Note that these represent only 228 of the 355 events included in the Phillips (2000) and Rowe et al. (2002b) analyses. These are the same 228 events shown in Figure 2. Figure 7. The European HDR site at Soultz-sous-Forêts, France. Induced microseismic events were recorded using downhole 4-component accelerometers in wells 4550, 4616, and 4601, and a hydrophone in well EPS1. Well GPK1 is the fracturing well. Figure 8. Source locations of induced seismicitiy from the 1993 Soultz hydraulic fracturing test, with source locations determined by the JHD method (Baria et al., 1995). Figure 9. Initial JHD locations for those events that were included in the multiplet analysis.. Shallower events, above 2700 m, are not plotted. The casing shoe is at the drilling depth of 2850 m, and the permeable zones which detected by well loggings are denoted by thick lines on the well locus. Figure 10. Multiplet analysis re-locations of the events shown in Figure 9. Multiplet centers of gravity were held fixed. Figure 11. Relocations of events from Figures 9 and 10, using multiplet-clustering analysis (in which multiplet centroids were relocated relative to one another using the intra-multiplet stacked waveforms to determine arrival time differentials). Figure 12. Map views of hypocenters located at a depth interval of 2850 to 2950 m. a) original, JHD locations. b) the same events, relocated using multiplet clustering. The short, thick lines intersecting the locations represent the strikes of multiplet planes. SH and Sh represent the directions of maximum and minimum horizontal stress, respectively.

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Figure 13. Map view of hypocenters located at a depth interval of 2950 to 3050 m. a) Original JHD locations. b) Relocations by multiplet-clustering analysis. The short, thick lines represent the strikes of multiplet planes. SH and Sh represent the directions of maximum and minimum horizontal stress, respectively. Figure 14. Source locations estimated by multiplet-clustering analysis (left), and simultaneously computed source locations showing location errors (right). The errors in phase arrival time difference estimation are assumed to follow a normal distribution, with the standard deviation at each station corresponding to the residuals of each phase pick.

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Figure 1

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Figure 6(c)

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Figure 11

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Figure 12

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Figure 13

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Figure 14