Joint Structures Determined by Clustering Microearthquakes
Using Waveform Amplitude Ratios
Adam Roff , W. Scott Phillips and Donald W. Brown
International Journal of Rock Mechanics and Mining Sciences
and Geomechanics Abstracts
A new method of clustering seismic events has been developed to identify features
within a large cloud of microearthquakes induced by the pressurization of a 3.5-km deep,
jointed region of granitic rock. The relative amplitudes of shear- and compressional-
waves were taken as an expression of the source mechanism for each microearthquake.
Then, the events were clustered according to their similarity in S/P ratio and a second
criterion, their spatial proximity to each other. Thus, each cluster contains events with
closely spaced hypocenters and similar S/P ratios, and therefore a high probability of the
same (or very similar) focal mechanism. This method was applied to a data set of 8,000
microearthquakes recorded during hydraulic stimulation of the Hot Dry Rock geothermal
reservoir at Fenton Hill, New Mexico, located on the western flank of the Valles Caldera.
Over 50 clusters of more than 10 events each were identified as planar features and over
20 such clusters were identified as linear features, together containing 15% of the usable
events. Two predominant sets of planar features strike north to N45*W, roughly tangent
to the ring fault system circling the caldera and dip 60* in either direction. These planes
represent joints that may be associated with stress fields accompanying caldera formation.
Most observed planes contain significant resolved shear within the current stress field.
However, wide ranges of equally probable orientations are not observed, indicating a
relatively unbiased sampling of the actual range of joint orientations. Most linear features
are oriented parallel to one or both sets of planar features and may be associated with joint
intersections or terminations. These results support a reservoir flow model composed of
water storage within aseismic joints oriented perpendicular to the minimum stress
direction and of limited dimension, connected by high impedance paths along joints
striking north to N45*W as defined by the cluster results.
Microearthquakes recorded in seismically active regions can provide useful
information about subsurface structures. However, it is often difficult to glean much
structural detail from a plot of the hypocenters alone. Scatter in the hypocenter locations
obscures features that are close together, and visualization of three-dimensional features in
a two-dimensional scatter plot is often difficult. Even with perfect hypocenter locations, it
would still be difficult to identify features in a cloud of many thousands of
Within the last eight years, several techniques have been developed to discern
structural details within such clouds of microseismic events. One recent method employs
an iterative technique of moving event hypocenters around within their error ellipsoids in
an attempt to concentrate, or focus, diffuse seismicity . The 3-point method of Fehler
 looks for planar features in an event cloud by taking all combinations of events three at
a time to find all possible orientations of planes within the data set. A statistical analysis
then identifies the most significant planar orientations given that some orientations will
merely be artifacts of the overall shape of the seismic cloud. These methods [1,2] rely
solely on the locations of the event hypocenters to define features in the event cloud.
Modified versions of the 3-point method [3,4] use fault-plane solution data along with
identified plane orientations of aftershocks to identify which of two nodal planes was the
slip plane of a main shock. This is a useful advance as both structure and mechanism can
be inferred from the results.
An alternative approach to these methods is to first collect groups of events with
similar focal mechanisms, and then look for patterns defined by their hypocenters. One
method of identifying similar events is through waveform cross-correlation across all
possible event pairs in the data set, so that events with high correlation can be grouped
together. An advantage to this approach is that event timing and location can be improved
in parallel. However, the cross-correlation and timing improvement process can be
computationally intensive for large data sets .
The method we have developed uses the ratio of the first-arrival S- to P-wave
amplitudes (S/P) at a given station as an expression of the earthquake focal mechanism.
Using this less sophisticated measure of similarity between microearthquakes to selectively
cluster events, we were able to identify numerous features within the microseismic cloud
with much less coding and computational time than would have been required using
waveform cross-correlation techniques.
In this paper we describe the application of this new method of analysis to a large
data set of microearthquakes that were induced during the 1983 massive hydraulic
fracturing (MHF) test performed at the Los Alamos National Laboratory's Fenton Hill Hot
Dry Rock (HDR) test site in north-central New Mexico (Figure 1). In this experiment,
21,600 m3 of water was injected in 62 hours into a packer-isolated, 21-m section of
openhole wellbore at a depth of 3460 m. The mean pumping conditions were a flow rate
of 106 l/s at a wellhead pressure of 48 MPa.
We begin our discussion with the motivation for this new method of microseismic
data analysis and then explain in detail how the method was applied to our particular data
set. The results from this analysis consist of a large number of microearthquake clusters
that are subsets of the total data set. Many of these clusters delineate planar and linear
features that appear to be related to preexisting joints along which slip was induced. We
anticipate that knowledge of the joint structure will help us to understand fluid flow
through the reservoir.
The amplitudes of P- and S-waves observed from an earthquake are affected by
source parameters such as fault-plane orientation and slip vector, as well as take-off angle
of the ray to the observer and the mechanical properties of the medium between the source
and receiver. For events that are close together, the ratio of S- to P-wave amplitude
remains a strong function of the source parameters, but is less affected by event size and
raypath differences and can be used as a measure of a microearthquake’s focal mechanism.
Unfortunately, the relationship between S/P ratio and focal mechanism is not a unique one
because different focal mechanisms can lead to the same S/P ratio at a particular
observation point. Furthermore the relationship is highly nonlinear, especially close to
nodal regions in the P-wave radiation pattern. Nevertheless, closely spaced earthquakes
with similar focal mechanisms should have similar S/P ratios at the same receiver.
The microearthquake data set that we analyzed was recorded during and
immediately following the December 1983 MHF test at the Fenton Hill HDR test site.
Seismic events were recorded by four downhole geophones (Figure 2) for 85 hours
beginning at the start of injection. Only a total of 844 events were digitized during the
experiment. Locations were obtained using P- and S-wave arrival times at the four
stations . Data were later retrieved from analog tapes, resulting in over 11,000
locatable events. Of these, the highest quality locations are plotted in Figures 3-A, 3-B, and 3-C. To
calculate S/P amplitude ratios for the cluster analysis, we used only the vertical component
of the triaxial geophone station located at a depth of 2865 m in borehole EE-1. Some
8,037 events yielded unsaturated seismograms at EE-1. For these 8,037 events, the RMS
velocity amplitude was calculated in a 10-ms window (approximately 1.5 periods) starting
at the arrival time for both P- and S-waves. S/P ratios for the entire data set ranged from
0.27 to 93.0 with a median value of 1.57.
To validate our use of S/P ratios to identify distinct features within the
microseismic cloud, we examined the S/P ratios for two separate clusters of events that
had been previously identified by eye. Figure 3c shows the locations of these two clusters
within the seismic cloud. Figure 4 shows three representative vertical component
seismograms for each of the two groups as recorded at station EE-1.
The seismograms show distinct differences between the two clusters, while
exhibiting strong similarity within each cluster. Note specifically the difference between
relative amplitudes of P- and S-waves for the two clusters. Figure 5 shows the
distribution of the S/P ratio for all events in clusters 1 and 2. Although each cluster has a
spread of S/P ratios, their distributions have distinct peaks. Our new method of analysis
exploits these differences to separate the entire data set into clusters.
Microearthquakes are clustered according to both their S/P ratios and their spatial
proximity, in an attempt to group events that share similar source orientations and
locations. To separate events, a single-link cluster analysis was used . The precise
algorithm is an equivalence class routine  which has been used to identify clusters of
similar earthquakes in the Anza seismic gap .
In single-link analysis, a true or false measure of equivalence between two events
determines whether or not they are included in the same cluster. However, an event in a
cluster need only be equivalent to one other event in the same cluster. In this way,
clusters of events with broad distributions in S/P ratio (such as clusters 1 and 2) should be
allowed to form. This is one advantage of using a single-link cluster analysis instead of
other grouping strategies.
Our method used a single parameter (S/P ratio) to characterize each earthquake's
focal mechanism. However, it is possible that events from widely separated areas of the
reservoir could appear to be identical if we used only this parameter as the measure of
equivalence. Since we were interested in the detailed internal structure of the reservoir, it
was necessary to impose a maximum separation distance of 100 m before two events were
considered for comparison.
The two-criterion clustering method is illustrated in Figure 6. Events 1-5 are all
within the allowable separation threshold of at least one other similar event, and thus are
clustered together. Event 6 is within the separation threshold of three of the clustered
events but fails the source mechanism equivalence test with all of them (the indicated fault
plane solutions). Event 7 passes the equivalence criterion but exceeds the separation
threshold with all the clustered events.
The measure of similarity used between two events was based on their proximity in
the S/P ratio distribution. For example, a similarity criterion of one percentile means that
two events are considered similar if less than 80 (1% of 8037) other events lie between
them in the ordered list of S/P ratios. The use of percentiles helps to overcome the non-
linear nature of the relationship between S/P ratio and source parameters.
If the criteria of S/P ratio similarity and maximum spatial separation are not set
strictly enough, every event in the data set passes the equivalence test with one or more
other events. This results in the formation of one large cluster containing all the events.
However, if the selection criteria are too strict, many events do not pass the equivalence
test with any other events and thus do not cluster at all and are discarded from the
analysis. To avoid these two extremes, we began with a set of criteria at which all events
clustered together (1 percentile and 100 m) and then incrementally tightened the S/P ratio
requirements for clustering. At each increment, the events were re-clustered and any
planar or linear clusters were saved. This process was continued until all events were
saved or were discarded in insignificantly small clusters (10 or fewer events). The
decision to save a cluster was based on the visual examination of the cluster using map and
orthogonal cross-section views oriented according to the largest cluster dimension (Figure
7). Cluster dimensions and orientations were calculated by eigenvector analysis of the
spatial covariance matrix,
where Xi, Yi and Zi are the coordinates of event i and the Einstein summation convention is
implied . Measures of planarity and linearity were also calculated,
XiXi XiYi XiZi
YiXi YiYi YiZi
ZiXi ZiYi ZiZi
planarity = 1 - lambda:2 / lambda:3 ;
linearity = 1 - lambda:1 / (lambda:2+lambda:3) ,
where the lambda:i are the eigenvalues in descending order of magnitude. These measures were
not used as selection criteria at this stage.
The set of clusters obtained using the single-link technique with progressively
tighter similarity requirements were grouped into planar and linear features by restricting
planarity and linearity measures to be greater than 0.7. This resulted in 53 planar and 23
linear clusters (Tables 1 and 2). Taking account of events in clusters common to both
groups, the number of events in these clusters total about 1200, or 15% of the events
available for analysis.
To view the spatial distribution of the planar clusters, the best fit plane through
each cluster was bounded by the smallest in-plane rectangle with horizontal top and
bottom edges that contained the projected hypocenter locations. A representative solid
rectangle was formed by adding the same width to all rectangles (Figure 7). Figure 8
shows the same view looking west as in Figure 3c, but with the representative solid
rectangles replacing the hypocenter locations. The planes we identified appear in spatially
distinct groups throughout the reservoir volume. This grouping of seismicity is also
visible in the event hypocenter plot (Figure 3c).
Although the overall Fenton Hill seismicity forms a flattened, ellipsoidal volume
striking approximately north (Figure 3a), the majority of the planes located during the MHF
test strike between north and N45*W and dip 60* or more, both to the east and west as
indicated by the lower hemisphere projection of poles to planes (Figure 9a). Eastward
dipping planes are twice as plentiful as westward dipping planes. Orientations of linear
features are shown in Figure 9b. Most linear features trend roughly parallel to strikes of
the predominant populations of planar features. Plunges are distributed in all directions
with near horizontal being most common.
The linear and planar features we identified are composed of about 1200
microearthquakes, so there still remain some 6800 other events that were discarded from
the analysis. One reason for this is that high thresholds of similarity were needed to
adequately split the data set into clusters. This results in narrow distributions of S/P ratio
in the clusters produced (compare Figure 5 distributions with that in Figure 7). Tighter
spatial constraints and looser S/P differences might have yielded larger numbers of events
in clusters, but this was not investigated. Another reason is that routinely determined
locations were relied on and clusters may have been ignored because of lack of structure.
Therefore, the 15% clustering obtained with the S/P ratio technique underestimates the
degree of clustering in the data set. The use of waveform cross-correlation as the
clustering parameter may also help to increase the degree of clustering. Waveforms carry
more information than S/P ratios and thus the microearthquakes would be potentially
more distinct from each other, yielding more clusters at low similarity thresholds. In
addition, improvement in relative arrival times of clustered events would lead to lower
relative location error and easy identification of structures. This technique should
decrease the number of events that need to be discarded from the analysis. Although the
computational burden will increase, the use of cross-correlation techniques have the
potential to further our understanding of the detailed structure of the reservoir.
The Fenton Hill site sits on the western flank of the Valles Caldera at a point
where the ring fault system strikes roughly N20*W (Figure 1), parallel to the mean strike
of the two main families of planar features found by the cluster analysis. The planar
features represent joints that may be associated with stresses that accompanied caldera
emplacement or collapse. Furthermore, the most populous of the two observed planar
families dips to the east, similar to the normal faults of the ring fault system closest to
The poles to the planes identified by application of the 3-point method to an 844-
event subset of the data from the same hydraulic stimulation experiment  show general
agreement with those found by our analysis (Figure 10). The 3-point results indicate
statistical trends of gross features in the data set, whereas clustering resolves the reservoir
structure on a finer scale, both methods giving similar orientations.
A number of wellbore/plane intersections are apparent in Figure 8. The locations
of two of these intersections correlate with independent information regarding the flow
paths of high pressure water through the rock mass. The intersection of an inferred plane
with the EE-2 wellbore at a depth of 3250 m coincides with a wellbore casing failure
caused by a high pressure flow connection intersecting the wellbore at this point. The
intersection of an inferred plane with the EE-3A wellbore around 3450 m is located in the
openhole region through which high pressure water was being pumped when fluid
connections to wellbore EE-2 were first achieved in the spring of 1986. The water
flowing from EE-3A to EE-2 during this flow test would most likely have occurred along
flow paths represented by interconnecting, previously opened joints. These coincident
phenomena indicate that high pressure water is present along at least some if not all the
identified joint planes.
Previous work on hydraulic fracturing at Fenton Hill indicates that shear-slip along
preexisting joints in the rock mass is the major cause of seismicity . The large S/P
amplitude ratios and P-wave polarity changes we observe from the events support the
concept of a shear mechanism. To further understand the dynamics of our reservoir, it is
important to compare observed planar orientations with the stress field. Stress
measurements at Fenton Hill have been summarized as s1 vertical, s3 horizontal, N104*E,
s1/s2=2, s2/s3=1.5, determined from pressurization and wellbore breakout data .
These directions match orientations expected for the Rio Grande Rift, although this area
has been classified as a transition stress region with a range of measured principal stress
orientations . This stress field is also consistent with the overall orientation of Fenton
Hill reservoir seismicity which fills a flattened, ellipsoidal volume (Figure 3), oriented
roughly perpendicular to the minimum principal stress. As in  the ratio of resolved
shear and normal stresses on a planar surface is plotted along with the observed planar
orientations in Figure 10. The two predominant populations of planar features are
oriented near the peak expected shear. However, the observations do not follow the
maximum shear pattern perfectly and a significant number of observations fall well away
from the peaks. Because wide ranges of equally probable orientations are not observed,
we have confidence that the range of observations is a relatively unbiased estimate of the
range of actual joint orientations. Exceptions to this would be joints oriented
perpendicular to any of the principal stress axes.
Another reservoir stress model is tightly constrained by focal mechanisms of nearly
200 large events recorded during injection by a network of seismometers on the earth's
surface, giving s1 horizontal, N155*E, s3 near vertical, (s1-s2)/(s1-s3)=0.5 . This is
quite different from the model discussed above. Differences between focal mechanisms
and pre-injection stresses were observed at Le Mayet de Montagne, France and were
attributed to local perturbations in the stress field resulting from relaxation along a fault
during fluid injection . Qualitatively, we can not resolve the difference between the
two stress fields because it is difficult to significantly reduce the vertical stress relative to
the horizontal stresses using pressurization and shear relaxation ideas along joints striking
north to N45*W. The similarity between the s1 direction from focal mechanisms and the
strikes of the observed planar features may be a clue to the mechanism at work.
Linear features are also prevalent in the set of clusters found in the hydraulic
stimulation data set. Linear clusters are identified as those with a long axis that is much
larger than the other two. However, a cluster can be both linear and planar if the ratio of
major and intermediate and the ratio of intermediate and minor axes are both large. Just
under half of the linear features can be placed in both categories (see Tables 1 and 2). All
linear clusters are oriented parallel to one or both sets of the observed planar features. We
believe these features are expressions of joint intersections or terminations. A test was
performed to compare the orientations of linear features with the distribution of planar
intersections, taking all possible pairs of the observed planar orientations. The density of
planar intersection orientations (per unit solid angle, radians) is normalized by the number
of unique planar pairs and contoured in Figure 11. The observed orientations match the
distribution of planar intersections well, especially the near-horizontal features. A more
detailed interpretation of the distribution of planar intersections must rely on the spatial
uniformity of the joint distribution which may not be completely valid. The linear features
that trend north or south are also consistent with intersections between cluster planes and
any north-striking vertical joints oriented perpendicular to the minimum stress that may
The earliest concept of the Hot Dry Rock reservoir at Fenton Hill consisted of
fluid flow through a few large vertical fractures striking north, aligned perpendicular to the
minimum principal stress. Initial analysis of seismic data resulted in the idea of multiple,
diffuse fluid paths . Later, results of the 3-point method  indicated the presence of
large planar features in the reservoir. These planes were oriented for shear and were not
oriented perpendicular to the minimum stress direction . The many planar features
identified by our method and their small size relative to the reservoir volume (Figure 8)
imply that the reservoir consists of a jointed volume of rock, with no single fracture
traversing the entire seismically active zone. This brings us to a model of the reservoir in
which water is stored in aseismic joints striking north and dipping near vertical,
perpendicular to the minimum principal stress (s3 horizontal, N104*E). The existence of
such joints is supported by the gradual recovery of wellhead pressure to a level consistent
with the magnitude of the minimum stress (10 MPa above hydrostatic) following reservoir
venting , as well as by the growth of overall reservoir seismicity roughly perpendicular
to the minimum stress direction (Figure 3). These easily opened joints would be low
impedance components of fluid flow paths and would be less likely to be observed
seismically because there is little resolved shear. However, these joints do not extend
uninterrupted for significant distances, otherwise flow communication between the initial
pair of wellbores (EE-2 and EE-3) would have been easily established early in the project
at low injection pressures of 10 to 15 MPa. It therefore appears that these storage joints
are truncated by the joint sets inferred from microearthquake clusters that strike between
north and N45*W and dip 60* in both directions. We envision a “rooftop” model of joints
striking oblique to the water storage joints, providing tortuous, high impedance flow paths
that connect storage joints and enable fluid to move large distances through the rock mass.
The high impedance flow paths are consistent with the high pressures (about 27 MPa)
required to pump a significant amount of water into the reservoir .
We have identified a large number of features in a cloud of microearthquakes
generated by the pressure stimulation of a 3.5-km deep, jointed, Precambrian granitic rock
mass. The locations and orientations of these features are defined by hypocenters of
microearthquake clusters. Similarity in the S- to P-wave amplitude ratios of all
microearthquakes in a given cluster implies a common slip mechanism. The co-planarity
of the hypocenters in many of these clusters suggests planes along which pressure dilation
and slip is occurring. Most of these planes strike parallel to normal faults of the nearby
ring fault system of the Valles Caldera. Of two sets of observed planes, the most
populous dips to the east, similar to the caldera ring faults. Planes are smaller and more
numerous, yet are similarly oriented to features found by applying a 3-point, statistical
method to the microearthquake hypocenters . Given estimates of the stress field from
pressurization and wellbore breakouts, the observed planes are oriented well for shear.
However, many high shear orientations are not observed, indicating that the range of
observed orientations is a reasonably unbiased estimate of the range of actual joint
orientations in the subsurface. Another estimate of stress is very well constrained by focal
mechanisms of the largest microearthquakes, giving the maximum principal stress parallel
to strikes of the observed planar features, but differences between the two stress estimates
are difficult to resolve using pressure dilation and shear relaxation ideas. Linear features
are also common in our set of microearthquake clusters and are related to joint
intersections. The orientations of linear features are consistent with the distribution of
intersections of all possible pairs of the observed planar features. From these results we
envision a “rooftop” model of the reservoir with water storage in joints of limited
dimension oriented perpendicular to the minimum stress. These joints are connected by
high impedance flow paths through joints represented by the observed planar orientations,
striking between north and N45*W and dipping 60* in both directions.
We would like to thank Leigh House, Mike Fehler, Norma McFarland and Rod
Flores for their roles in providing the data used in our analysis and Ruth Bigio and
Florence Fujita for their help with the figures. The paper has benefited greatly from
reviews by Mike Fehler and two anonymous referees. Thanks also to Fred Moreno for
discussions about caldera structure and to Jim Albright for describing early work on
microearthquake waveform clustering. This work was supported by the U. S. Department
of Energy, Office of Basic Energy Sciences, Division of Geosciences and Engineering
under contract W-7405-ENG-36 and the Geothermal Technology Division through its Hot
Dry Rock geothermal energy development program.
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Figure 1. Map showing the Valles Caldera area and the location of the Fenton Hill HDR
Figure 2. Locations of borehole geophone tools (filled circles) deployed during the MHF
experiment. EE-1 and EE-3 are three-component tools while PC-1 and GT-1 are
single-component vertical tools.
Figure 3. Three orthogonal views of MHF seismicity: a) map view, b) cross-section
looking north, and c) cross-section looking west, with circles designating clusters
1 and 2 discussed in the text. Wellbores are indicated where they are not obscured
by the seismicity. Wellheads are represented by filled circles.
Figure 4. Vertical component seismograms for three events each from clusters 1 (top
three) and 2 (bottom three) versus time in seconds relative to the P-wave first
Figure 5. Distributions of the S/P ratio for example clusters 1 (triangles) and 2 (squares),
normalized so that peak values are unity.
Figure 6. Illustration of the two-criteria clustering method.
Figure 7. One of the planar clusters identified by the S/P ratio analysis. Counter-
clockwise from bottom right : view along strike, rotated map view, view across
strike, S/P ratio distribution for this cluster and temporal distribution of events in
this cluster. Hypocenter plots also contain an outline of the solid rectangle used to
view the spatial distribution of planar clusters.
Figure 8. Cross-section view looking west (as in Figure 3c) of the solid rectangles
representing planar clusters. Note locations of plane-wellbore intersections and
the wellbore failure.
Figure 9. Lower hemisphere, equal area projections of (a) poles to planar clusters and (b)
axes of linear clusters identified by the S/P ratio method.
Figure 10. Lower hemisphere, equal area projection of poles to planar clusters (dots),
poles to planar features identified by the 3-point method (triangles) and contours
of the ratio of shear to normal stress acting on a plane as in . Intermediate and
minimum principal stress directions are noted, maximum principal stress is vertical.
Figure 11. Lower hemisphere, equal area projection of axes of linear features (dots) and
contours representing the distribution of planar intersections as described in the