35

3.3. Waveform Cross-Correlation, Earthquake Locations and HYPODD

3.3.1 Method

More accurate relative earthquake locations depend on more precise relative phase

arrival observations so I exploit the similarity of waveforms for pairs of earthquakes in

the frequency domain. Using this technique I will try to produce a better resolved picture

of the spatial distribution of the 2001 Enola sequence. The absolute location of the swarm

may not be better resolved (Figure 15). However, this technique helps to determine the

internal spatial structure of the swarm through event relative locations. I again use

HYPODD to relocate the 2001 earthquakes but this time using relative arrival times of

principal seismic phases recorded at each station.

Figure 15. Station – swarm distances. 2001 Enola earthquakes are spatially confined in a small area, in particular with respect to the station distribution (SW cluster marked with the red circle). Seismic waves leaving from the swarm area are likely to have close to identical paths at a station like GUR, HOL, WOL, etc.

36

Two near-by events, with seismic waves radiating along almost identical paths, are

likely to produce very similar waveforms at the same station. Two earthquakes with

similar waveforms are called a doublet. The waveform similarity is illustrated in Figure

16.

Figure 16. Similarity of the waveforms as recorded on the broadband site (GUR), on the vertical component within an hour of Julian day 182. No filtering applied. There is also at least one converted phase (or maybe a basement reflector) between the P and S phase arrivals. Horizontal scale in seconds, vertical in counts.

37

The site response is assumed to be time invariant for a doublet. The observed spectrum

of an earthquake F(f) at a station is approximately given by:

)()()()( fStfSpfSsfF ⋅⋅= , where Ss(f), Sp(f) and St(f) are the source, propagation and

site response spectra, respectively. Waveform similarity of a doublet requires close to

identical source as well as medium properties. Only doublets recorded at the same station

are correlated (see Figure 15). This technique greatly improves earthquake location

alleviating uncertainties in the phase picking procedure made by a network analysist.

The results of the waveform cross correlation are the weighted time differences

between arrival times of each doublet. Time difference of P and S arrivals are used

separately as an input for HYPODD.

Here I briefly focus on the waveform cross correlation technique and a simple testing

procedure. Appendix B contains several others.

There are two Enola 2001 data subsets. One consists of a data set recorded by the

Kinemetrics’ K2 accelerographs recording at 200 samples per second (200 Hz). The other

was recorded using a Guralp CMG-4, a broadband velocity instrument, set up for the

acquisition at 100 samples per second (100 Hz). Even though the sampling rates are

different, a re-sampling procedure is not required; a doublet is analyzed at one station at

the time.

To process the waveforms I use the Fast Fourier Transform (FFT) on a windowed P and

S phase. P and S wave waveform cross-correlations are executed separately. Later both

results are combined to further constrain earthquake locations.

38

For P phase waveform cross correlation I use the vertical component and the N-S

component for the S phase.

The data preparation is as follows:

1. P and S phase arrivals of the 100 largest events (the algorithm for the selection is

explained in Chapter 2) were manually picked.

2. Using HYPOELLIPSE the earthquakes were located using a velocity model

(Table 3, page 25, Chapter 3.1).

3. P and S arrival times were extracted from the HYPOELLIPSE output files (See

Appendix C for details.)

4. The mean (offset) from each seismogram was removed.

5. Using the results from Step 3 each seismogram was windowed starting 0.15 sec

before the P and S arrivals and ending 0.50 sec after the arrival. This step

separates P from S arrivals.

6. The windowed P and S arrivals were band-pass filtered using a 1 - 40 Hz and 1 -

20 Hz, 4th order Butterworth filter, respectively. A Hanning window tapered off

the trace ends.

7. Fast Fourier Transforms of the windowed P arrivals for each doublet were

calculated. The same procedure was conducted for the windowed S arrivals.

Once the data preparation steps were complete I used the spectral waveform cross

correlation procedure as proposed by Poupinet (1984) to produce relative P and S phase

arrivals for each doublet.

39

The cross spectrum S (f) is defined by:

)( Α ⋅ )(= fff 21 *A )( S (8)

Where A1 and A2 are the spectra of the windowed phases and the asterisk denotes

complex conjugate. The coherence is calculated using the expression:

)()(AS

)( C 21

2

fAff

f⋅

)( = (9)

Spectra A1 (f), A2 (f) and S (f) are smoothed using a 4 point running average window.

The coherence is a direct measure of how similar two spectra are so (9) can be used as a

weighting function.

The phase part Φ(f) of the cross spectrum S (f) (8) is used to obtain the time delay ∆t

between the two windowed signals. By fitting a straight line (least squares method) to

Φ(f), starting from the origin, it is possible to evaluate ∆t from:

ftf ⋅∆⋅=Φ π2)( (10)

So the delay ∆t is proportional to the slope of the line. The least-squares fit is weighted

by a factor at each frequency. Using (9) we can define the weight as:

40

)(1)(

2

2

fCfC

− (11)

Moreover, each time difference ∆t between two doublet/waveforms is associated with

the arithmetic average of C(f) squared. This number illustrates the fidelity of the obtained

time difference for a doublet. The function C(f) ranges from 0 (no spectra similarity) to 1

(spectra are identical). The weighting function (11) fails when the compared waveforms

are identical.

The time differences (∆t) are further processed with HYPODD where additional

reweighting schemes (based on RMS values) may be used. Based on these time

differences for each doublet and files with HYPOELLIPSE individual locations, the DD

can be applied to relocate the 2001 Enola sequence.

The next sequence of figures illustrates a simple test of the waveform cross correlation

algorithm. In this example, a vertical broadband seismogram was delayed by 0.05 sec.

The test consists of running the seismograms through the algorithm in order to obtain the

delay (∆t) based on the P arrival using the presented set of equations. Further tests are

included in Appendix B.

41

Figure 17. A vertical accelerogram at the BAR site. P phase is isolated using the information from the manual pick file. The dimensions of the window are: 0.15 sec before the P arrival and 0.5 sec after the arrival. A 4th order Butterworth band-pass filter, 1 to 40 Hz, was applied before the windowing procedure. I use a simple Hanning window to taper the ends of the traces before calculating the spectra. The red line is the original trace and the blue line is the same trace delayed 0.05 sec.

In Figure 17 the red trace is the “original” filtered P arrival. The blue trace is the same

as the red one delayed by 0.05 sec (20 samples). This is an example of a doublet. So how

far off is the calculated delay using the equation from the given one of 0.05 sec?

42

Figure 18. Amplitude spectra of both traces (the color scheme is preserved: red line is the spectrum of the red trace, and blue line is the spectrum of the blue trace, both from the Figure 17. The spectra are identical as expected from the same waveforms. Note that there is a significant amount of energy (>40 Hz) even after filtering with the 4th order band-pass Butterworth filter with the upper cut-off frequency of 40 Hz.

Waveforms (P and S arrivals) of a doublet are windowed based on an operator pick

file and when plotted on the same axes (as in Figure 17) a certain level of alignment

between waveforms exists. The alignment is directly proportional to how consistent a

network analyst was while picking phases. The first motion of both windowed P arrivals,

for example, will be perfectly aligned (no delay) if the arrivals were picked based on the

43

same criteria. Of course, this zero delay is arbitrary. It is based on the pick file. I call it

the relative (plotting) delay.

Figure 19. Cross spectrum (magnitude) of the two waveforms. The same spectra of the two functions also coincide at the same frequencies (12 and 22 Hz).

The actual time difference (delay) for a doublet depends on the (assumed) small

hypocentral separation between the earthquakes. The earthquakes might have taken place

days/months apart. One earthquake in a doublet (the red trace) defines the time reference

44

frame. The algorithm calculates the travel time necessary for a P wave originating from

the hypocenter to arrive at the station based on the origin and the observed time,

separately, for both earthquakes in a doublet. The observed time is the operator picked P

arrival. The time difference for two travel times (i.e. two P arrivals for two earthquakes in

a doublet) I call the initial delay.

Figure 20. Coherence function between the two traces as given by (9). The weight (quality) of the calculated delay (Figure 21) is expressed as the arithmetic average of C (f) up to 50 Hz (25 Hz for the broadband seismograms) function to the second power (C2(f)). Here the assigned (“quality” of waveform cross-correlation) weight is 0.99985. That is the maximum weight for the perfectly similar (identical) traces. It differs from the expected value of 1 due to numerical rounding.

45

Now the calculated delay (based on P or S arrivals) is sum of the initial and the relative

delays.

Figures 17-20 show two input functions (the “original” and the delayed

seismogram), their spectra, the cross spectrum function and the coherence function,

respectively (see captions for details).

Figure 21. The phase of the cross-spectrum function S (f). Red line is the calculated delay (no weights) between the two traces (Figure 17) as defined by (10). The delay is: 0.049957 sec. Dashed black line (here it coincides with red line) is the weighted best fit (least squares) for the data given by blue dots (the phase of the cross spectrum). See Figure 22. The sample rate of the accelerograph is 200 Hz (0.005 sec/sample).

46

According to Figure 21 the phase stays linear through out the frequency range.

Figure 22 shows the weights based on the coherence function. It suggests that the weights

are different for different frequencies even though the waveforms are identical. The

amplitude of the coherence function (being larger when the cross spectrum reaches

maxima) causes this difference.

Figure 22. Weighted phase. This time, the weights, as given by (11) are used when calculating the least squares fit (note the vertical scale difference in Figures 21 and 22). The delay is now: 0.049956 sec. So the calculated and weighted delays differ from the initially given delay of 0.05 sec for barely 0.000043 and 0.000044 sec, respectively! Note that the sampling rate is 0.005 sec. Thus, the precision of the technique (in this “ideal” case) is ~ 100 times the rate of data acquisition!

47

Note the order of magnitude of the phase (106). The coherence (based on smoothed

spectra) for the identical waveforms barely departs from 1 (Figure 20). Therefore, this

large order of magnitude is due to large weights. Numerical rounding and the numerical

implementation of (11), when the denominator gets very large, give “humps” in the

weighted phase spectrum. The “humps” coincide with the maxima in the cross spectrum

and coherence function (~ 12 and ~ 22 Hz, Figure 19 and Figure 20).

Figure 23 shows the cross-correlation method for a real earthquake doublet.

48

Fig

ure

23. A

tes

t ba

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on t

wo

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ear

thqu

akes

. The

inp

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ual

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over

.

49

Figure 24. The format of the waveform cross correlation output is further used as a HYPODD input file. Bold letters are doublets ID’s. In the same line, zeroes indicate the correction for the origin time when the cross correlation data are used together with catalog data (i.e. an analyst phase picks) and the cross correlation and the catalog data have different origin times stored in the file headers. The first column lists station codes where a particular doublet is observed. The second column represents relative time differences (in seconds) for doublets as obtained using the cross correlation technique. The third column contains the “quality factor” for the cross correlation (Figure 20). The fourth column list the phase used for the doublet (P for a P and S for an S phase, respectively). Weights of 1 are due to numerical rounding (weight ≥ 0.999).

At the very end an output file is automatically generated as a product of the waveform

cross correlation (Figure 24). This is the input file for HYPODD.

50

3.3.2. Results

This time I use relative phase arrival times produced by the waveform cross-

correlation technique as input to HYPODD (example Figure 25). The resulting analysis

yields the final picture of the 2001 Enola earthquake locations. Following the data

subdivision scheme of Chapter 3.2.2. I separated the location procedure into:

Figure 25. 2001 Enola earthquake locations. The blue triangle is ENO site. Black dots are earthquakes located using HYPOELLIPSE on both P and S arrivals (individual-loc). Red dots are earthquakes located using only waveform cross correlation data for P arrivals. Error bars are on the order of meters.

51

a) earthquake locations using P waveform cross-correlation data

b) earthquake locations using S waveform cross-correlation data

c) earthquake locations using P and S waveform cross-correlation data

It appears that the earthquakes form two clusters, based on separate P and S relative

arrival times (Figure 25 and Figure 26). The one to the north, based on this map view,

seems to be separated from the one to the south by a seismically quiescent zone.

Figure 26. 2001 Enola earthquake locations using S waveform cross correlation technique. The locations are very similar to the ones in Figure 25 where only P phase data are used. Location errors (on the order of meters) are too small to be noted in the figure.

52

The DD algorithm considered 90 out of 93 individually located earthquakes. Both

clusters (based on the map view) show a certain degree of lineation (striking NW-SE).

Figure 26, where only S arrivals are used, does not reveal significant changes in the

shape of the clusters as compared to Figure 25, where only P arrivals are used. The SW

cluster seems to be moved closer to the NE cluster (referenced to black dots,

HYPOELLIPSE locations in Figure 15).

More important, the internal (epicentral) structure of the clusters changes to some

extent but it is difficult to draw unequivocal conclusions based solely on the map view.

Figure 27 shows earthquake locations constrained using both P and S arrivals. I believe

this to be the final and “most trusted” picture of 2001 Enola relative earthquake locations.

Both P and S relative arrivals are calculated using the highly reliable waveform cross

correlation technique. The location errors (HYPODD) are on the order of meters.

The single event locations obtained using HYPOELLIPSE (black dots, Figure 27)

provide the spatial reference frame and the waveform cross-correlation locations reveal

the internal structure of the 2001 sequence. The HYPOELLIPSE single event locations

give a general picture of the swarm location. The relative locations, on the other hand,

show a very accurate picture (errors on the order of meters) of the swarm’s internal

spatial structure. The earthquakes do not appear to be aligned on a single fault plane. Nor

do the clusters seem to be clearly outlining separate fault planes. However, each cluster,

based on the map view (Figure 27), appears to have a NW-SE trend.

53

Figure 27. 2001 Enola earthquake locations (total of 90) using both P and S waveform cross correlation data.

The cross sections (Figure 28) reveal clustered 2001 Enola seismicity. The clusters

seem to be connected by a cloud of seismicity at the depth of ~ 5 km where the Paleozoic

– Precambrian boundary is.

Based on waveform similarity more earthquakes could be selected and sorted in groups

with a common source. I speculate it would be possible to get a more comprehensive

picture of the 2001 Enola earthquake clustering if more earthquakes were located. I do

not think more clusters would be revealed. The largest earthquakes define the main

seismicity zones.

54

Figure 28. NS and EW cross-sections. Earthquake locations are constrained with both P and S waveform cross correlation data. The major seismicity lies within a 1.5 kilometer-thick layer at the depth of the Precambrian basement. There are two apparent clusters of seismicity (left plot). The one to the south appears to be deeper. Both clusters seem to share a common cloud of earthquakes at depth of ~ 6 km.

Adding more locatable earthquakes is not an easy problem. The whole data set of the

2001 sequence should be organized in a database that would ease associating an event

with multiple stations. This is evident even for a relatively small data set such as the 2001

Enola earthquake sequence.

55

Figure 29. Two location cubes show two clusters of seismicity, in particular the cube to the left. The deeper SW cluster, to the left in the left 3-D section, (the SW cluster in Figure 27) may appear as westward ~ 50º dipping, SW-NE striking (appears as a NW-SE lineation on the map view in Figure 27). Its 3-dimensional shape seems to be tubular rather than planar.

Figure 29 does not reveal a simple faulting geometry. The SW cluster exhibits a sort of

tubular shape. It is not clear, at this point, whether that shape developed from depth

towards the surface (temporal migration) or it was completely random in time.

The spatial dimension of the Enola seismicity does not allow me to resolve the “single

fault” question in a less opaque manner. However, I cannot completely rule out a

possibility that these two clusters indeed form a fault plane that ruptured in patches with

an aseismic zone between them. Moreover, there could be two separate fault planes

which dimensions are only indicated by the size of the clusters.

Several factors make an interpretation of the 2001 sequence in a tectonic and structural

context very difficult. These factors include absence of mapped faults in the strict swarm

56

crustal volume, lack of apparent fault planes (based on the earthquake spatial structure)

and clustering of seismicity both in space and distinctively in time.

It is not likely that the Enola zone would produce an earthquake of magnitude 6 or

higher due to the small, possibly highly fractured source volume and the shallow depth of

the earthquakes (Chiu et al., 1984).

Not only does the entire Enola zone occupy a small crustal volume, some 10 km3, but

the seismicity even within this small volume is tightly clustered. The clustered character

of seismicity stresses the importance of the specific, highly concentrated seismogenic

properties. Moreover, the clusters do not show a definite lineation that might be

interpreted uniquely as a fault plane. This might indicate that the zone at the hypocentral

depths is filled by small scale fractures that failed producing small size earthquakes.

The migration of seismicity, discussed further in the next chapter, indicates a possible

role of fluids in the Enola earthquake factory. Špicák and Horálek (2001) discussed

migration of seismicity during an intraplate swarm, possibly controlled by fluids,

pointing out a possibility that the swarm might not have happened otherwise.

The clusters seem to connect at a depth of 5-6 km by diffuse seismicity. Closer to the

surface the connection disappears. Maybe by locating more earthquakes this apparent

aseismic gap would be filled with smaller size earthquakes. The located largest

earthquakes, in my opinion, define well enough the shape of seismicity of the 2001

sequence. It is possible then that fluids have migrated, originating from depths of ~7-8

km, splitting in two channels at ~5 km and diffusing into the cluster defined zones

helping fractures to fail and produce the earthquakes. Examining the steep dipping

geometry of the cluster could support this hypothesis.

57

In my opinion the rest of the 2001 Enola seismicity would also group within the two

clusters, organizing some 2,500 earthquakes, separated already by the order of 10s of

meters in a highly concentrated seismogenic zone.

What could be causing this highly localized seismogenic zone still remains

unanswered.

The 1982 sequence was the first seismic episode to be observed instrumentally in the

Enola region. Over a period of 2 years the sequence produced over 30,000 earthquakes.

Now, 20 years later another 1982-like seismic episode took place within the same 4 x 4

km area this time a bit less productive in terms of earthquake numbers, producing some

2500 earthquakes over a period of 2 months. Even though the instrumented time spans

are different, the daily seismicity rates for both swarms reveal that the 1982 sequence was

more abundant in earthquake production. This tremendous number of earthquakes,

relatively small in magnitudes (M < 3) was located in a ~ 8 km3 crustal cube centered at ~

4 km depth. Paleozoic sandstones and carbonates occur up to a depth of ~ 5 km where the

Precambrian basement starts (Schweig et al., 1992). Despite numerous faults surrounding

the Enola region that could have been as good, if not more favorable, hosts of the

seismicity, a region without mapped faults produced both sequences. An evidence of

clear lineation that could be interpreted as a fault/s has not been found for the 1982

sequence (Chiu et al., 1984).

58

3.4. The Earthquake Chronology

Figure 30. Chronology of 2001 Enola sequence. The left plot shows the activity up to 152 Julian day (second to last burst in seismicity. See Figure 4, Chapter 2). Plot on the right (blue dots) shows the activation of the shallow cluster (to the NE). “Blue” earthquakes occurred in just two days, day 181 and 182 (the last burst in seismicity. See Figure 4, Chapter 2).

The 2001 Enola sequence exhibits a peculiar migration in time. The NE cluster was

barely active until the last few last days of the network deployment (Figure 30). It

remained activate only for two days producing about 50 large size earthquakes (within

the population of 100 biggest). This cluster also contributes one of the largest earthquakes

in the 2001 sequence. The deeper SW cluster did not have a distinct time pattern. The

earthquakes in this cluster occurred at different depths over a period of about two months.

Chiu et al. (1984) investigated the spatial migration in time for the 1982 sequence,

grouping 88 events in 12-day periods. The epicentral region of each major sequence, i.e.,

a mainshock plus intermediate foreshocks and aftershocks was aseismic before the major

sequence commenced. The seismic activity before each major sequence occurred in the

59

region surrounding that activity. As the major sequence developed, the surrounding zone

went seismically quiet. They further concluded that these observations indicated that

patterns of strain accumulation and release in the swarm source zone had developed and

changed in short periods of time – hours to days.

Putting together the above observation with the fact that the 2001 sequence also

shows temporal migration (considering the largest selected earthquakes and their

clustering on day 182) brings the temporal similarity of both sequences to our immediate

attention.

What temporal process could lead to observed clustering for both sequences separated

by 20 years? Would it be possible that the proposed fractured media in the strict swarm

area (Chiu et al. 1984; Schweig et al. 1991 and Booth et al., 1990) is filled with fluids

that migrated during both sequences in a similar manner and controlled the seismicity

rates both spatially and temporally?

There is one more thing that needs to be mentioned: Selecting the 100 largest

earthquakes and plotting them chronologically does not necessarily mean that the

seismicity of the deep SW cluster “shut off” when the shallow NE cluster emerged. It

only brings out the fact that these last ~ 50 earthquakes on 182 Julian day were larger

than possible smaller magnitude events that might have been filling out the volume of the

deep SW cluster.

Again, these 100 largest earthquakes illustrate the main features but leave the picture

of the 2001 sequence seismicity a bit incomplete. Locating more earthquakes would

theoretically complete the spatial and temporal behavior of the 2001 sequence.