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Evidence for the splitting of shear waves from waveform and focal mechanism analyses
238
Physics of the Earth and Planetary Interiors, 61 (1990) 238—252 Elsevier Science Publishers B.V., Amsterdam — Printed in The Netherlands
Evidence for the splitting of shear waves from waveform and focal mechanism analyses Satoshi Kaneshima 1, *, Naoki Maeda 2 and Masataka Ando ~ ‘Earthquake Research Institute, University of Tokyo Yayoi 1-1-1, Bunkyo-ku~Tokyo 113 (Japan) 2 Department of Geoscience, National Defense Academy, Yokosuka 239 (Japan) ~Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji Kyoto 611 (Japan) (Received September 19, 1989; revision accepted December 24, 1989)
Kaneshiina, S., Maeda, N. and Ando, M., 1990. Evidence for the splitting of shear waves from waveform and focal mechanism analyses. Phys. Earth Planet. Inter., 61: 238—252. A temporary seismograph station was sited above the aftershock area of an intermediate crustal earthquake (M 4.9) in the Kinki district, Japan. The results from analysing digital three-component seismograms and numerically determining focal mechanisms of aftershocks have provided clear evidence for the splitting of shear waves attributed to crustal anisotropy. Faster shear waves from most of the aftershocks are polarized WNW—ESE, regardless of their azimuths and incident angles. Such shear wave motions are often significantly inconsistent with the focal mechanisms of the aftershocks determined using P-wave first motions. For many of the events, slower shear waves, polarized orthogonally to the faster shear wave direction (NNE—SSW), are observed to arrive about 0.1 s later. Two vectors showing particle motions of faster and slower shear waves in the horizontal plane are summed, to reconstruct polarizations of shear waves before splitting. For events with sufficiently high signal-to-noise ratios of shear waves and well determined focal mechanisms, the reconstructed polarizations are consistent with the focal mechanisms within the range of uncertainty. Such consistency is not clearly detected for the other events, possibly because of large noise effects and poorly constrained fault-plane solutions The direction of faster shear wave polarization (WNW—ESE) generally coincides with that observed at three other stations located within 15 km of the temporary station. In the study area, the fabric of crustal anisotropy is almost uniform over the scale of 15 km. but appears to exhibit small local fluctuations.
1. Introduction Recently the number of reports on the observations of shear wave splitting attributed to crustal anisotropy have been increasing (Booth et al., 1985; Kaneshima et al., 1987). Most of such studies have examined shallow crustal earthquakes (focal depths less than about 15 km), and have observed parallel or sub-parallel alignments of faster shear waves. Such alignments are commonly inter*
Present address: Department of Terrestrial Magnetism, 5241 Broad Branch Road, N.W. Washington, D.C. 20015, U.S.A.
0031-9201/90/$03.50 © 1990
—
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preted as the results of shear wave splitting (Crampin and McGomgle, 1981; Booth et al., 1985). Arrivals of slower waves polarized orthogonal to the faster waves are more crucial evidence for the phenomenon. Such split arrivals of shear waves, however, are much more difficult to detect than parallel alignments of faster shear waves. This is because slower shear waves are quite easily masked by reverberations after faster shear wave arrivals, which may be diffracted either by lateral crustal heterogeneities or by surface irregularities (Kaneshima and Ando, 1989). A parallel alignment of faster shear waves could be generated
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EVIDENCE FOR SPLI1TINO OF SHEAR WAVES
either by surface irregularities, or by some particular combinations of earthquake focal mechanisms. An observed parallelism of faster shear waves, thus, should be treated cautiously, when split arrivals of two shear waves are not clearly recognized on three-component seismograms of each earthquake. It is desirable to examine shear wave polarizations radiated from double-couple sources and before anisotropy-induced splitting, by determining fault-plane solutions of each earthquake used in shear waveform analyses. Unfortunately this is not easy owing to some reasons described below. In splitting analyses, shear waves with incident angles less than the critical angle (350 for the Poisson’s ratio of 0.25) should be examined, in order to minimise waveform distortion generated by the free surface (Nuttli, 1961; Evans, 1984). This restriction usually forces us to select earthquakes with smali epicentral distances (< 10 km when using crustal earthquakes). If an earthquake takes place within 10 km from a station and is > M = 2, it is commonly difficult to obtain complete (unsaturated) three-component seismograms of the earthquake in ordinary seismic observations owing to the lack of a high dynamic range recording system. However, the ordinary spacing of permanent seismograph stations in Japan (longer than 10 km in most places) means that an earthquake must be > magnitude M =2, for the reliable estimation of its focal mechanism. Therefore, we are faced with the difficulty of obtaining unsaturated seismograms and a well— constrained focal mechanism of an earthquake at the same time. Ando et al. (1980, 1983) analysed waveforms of deep earthquakes (focal depth of about 300 km) on the subducting Pacific Plate beneath Honshu, Japan, and detected clear split arrivals of shear waves passing through the upper mantle which is possibly partially molten. They also found that shear wave particle motions corrected for splitting effects are consistent with the double-couple focal mechanisms. Further evidence for shear wave splitting attributed to upper-mantle anisotropy has been detected on shear wave seismograms of ScS phases from deep earthquakes (focal depths of about 500 km) (Ando, 1984; Fukao, 1984). These —
—
upper mantle studies analysed shear waveforms
with much lower frequency (0.1—1.0 Hz) than in ordinary crustal studies (5—10 Hz). Kaneshiina et al. (1987) and Peacock et a!. (1988) indicated that the observed faster shear wave particle motion directions significantly differ from those calculated from the fault-plane solutions. However, they did not try to recover source radiation of shear waves using the slower split shear waves. Detailed polarization studies of crustal earthquakes similar to the upper-mantle studies are required for reiable detection of shear wave splitting due to crustal anisotropy. In this work we perform such polarization studies on crustal earthquakes of an aftershock sequence in the Kinki district of Japan, which were recorded at a seismograph station close to their epicenters. Point source double-couple fault-plane solutions of many of those earthquakes are determined as objectively as possible using both the polarities and amplitudes of P-wave first motions, and the uncertainty in their determination is estimated. Incident shear wave particle motions are reconstructed from the observed split shear waves from the aftershock sequence, and cornpared with the shear wave polarizations generated by the focal mechanisms.
2. Aftershock observation On May 28, 1987 an intermediate earthquake (M = 4.9, determined by the Japan Meteorological Agency (JMA)) occurred near the centre of the seismic network of the Abuyama Seismological Observatory, Kyoto University (35 O()() ‘N, 1350 32’E, depth = 17 km, by the JMA) (Fig. 1). This is a typical thrust-type earthquake with the P-axis striking E—W (Maeda, 1988), followed by a sequence of aftershocks continuing for about six months. During about three months, from July to September 1987, a short-term seismograph station Kameoka (KMO) was sited just above the aftershock area (Fig. 1). The station was located on the hillside of a mountain with an elevation of 430 m, equipped with three-component velocity seismographs of 1-s free period. Signals are low-
240
S. KANESHIMA ET AL.
pass filtered (cut-off frequency 30 Hz) (bike and Matsumura, 1985), digitized with a sampling rate of 210 Hz, and recorded on a floppy disk using a personal computer (NEC, PC-9801E) (Hirano, 1986). The dynamic range of the recording system is 12 bits (66 db). Three-component digital seismograms of more than 70 aftershocks were obtained during this observation. Their hypocentres were located using P-wave arrival times at the telemetered stations of the Abuyama Observatory (solid circles in Fig. 1) (Maeda, 1988). The velocity structure used in the hypocentre location is a horizontally layered model (Table 1) (Maeda and Watanabe, 1984). Out of 51 well-located aftershocks, 40 events with incident angles less than 350 have been used for our waveform analysis and their hypocentres are shown in Fig. 2. The azimuths and incident angles of the earthquakes are listed in Table 2. Figure 3 shows examples of seismograms and particle motion di-
~~
agrams recorded at KMO. The local magnitudes of the events are in the range M = 0.0—2.3. For most of the events, epicentral distances are less than 5 km and focal depths are about 12 km (Fig. 2). Incident angles of shear waves of most earthquakes are less than 150, and therefore the effects of a free surface on shear waveforms will be small.
3. Analyses and results 3.1. Shear wave splitting In an elastic medium there exist two shear waves, which are degenerate, as long as the medium is isotropic (Aki and Richards, 1980). If the medium possesses any type of seismic anisotropy, the shear waves separate into two orthogonally polarized quasi-shear waves with different propagation speeds (Nur, 1971; Crampin, 1978). This
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EVIDENCE FOR SPLn-riNo OF SHEAR WAVES
TABLE 1
ough understanding of the primary cause of the
P-wave velocity structure of the crust below KMO
crustal anisotropy beneath KMO. In this study we
phenomenon is called ‘shear wave birefringence’ or ‘shear wave splitting’. The cause of crustal anisotropy generating shear wave splitting may be
assume that the crustal medium beneath KMO possesses seismic anisotropy of hexagonal type with a vertical symmetry plane, which can be generatedby a parallel alignment of vertical cracks (Crampin, 1978; Hudson, 1981) (Fig. 4a). Kaneshima et al. (1987) suggested that the crustal medium below a station only about 10 km south of KMO possesses the seismic anisotropy induced by such a crack alignment. Our assumption, there-
preferred orientation of minerals, or alignment of cracks, or periodic thin layers. There is theoretical and observational evidence to support the theory that in the crust crack alignment mainly generates anisotropy (e.g. Crampin, 1987). At the moment, however, we have no critical information that would enable a thor-
fore, seems conceivable, although it should be confirmed by considerable observation. Theoretical studies indicate that for this type of anisotropy faster shear waves are polarized parallel to the crack strike (Crampin, 1978; Crampin and McGonigle, 1981) and slower split shear waves polarized orthogonal to the faster waves (Fig. 4a).
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S. KANESHIMA ET AL
TABLE 2 Ray path and split shear wave parameters of local earthquakes recorded at KMO No.
DL(°)
DC(°)
1 3
AZM(°) 327.0 150.1
INC(°) 4.0 5.5
267 120
~‘N~’
4 6
62.5 168.0
10.8 5.3
120 114
7 8 9 10 11 12 13 14 15
148.9 144.7 158.5 116.9 99.4 101.7 130.9 126.7 68.0
8.0 2.9 13.5 22.8 10.6 10.6 3.4 10.4 11.2
209 291 329 111 96 130 117 125 305
16
66.3
11.6
244
17 18 19 20 21 22 24 25 26 27 28
199.1 122.8 254.2 129.7 116.8 112.2 323.2 1.6 143.6 65.0 138.3
21.6 4.7 0.8 3.8 19.8 8.4 1.4 24.2 20.7 5.3 29.0
297 119 220 309 118 105 283 305 308 118 114
29 30 31 32 33 35 37 39
105.6 74.3 165.8 167.5 98.3 100.3 96.1 57.2
10.2 23.4 13.9 10.5 7.2 7.6 7.0 4.9
108 3 115 114 114 114 113 104
41 45 46 47 48 49 50
119.1 87.1 83.9 117.0 119.9 154.7 131.7
32.3 15.1 33.9 5.1 3.1 5.4 9.8
114 124 116 88 280 25 108
—17— 22 60 — 80
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Type
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112 —131 52—119
311 (i) 74(i) 169 (e) 130 (e) 65 (i)
0.03 0.07 0.11 0.04 0.08
192 — 244 —11—10
240 (i) 53 (e)
* * *
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*
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172 —188 118—176 (T-axis) 71—94
172 (e) 82 (i)
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* * *
* * *
*
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84 —142 40 — 60 55 — 95 163 — 205 31— 126 (T-axis)
150 (i) 65 (i) 67 (i) 76 (i) 69 (i)
B 0 0 N B
0.10 0.07 0.07 0.07 0.09
* * *
* * *
*
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0.07
* * *
Null-axis 66 — 93 84 —134 (Null-axis) 60— 134 (Null-axis) Null-axis 75— 85 * * *
241 146 86 330
(i) (e) (i) (e)
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0 *
0 B
0.10 0.00
*
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68 (e)
76 (i)
0 N
0.10 0.03
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313 (i)
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0.03
Azimuth (AZM), incident angle (INC), and all other orientations are measured clockwise from north. DL, DO, and DC indicate the faster shear wave particle motion direction (Af), the shear wave radiation before splitting (At), and the range of shear wave particle motion directions calculated from feasible focal mechanisms (A~J,,),respectively. The symbols ‘i’ and ‘e’ denote impulsive and emergent arrivals of shear waves. ‘Type’ classifies the events according to the fitness of the orientations of A~or A to the ACm directions as follows; (0) As,, is consistent with A’,,; (F) A 1 is consistent with A~,,;(B) both As,, and Af are consistent with A~(N) neither A~,nor ~ are consistent with A’~m.DT indicates delay time between faster and slower shear waves, measured on the rotated seismograms as the difference in arrival times between the split shear waves.
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Fig. 3. Examples of three-component seismograms: observed Up-Down, North-South, and East-West seismograms (top left); radial (TA) and transverse (LR) seismograms (bottom left). T, A, L and R indicate the direction toward (1) and away (A) from event, left side (L) and right side (R) viewing station from the event. Particle motion diagrams are giveii for the intervals shown in the rotated seismograms with bars (right).
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and A, are the vectors indicating the partide motions of the initial shear waves at the source point, the faster shear waves, and the slower split shear waves, respectively. (b) and (c) schematic figures showing our reconstruction procedure.0(b) E,Recorded and S20°horizontal W, which seismograms are, respectively, (top),parallel and seismograms to, and orthogonal rotated totoshow the faster the horizontal shear wave ground motions motion (bottom). in the (c) directions (left) Two Nibvectors showing how the
particle motions of the faster shear wave (A 1) and slower shear wave (A,) are added to recover the shear wave radiation before splitting at the source (A9,,). The particle motion is compared with Am (top right) which is calculated from the fault-plane solution (bottom right). Thin solid lines in the fault-plane solution represent the projection of shear wave polarization directions. The symbols P and T indicate the P-axis and the T-axis, respectively. Attenuation factors of faster and slower shear waves are assumed to be identical.
3.2. Reconstruction of shear wave radiation before splitting
Our waveform analysis comprises the four steps described below. First, the ground motion directions of the faster shear wave arrivals are inspected using diagrams of particle motions in the horizontal planeof(Fig. 3). waves The faster partide with motion directions shear are plotted arrows on equal area projection diagrams (Fig. 5). These equal area diagrams show that the faster shear waves are approximately polarized Nib0 E— Silo0 W regardless of their azimuths
and incident angles (Fig. 5). It is also obvious that most of the exceptions are deduced from unclear shear wave arrivals (dotted arrows in Fig. 5). Such aligned polarizations of faster shear waves are often interpreted as evidence for shear wave splitting (e.g. Booth et aL, 1985; Kaneshima et al., 1987). From now on, we call N110°Ethe 0 W: (posinegative) and fasterS20° shear directionslower (Sib shear wave tive) W wave the (positive) direction (N20 °E:negative). Second, the observed horizontal component seismograms (north—south and east—west) are rotated into the seismograms of the faster shear
245
EVIDENCE FOR SPLITFING OF SHEAR WAVES
(a)
KMO N=
4.0
(b) N= 30
Fig. 5. Equal area projections of faster shear wave particle ‘motion directions (indicated by solid and broken arrows) out to the incident angles of 350 (a) and 150 (b). Solid and broken arrows indicate reliable and less reliable data, respectively.
wave (Nib0 E— SilO0 W) and the slower shear wave (S20 0 W—N20°E) directions (Fig. 4b). Since both shear waveforms contain significant amplitudes of the vertical component, a 3-D rotation of the coordinate axes might be preferable. Nevertheless, in this case the short-term seismograph sta-
It should be emphasized that only relative amplitudes of the two shear waves, not absolute amplitudes, are considered here. Absolute amplitudes could be seriously affected by many factors, such as source intensity (magnitude), radiation pattern, and focusing and defocusing due to lateral hetero-
tion is located very close to the centre of the aftershock area, so that most of the shear waves have incident angles less than 150 at the surface. We believe that the 2-D rotation of the coordinates (in the horizontal plane) used in our analysis is meaningful as the first approximation and does not lead to erroneous results. In the third step, relative amplitudes of the faster (Af) and slower (AS) shear wave pulses (background noise level to first peak) are inspected on the rotated seismograms (Fig. 4b, bottom). For the events with sufficiently impulsive shear waveforms (classified as Type ‘i’ in DO column in Table 2), the measured amplitudes are reliable possibly with an error less than 20%. For the
geneity in the crust. On the other hand, relative amplitudes between faster and slower shear waves are expected to be insensitive to such factors, because both shear waves propagate along approximately the same ray path as long as anisotropy is weak. Finally, these two vectors are summed to reconstruct shear wave motion radiated from the source (A~in Fig. 4c), which will be termed ‘shear wave radiation before splitting’. Before summation of the two vectors, we should correct for the effects of seismic attenuation which can differ between the faster and slower shear waves. The contributions of an alignment of cracks to the inverse of quality factor (l/Q 1 and l/Q2 for faster shear wave and slower shear wave, respectively) have been evaluated by Hudson (1981) and Crampin (1984). The typical ray path length (L), the dominant frequency of shear waves (f~)~ and the average shear wave velocity (J’) for this study may be approximately taken 1. The values of as 1/Q15 km, 10 Hz, and 3.5 km s 1 and l/Q2 calculated
events with emergent shear waves (Type ‘e’ in Table 2), on the other hand, the amplitudes should involve a much larger error. Since the particle motion directions of faster and slower split shear waves have been presumed, we obtain two 2-D vectors showing particle motions in the horizontal plane of two split shear waves (Af, A~in Fig. 4c).
246
S. KANESHIMA aT AL.
from the formula by Hudson (1981) are about 0.0001 and 0.001, respectively, for the propagation of 10-Hz shear waves (V5 3.5 km s~)through
the initially radiated shear waves and we are not
an elastic medium containing thin cracks of 20 m radius and a crack density of 0.1. The attenuation coefficients of slower shear waves exp[ irf0 L/ Q2J’~] are 0.8—0.9 times those for faster shear waves exp[ I7f0L/Q1J’~].The difference in dissipation between the two waves, therefore, amounts to 10—20% at most. The difference may be overestimated, since, as will be discussed later, the crack density estimated for this area is smaller than 0.1. Consequently, it would be difficult to detect such small differences, even if the shear wave seismograms have sufficiently high signalto-noise ratios and focal mechanisms are well determined. In this study we assume that the difference between the attenuation factors of the two shear waves is negligible. It must be emphasised again that we examine only the polarization angles of
3.3. Numerical estimation of the fault-plane solutions
concerned with their absolute amplitudes.
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Fault-plane solutions of the aftershocks used in the shear waveform analysis are determined using the polarities (up and down) and amplitudes of P-wave first motions recorded at the telemetered stations of the Abuyama network (solid and open circles in Fig. 1) (Maeda, 1988). It is usually difficult to uniquely determine fault-plane solutions of micro—earthquakes (M < 2). We apply a numerical fault-plane solution determination method (Aoki, 1986; Maeda, 1988) to the aftershocks. This method uses Fourier analysis for a P-wave polarity distribution function on a focal sphere (for example, +1 for positive first motions, —1 for negative motions). A Null-axis is sought on the focal sphere. For each Null-axis supposed,
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Fig. 6. (a) Typical best-fit fault-plane solutions of the micro—earthquakes used in this study. Open and solid circles indicate dilatation and compression, respectively. F- and T-axes are shown as open squares and crosses, respectively. (b) Equal area projection of P-axes in the best-fit fault-plane solutions. The outer circle shows the dip of 900. (c) as (b) for the T-axes.
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EVIDENCE FOR SPLI1TING OF SHEAR WAVES
the focal sphere is rotated so that the Null-axis becomes vertical and the polarity should be a function of azimuth only. The polarity distribution is approximated by a periodical square function with a period of ~r.The direction of a nodal plane is constrained by the phase angle of the Fourier component at period i~. For the solutions which fit the observed P-wave polarities at all stations, the P-wave amplitudes are calculated using an empirical formula and are compared with the observations (Maeda, 1988). Any solution With a standard deviation of less than 0.4 of the residual logarithmic amplitudes, which represents the differences between the calculated and the observed logarithmic amplitudes, is considered as a feasible solution. Then we estimate the uncertainty involved in the fault-plane determination, considering the diversity of the feasible solutions. Fault-plane solutions of about 30 out of the ‘~ events used in the waveform analysis are well determined (Fig. 6). Both thrust and strike-slip earthquakes with P-axes striking nearly E—W have occurred. As shown in the equal area plots of P and T-axes (Fig. 6b and c), thrust-type earthquakes, similar to the main shock, are dominant (Maeda, 1988). There is no significant difference in the focal depths between the strike-slip events and the thrust events, We calculate the horizontal particle motion directions of shear waves radiated from a doublecouple point source (A’~m in Fig. 4c), using the formulae of Aid and Richards (1980). Here we assume the horizontally layered structure given in Table 1 as the velocity model beneath the temporary station. Although no information about detailed 3-D crustal structure is available at present, it may be reasonable to use such a layered model as the first approximation. We also assume
3.4. Effects of the uncertainty in hypocentre location
To estimate uncertainty of shear wave motions, location errors of the aftershocks should also be assessed. In this study the aftershocks are located using P- and S-wave arrival times recorded at the telemetered seismograph stations belonging to the Abuyama network (Fig. 1). Errors in the epicentre locations have been estimated to be <0.25 km in the aftershock area (Maeda and Watanabe, 1984). Focal depth errors have not been explicitly evaluated, but are expected to be less than twice those of the epicentres. We relocate the aftershocks used in the waveform analysis using a kind of master event technique, which is almost equivalent to the joint hypocentre determination (JHD) (Ito and Kuroiso, 1979). One of the aftershocks recorded at more than 10 telemetered stations is selected as the master event. Other events are located relative to the master event. The nominal absolute hypocentres of the aftershocks are calculated by adding the hypocentre coordinates of the master event to their relative coordinates. This process is repeated with each of 17 aftershocks being selected as the master event. For each aftershock, the standard deviations of the nominal hypocentre coordinates are considered as the error of the location. The result shows that, for most of the events, the errors of epicentral distances and focal depths are expected to be less than 0.15 km and 0.3 km, respectively. These correspond to the errors of azimuths and incident angles of 50 and 10, respectively. Such small errors are found to only slightly widen the uncertainty range of Ac,~and hardly affect the results.
that relative amplitudes of the split shear waves are not seriously affected by laterally heterogeneous structure beneath the station. Because of the non-uniqueness of the focal mechanisms, the orientations of ACm are scattered across a considerable range (the hatched fan shape in Fig. 7). The orientations of A~,,are compared with those of the
3.5. Evidence for shear wave splitting
shear wave radiation before splitting (At) (see Fig. 4c).
arrow), A95~ (thick solid arrow), and the range of ACm calculated from the solutions (hatched fan
Slower shear wave arrivals have been identified on the rotated seismograms of 27 out of the 40 aftershocks used (Table 2). Some examples are
shown in Fig. 7, together with feasible fault-plane solutions, A1 (thin solid arrow), A~(thin broken shape).
248
S. KANESHIMA ET AL
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Fig. 7. Feasible fault-plane solutions, together with the P-wave first motions (open circle: dilatation, solid circle: compression), P-axes (squares) and T-axes (crosses), are shown in the top left diagrams in Fig 7(a)-(d) for four different events. The horizontal seismograms in the set of three component seismograms on the right of each figure are rotated so that one of the two traces indicate ground motion in the direction of Ni10°E—Sii0°W, which is the faster shear wave polarization direction, and the other is in the orthogonal direction S20°W—N20°E. The amplification of the vertical component seismograms is one fifth of those of the horizontal components. The thick solid arrow, thin solid arrow, thin dashed arrow in the bottom left diagrams indicate A°,,(shear wave radiation before splitting), A (faster shear wave particle motion), and A~(slower shear wave particle motion), respectively. The 0m calculated from the feasible focal mechanisms. hatched fan shape represents the range of the orientations of A
249
EVIDENCE FOR SPLITTING OF SHEAR WAVES
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Most of the events which show the A~direction approximately within the range of Am orientations have impulsive waveforms of faster and
slower shear waves (Fig. la—c; Type 0 in Table 2). For these events, the directions of Af do not coincide with those of A~even after considering
250
S. KANESHIMA ET AL.
non-uniqueness of the focal mechanisms. Inconsistency between faster shear wave particle motion and focal mechanism has already been reported by Kaneshima et al. (1987) and Peacock et al. (1988). The examples in this study not only show such inconsistency but also indicate that the shear wave radiation before splitting is consistent with the feasible fault-plane solutions. Significant mismatch between the directions of A~,and ACm tends to be observed for the events which show emergent arrivals of faster and slower shear waves (Type N, Table 2). The mismatch is, therefore, likely to result from misreading of shear wave arrivals. For four events of Type B, the A~ direction is poorly constrained (Table 2; Fig. 7d), since the temporal station is located near the T-axis or the Null-axis on the focal sphere. Consequently, both As,, and A have their orientations within the range of ACm directions. There is a case for which A rather than A~,,is consistent with the ACm direction regardless of its impulsive waveform (Type F, Table 2). Although we have no reasonable explanation of such an exception, it could be attributed to noise in the seismogram or errors involved in the focal mechanism determination, It is remarkable that most of the events showing consistency between the orientations of A~ and A’~m have incident angles smaller than 100 (Type 0, Table 2), while many of the events showing a poor match (Type N and Type F, Table 2) have incident angles larger than 100. For the former events, shear waves may suffer only minor waveform distortions owing to heterogeneity just beneath the station, and therefore, our reconstruction procedure has worked well.
-
-
4. Discussion Detailed analyses of earthquake focal mechanisms have been used in the study of shear wave splitting induced by crustal anisotropy. We believe that our results have confirmed the phenomenon of shear wave splitting. It should be repeated that we presume a parallel alignment of cracks as the cause of seismic anisotropy. For reasons discussed in a previous section, we also assume that the
difference between the attenuation factors of both shear waves is negligible. However, besides those treated by Hudson (1981) and Crampin (1984), there are other sources of relative attenuation between split shear waves in realistic fluid-filled cracked media, such as fluid movement in cracks. These so far unquantified effects may result in higher relative attenuation values. The results ohtamed in the present study may suggest that such effects are insignificant within the crust beneath KMO. For preferred alignments of minerals as the alternative cause of crustal anisotropy, no mechanism has been proposed so far which predicts attenuation factors significantly different between split shear waves. Therefore, the pattern of attenuation differences between two shear waves as well as that of traveltime differences cannot be used to distinguish which is the primary cause of crustal anisotropy, crack alignment or mineral orientation. At the present stage, there seems to be no effective method to resolve this problem. It would be necessary to analyse shear wave sesismograms of much higher frequency recorded in a borehole where shear waves are free from the large free surface effects. The direction of faster shear waves (WNW— ESE) slightly differs from that of the average P-axis direction (E—W). Around the temporary station, strike-slip earthquakes with P-axes nearly E—W have dominantly taken place (Ito and Watanabe, 1977), and the common fault-plane solution is shown in Fig. 8. Combining the focal mechanisms with the surface traces of active faults (Research Group for Active Faults, 1980), the upper crust in this region is inferred to be subject to the E—W compression. Provided that the crustal anisotropy is actually caused by crack orientation, the cracks should strike WNW—ESE. Thus, the simple dilatancy model which predicts stress-induced opening of tensile cracks parallel to the maximum compression and perpendicular to the minimum compression (Nur, 1971; Crampin, 1987) may have to be slightly modified. The estimated crack strike (WNW—ESE) appears to coincide with that of the surface trace of an active fault near KMO (Fig. 8). Kaneshima (1990) suggested that cracks in the vicinity of an active fault are aligned
251
EVIDENCE FORSPLITTING OF SHEAR WAVES
-
around the study location but possesses small local fluctuations. Delay times between faster and slower split
...~ ~
~
YG
shear waves were measured on the rotated seismograms as the difference in arrival times between 35°N ~
MYO2 MYO ~
/
/
\
.
10km
13~.5°E,—~
Fig. 8. Equal area rose diagrams showing the distributions of faster shear wave motion directions for KMO (this study), YGI, MYO (Kaneshima et aL, 1987), and MYO2 (Kaneshima, 1990) plotted on a map of the study area. Thin solid lines mdicate surface traces of Quaternary active faults (after Kaneshima, 1990). The typical focal mechanism of crustal earthquakes in this area is shown (Ito and Watanabe, 1977). Open and solid circles denote the 7’- and P-axes, respectively.
parallel, not to the maximum compression but, to the fault plane. The 1987 main shock and most of the aftershocks have thrust-type focal mechanisms with P-axes striking nearly E—W (Fig. 6) (Maeda, 1988). This suggests that the magnitudes of the intermediate and the minimum compression are similar to each other and much smaller than that of the maximum compression (OH >> ~ 0h~ where 0H’ 0h’ and ~ are the maximum horizontal compression, the minimum horizontal compression and the vertical compression, respectively). If the stress state actually has large effects on the cracks beneath KMO, the distribution of cracks striking in one direction and dipping randomly seems more likely to exist than the parallel alignment of vertical cracks. The randomly dipping parallel crack model can explain the observations of parallel alignments of faster shear waves (Kaneshima et al., 1988). The direction of faster shear wave polarizations is generally coincident with those observed at several stations in this region (Fig. 8) (Kaneshima et al., 1987; Kaneshima, 1990). However, there are small but noticeable differences in the directions from station to station. This implies that crustal anisotropy, possibly equivalent to the geometry of cracks, is almost uniform over an area of 15 km
the two shear waves (DT in Table 2). The delay times per unit kilometre of ray path lengths are found to be approximately 0.01 s km~, which corresponds to 3.5% velocity difference between split shear waves. Assuming that the anisotropy is generated by a parallel vertical crack alignment, the crack density (a3n, where a and n are the typical radius of circular cracks and the number density of cracks respectively) is expected to be 0.04. The degree of anisotropy is generally consistent with that observed at the station 15 km south of the aftershock area (Kaneshima et al., 1987) and other stations in Japan (Kaneshima, 1990).
5. Conclusions Shear wave splitting has been detected on three-component seismograms recorded during a short-term observation of aftershocks of an intermediate crustal earthquake, in Japan. Most of the faster shear waves are polarized WNW—ESE, and these polarizations differ significantly from those calculated from the fault-plane solutions of the aftershocks. Two 2-D vectors representing the polarizations of the faster and slower split shear waves in the horizontal plane are summed to recover the shear wave polarizations radiated from a point source and before splitting owing to anisotropy. For 10 aftershocks, the shear wave radiation before splitting is coincident with that generated by the fault-plane solutions. The results confirm that the observed splitting and polarization alignments in the aftershock area are the result of seismic anisotropy, rather than topographic effects or particular focal mechanisms.
Acknowledgements Our special thanks are given to Norio Hirano for his support on the aftershock observation. We
252
S. KANESHIMA ET AL.
also thank David Booth for critically reviewing this manuscript. This research was ~rti~ ported by the Grant-in-Aid for Encouragement of Young Scientist Research of the Ministry of Edu~
cation, Science and Culture.
References Aid, K. and Richards, P.G., 1980. Quantitative Seismology, Theory and Methods. Freeman, San Francisco, 932 pp. Ando, M., 1984. ScS polarization anisotropy around the Pacific ocean. J. Phys. Earth, 32: 179196. Ando, M., Ishikawa, Y. and Wada, H., 1980. S-wave ~ sotropy in the upper mantle under a volcanic area in Japan. Nature, 268: 43—46. Ando, M., Ishikawa, Y. and Yamazaki, F., 1983. Shear wave polarization anisotropy in the upper mantle beneath Honshu, Japan. J. Geophys. Res., 88: 5850—5864. Aoki, H., 1986. Focal mechanism computation by means of Fourier analysis. ZISIN, 39: 251—256 (in Japanese). Booth, D.C., Crampin, S., Evans, R. and Robert, 0., 1985. Shear-wave polarizations near the north Anatolian Fault: I, evidence for anisotropy-induced shear-wave splitting. Geophys. J. R. Astron. Soc., 83: 6173. Crampin, S., 1978. Seismic wave propagation through a cracked solid: polarization as a possible dilatancy diagnostic. Geophys. J. R. Astron. Soc., 53: 467496. Crampin, S., 1984. Effective anisotropic elastic constants for wave propagation through cracked solids. Geophys. J. R. Astron. Soc., 53: 135—145. Crampin, S., 1987. Geological and industrial implications of extensive-dilatancy anisotropy. Nature, 328: 491496. Crampin, S. and McGonigle, R., 1981. The variation of delays in stress-induced polarization anomalies. Geophys. J. R. Astron. Soc., 64: 1115—1131. Evans, R., 1984. Effects of the free surface on shear-wave trains. Geophys. J.R. Astron. Soc., 76: 165—172. Fukao, Y., 1984. Evidence from core-reflected shear waves for anisotropy in the Earth’s mantle. Nature, 309: 695—698. Hirano, N., 1986. A system for the temporary observation of earthquakes using a personal computer. Ann. Disas. Prey. Res. Inst., Kyoto Univ., 29, B-i: 29—37 (in Japanese).
Hudson, J.A., 1981. Wave speeds and attenuation of elastic waves in material containing cracks. Geophys. J. R. Astron. Soc., 64: 133—150. Ito, K. and Kuroiso, A., 1979. Detailed spatial distributions of foreshock and aftershock activities of small earthquakes. ZISIN, 32: 317—327 (in Japanese). Ito, K. and Watanabe, K., 1977. Focal mechanisms of very shallow earthquakes in the vicinity of Lake Biwa. ZISIN, 30: 43—54 (in Japanese). Kaneshima, S., 1990. OrigIn of crustal anisotropy: shear-wave splitting studies in Japan. J. Geophys. Res., in press. Kaneshima, S. and Ando, M., 1989. An analysis of split shear-waves observed above crustal and uppermost-mantle earthquakes beneath Shikoku, Japan: implications in effective depth extent of seismic anisotropy. J. Geophys. Res., 94: 14077—14092. Kaneshima, S., Ando, M. and Crampin, S., 1987. Shear-wave splitting above small earthquakes in the Kinki district of Japan. Phys. Earth Planet. Inter., 45: 45—58. Kaneshima, S., Ito, H. and Sugihara, M., 1988. Shear-wave splitting observed above small earthquakes in a geothermal area of Japan. Geophys. J., 94: 399—411. Maeda, N., 1988. Method for computing focal mechanisms for an earthquake cluster — aftershocks of the earthquake with M4.9 occurred in Kyoto.-Osaka Border Region on May 28, 1987. ZISIN, 41: 323—333 (in Japanese). Maeda, N. and Watanabe, H., 1984. Mode of activity of micro-earthquakes: in the case of the middle and northern parts of Kinki district, southwestern Japan. ZISIN, 37: 579—598 (in Japanese). Nur, A., 1971. Effects of stress on velocity anisotropy in rocks with cracks. J. Geophys. Res., 76: 2022—2034. Nuttli, 0., 1961. The effect of the Earth’s surface on the S wave particle motion. Bull. Seismol. Soc. Am., 51: 237—246. Oike, K. and Matsumura, K., 1985. A new recording system of seismic waves using audio recorder. ZISIN, 38: 359—364 (in Japanese). Peacock, S., Cramplin, S., Booth, D.C. and Fletcher, J.B., 1988. Shear-wave splitting in the Anza seismic gap southern California: temporal variations as possible precursors. J. Geophys. Res., 93: 3339—3356. Research Group for Active Faults, 1980. Active faults in Japan. University of Tokyo Press, 363 pp.
Physics of the Earth and Planetary Interiors, 61 (1990) 238—252 Elsevier Science Publishers B.V., Amsterdam — Printed in The Netherlands
Evidence for the splitting of shear waves from waveform and focal mechanism analyses Satoshi Kaneshima 1, *, Naoki Maeda 2 and Masataka Ando ~ ‘Earthquake Research Institute, University of Tokyo Yayoi 1-1-1, Bunkyo-ku~Tokyo 113 (Japan) 2 Department of Geoscience, National Defense Academy, Yokosuka 239 (Japan) ~Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji Kyoto 611 (Japan) (Received September 19, 1989; revision accepted December 24, 1989)
Kaneshiina, S., Maeda, N. and Ando, M., 1990. Evidence for the splitting of shear waves from waveform and focal mechanism analyses. Phys. Earth Planet. Inter., 61: 238—252. A temporary seismograph station was sited above the aftershock area of an intermediate crustal earthquake (M 4.9) in the Kinki district, Japan. The results from analysing digital three-component seismograms and numerically determining focal mechanisms of aftershocks have provided clear evidence for the splitting of shear waves attributed to crustal anisotropy. Faster shear waves from most of the aftershocks are polarized WNW—ESE, regardless of their azimuths and incident angles. Such shear wave motions are often significantly inconsistent with the focal mechanisms of the aftershocks determined using P-wave first motions. For many of the events, slower shear waves, polarized orthogonally to the faster shear wave direction (NNE—SSW), are observed to arrive about 0.1 s later. Two vectors showing particle motions of faster and slower shear waves in the horizontal plane are summed, to reconstruct polarizations of shear waves before splitting. For events with sufficiently high signal-to-noise ratios of shear waves and well determined focal mechanisms, the reconstructed polarizations are consistent with the focal mechanisms within the range of uncertainty. Such consistency is not clearly detected for the other events, possibly because of large noise effects and poorly constrained fault-plane solutions The direction of faster shear wave polarization (WNW—ESE) generally coincides with that observed at three other stations located within 15 km of the temporary station. In the study area, the fabric of crustal anisotropy is almost uniform over the scale of 15 km. but appears to exhibit small local fluctuations.
1. Introduction Recently the number of reports on the observations of shear wave splitting attributed to crustal anisotropy have been increasing (Booth et al., 1985; Kaneshima et al., 1987). Most of such studies have examined shallow crustal earthquakes (focal depths less than about 15 km), and have observed parallel or sub-parallel alignments of faster shear waves. Such alignments are commonly inter*
Present address: Department of Terrestrial Magnetism, 5241 Broad Branch Road, N.W. Washington, D.C. 20015, U.S.A.
0031-9201/90/$03.50 © 1990
—
Elsevier Science Publishers B.V.
preted as the results of shear wave splitting (Crampin and McGomgle, 1981; Booth et al., 1985). Arrivals of slower waves polarized orthogonal to the faster waves are more crucial evidence for the phenomenon. Such split arrivals of shear waves, however, are much more difficult to detect than parallel alignments of faster shear waves. This is because slower shear waves are quite easily masked by reverberations after faster shear wave arrivals, which may be diffracted either by lateral crustal heterogeneities or by surface irregularities (Kaneshima and Ando, 1989). A parallel alignment of faster shear waves could be generated
239
EVIDENCE FOR SPLI1TINO OF SHEAR WAVES
either by surface irregularities, or by some particular combinations of earthquake focal mechanisms. An observed parallelism of faster shear waves, thus, should be treated cautiously, when split arrivals of two shear waves are not clearly recognized on three-component seismograms of each earthquake. It is desirable to examine shear wave polarizations radiated from double-couple sources and before anisotropy-induced splitting, by determining fault-plane solutions of each earthquake used in shear waveform analyses. Unfortunately this is not easy owing to some reasons described below. In splitting analyses, shear waves with incident angles less than the critical angle (350 for the Poisson’s ratio of 0.25) should be examined, in order to minimise waveform distortion generated by the free surface (Nuttli, 1961; Evans, 1984). This restriction usually forces us to select earthquakes with smali epicentral distances (< 10 km when using crustal earthquakes). If an earthquake takes place within 10 km from a station and is > M = 2, it is commonly difficult to obtain complete (unsaturated) three-component seismograms of the earthquake in ordinary seismic observations owing to the lack of a high dynamic range recording system. However, the ordinary spacing of permanent seismograph stations in Japan (longer than 10 km in most places) means that an earthquake must be > magnitude M =2, for the reliable estimation of its focal mechanism. Therefore, we are faced with the difficulty of obtaining unsaturated seismograms and a well— constrained focal mechanism of an earthquake at the same time. Ando et al. (1980, 1983) analysed waveforms of deep earthquakes (focal depth of about 300 km) on the subducting Pacific Plate beneath Honshu, Japan, and detected clear split arrivals of shear waves passing through the upper mantle which is possibly partially molten. They also found that shear wave particle motions corrected for splitting effects are consistent with the double-couple focal mechanisms. Further evidence for shear wave splitting attributed to upper-mantle anisotropy has been detected on shear wave seismograms of ScS phases from deep earthquakes (focal depths of about 500 km) (Ando, 1984; Fukao, 1984). These —
—
upper mantle studies analysed shear waveforms
with much lower frequency (0.1—1.0 Hz) than in ordinary crustal studies (5—10 Hz). Kaneshiina et al. (1987) and Peacock et a!. (1988) indicated that the observed faster shear wave particle motion directions significantly differ from those calculated from the fault-plane solutions. However, they did not try to recover source radiation of shear waves using the slower split shear waves. Detailed polarization studies of crustal earthquakes similar to the upper-mantle studies are required for reiable detection of shear wave splitting due to crustal anisotropy. In this work we perform such polarization studies on crustal earthquakes of an aftershock sequence in the Kinki district of Japan, which were recorded at a seismograph station close to their epicenters. Point source double-couple fault-plane solutions of many of those earthquakes are determined as objectively as possible using both the polarities and amplitudes of P-wave first motions, and the uncertainty in their determination is estimated. Incident shear wave particle motions are reconstructed from the observed split shear waves from the aftershock sequence, and cornpared with the shear wave polarizations generated by the focal mechanisms.
2. Aftershock observation On May 28, 1987 an intermediate earthquake (M = 4.9, determined by the Japan Meteorological Agency (JMA)) occurred near the centre of the seismic network of the Abuyama Seismological Observatory, Kyoto University (35 O()() ‘N, 1350 32’E, depth = 17 km, by the JMA) (Fig. 1). This is a typical thrust-type earthquake with the P-axis striking E—W (Maeda, 1988), followed by a sequence of aftershocks continuing for about six months. During about three months, from July to September 1987, a short-term seismograph station Kameoka (KMO) was sited just above the aftershock area (Fig. 1). The station was located on the hillside of a mountain with an elevation of 430 m, equipped with three-component velocity seismographs of 1-s free period. Signals are low-
240
S. KANESHIMA ET AL.
pass filtered (cut-off frequency 30 Hz) (bike and Matsumura, 1985), digitized with a sampling rate of 210 Hz, and recorded on a floppy disk using a personal computer (NEC, PC-9801E) (Hirano, 1986). The dynamic range of the recording system is 12 bits (66 db). Three-component digital seismograms of more than 70 aftershocks were obtained during this observation. Their hypocentres were located using P-wave arrival times at the telemetered stations of the Abuyama Observatory (solid circles in Fig. 1) (Maeda, 1988). The velocity structure used in the hypocentre location is a horizontally layered model (Table 1) (Maeda and Watanabe, 1984). Out of 51 well-located aftershocks, 40 events with incident angles less than 350 have been used for our waveform analysis and their hypocentres are shown in Fig. 2. The azimuths and incident angles of the earthquakes are listed in Table 2. Figure 3 shows examples of seismograms and particle motion di-
~~
agrams recorded at KMO. The local magnitudes of the events are in the range M = 0.0—2.3. For most of the events, epicentral distances are less than 5 km and focal depths are about 12 km (Fig. 2). Incident angles of shear waves of most earthquakes are less than 150, and therefore the effects of a free surface on shear waveforms will be small.
3. Analyses and results 3.1. Shear wave splitting In an elastic medium there exist two shear waves, which are degenerate, as long as the medium is isotropic (Aki and Richards, 1980). If the medium possesses any type of seismic anisotropy, the shear waves separate into two orthogonally polarized quasi-shear waves with different propagation speeds (Nur, 1971; Crampin, 1978). This
w •
0
~HO 1111K
•
11111
OHM
35N ABU
UJI KIN
) •0
135~E
136.E
I
I
50 km Fig. 1. Location of the aftershock area in which the temporary station KMO is sited is shown as a star in a map of the Kinki district, Japan (modified from Maeda, 1988). Solid circles indicate the location of seismic stations belonging to the Abuyama Seismological Observatory, Kyoto University. Open circles are the stations of other Observatories (DPRI, Kyoto University; Wakayama Microearthquake Observatory, Tokyo University; Nagoya University).
241
EVIDENCE FOR SPLn-riNo OF SHEAR WAVES
TABLE 1
ough understanding of the primary cause of the
P-wave velocity structure of the crust below KMO
crustal anisotropy beneath KMO. In this study we
phenomenon is called ‘shear wave birefringence’ or ‘shear wave splitting’. The cause of crustal anisotropy generating shear wave splitting may be
assume that the crustal medium beneath KMO possesses seismic anisotropy of hexagonal type with a vertical symmetry plane, which can be generatedby a parallel alignment of vertical cracks (Crampin, 1978; Hudson, 1981) (Fig. 4a). Kaneshima et al. (1987) suggested that the crustal medium below a station only about 10 km south of KMO possesses the seismic anisotropy induced by such a crack alignment. Our assumption, there-
preferred orientation of minerals, or alignment of cracks, or periodic thin layers. There is theoretical and observational evidence to support the theory that in the crust crack alignment mainly generates anisotropy (e.g. Crampin, 1987). At the moment, however, we have no critical information that would enable a thor-
fore, seems conceivable, although it should be confirmed by considerable observation. Theoretical studies indicate that for this type of anisotropy faster shear waves are polarized parallel to the crack strike (Crampin, 1978; Crampin and McGonigle, 1981) and slower split shear waves polarized orthogonal to the faster waves (Fig. 4a).
Layer no.
V~,(km s~)
1 2 3
55 60 6.7
~ 50
130 -.
KMO
w E + + C
+++
+
N
KMO.~
______N
10 km
+
E
+~
+
+$~+
10 km
Depth
s
Fig. 2. Epicentral map, east-west and north-south vertical cross-sections. A triangle indicates the location of the temporary seismic station (KMO). Crosses represent the micro-earthquakes used in this study.
242
S. KANESHIMA ET AL
TABLE 2 Ray path and split shear wave parameters of local earthquakes recorded at KMO No.
DL(°)
DC(°)
1 3
AZM(°) 327.0 150.1
INC(°) 4.0 5.5
267 120
~‘N~’
4 6
62.5 168.0
10.8 5.3
120 114
7 8 9 10 11 12 13 14 15
148.9 144.7 158.5 116.9 99.4 101.7 130.9 126.7 68.0
8.0 2.9 13.5 22.8 10.6 10.6 3.4 10.4 11.2
209 291 329 111 96 130 117 125 305
16
66.3
11.6
244
17 18 19 20 21 22 24 25 26 27 28
199.1 122.8 254.2 129.7 116.8 112.2 323.2 1.6 143.6 65.0 138.3
21.6 4.7 0.8 3.8 19.8 8.4 1.4 24.2 20.7 5.3 29.0
297 119 220 309 118 105 283 305 308 118 114
29 30 31 32 33 35 37 39
105.6 74.3 165.8 167.5 98.3 100.3 96.1 57.2
10.2 23.4 13.9 10.5 7.2 7.6 7.0 4.9
108 3 115 114 114 114 113 104
41 45 46 47 48 49 50
119.1 87.1 83.9 117.0 119.9 154.7 131.7
32.3 15.1 33.9 5.1 3.1 5.4 9.8
114 124 116 88 280 25 108
—17— 22 60 — 80
DO(°)
Type
DT(s)
*
80(i)
0
0.05
***
*
22 —156 (T-axis) 209— 220 —27—17 195 — 210
147 (i)
B
0.11
209 (i) 268 (e) 169 (e)
0 N N
* * *
* * *
* * *
*
* * *
*
0 N
0.08 0.07 0.11 0.07 0.14
335 (e)
N
0.14
*
112 —131 52—119
311 (i) 74(i) 169 (e) 130 (e) 65 (i)
0.03 0.07 0.11 0.04 0.08
192 — 244 —11—10
240 (i) 53 (e)
* * *
* * *
*
* * *
172 —188 118—176 (T-axis) 71—94
172 (e) 82 (i)
0 F
0.12 0.10
0(N)
0.08
***
***
*
* * *
* * *
*
* * *
84 —142 40 — 60 55 — 95 163 — 205 31— 126 (T-axis)
150 (i) 65 (i) 67 (i) 76 (i) 69 (i)
B 0 0 N B
0.10 0.07 0.07 0.07 0.09
* * *
* * *
*
* * *
*
0.07
* * *
Null-axis 66 — 93 84 —134 (Null-axis) 60— 134 (Null-axis) Null-axis 75— 85 * * *
241 146 86 330
(i) (e) (i) (e)
* *
0 *
0 B
0.10 0.00
*
* * *
68 (e)
76 (i)
0 N
0.10 0.03
*
~‘““
* * * *
313 (i)
*
***
*
***
*
0.03
Azimuth (AZM), incident angle (INC), and all other orientations are measured clockwise from north. DL, DO, and DC indicate the faster shear wave particle motion direction (Af), the shear wave radiation before splitting (At), and the range of shear wave particle motion directions calculated from feasible focal mechanisms (A~J,,),respectively. The symbols ‘i’ and ‘e’ denote impulsive and emergent arrivals of shear waves. ‘Type’ classifies the events according to the fitness of the orientations of A~or A to the ACm directions as follows; (0) As,, is consistent with A’,,; (F) A 1 is consistent with A~,,;(B) both As,, and Af are consistent with A~(N) neither A~,nor ~ are consistent with A’~m.DT indicates delay time between faster and slower shear waves, measured on the rotated seismograms as the difference in arrival times between the split shear waves.
243
EVIDENCE FOR SPUrrING OF SHEAR WAVES
(a)
t~MOO3587/09/05 37k 26 2l~
~ ~
~
AZM.
Iii
I I
KAG~ .~i T
I
0
1
2
3
I
RrP
OI5jSECj.5~L5
(b) ~
~
&
~
KMOO37 87/09/06 lob
_____________
46m 24~ DEP.
~L
11.39
1
.6,8
0123,
3
~
R~
~
Fig. 3. Examples of three-component seismograms: observed Up-Down, North-South, and East-West seismograms (top left); radial (TA) and transverse (LR) seismograms (bottom left). T, A, L and R indicate the direction toward (1) and away (A) from event, left side (L) and right side (R) viewing station from the event. Particle motion diagrams are giveii for the intervals shown in the rotated seismograms with bars (right).
244
S. KANESHIMA
(a)
Station
00
~0o
Er AL
(b)
0
0-=~o0
Source
~---...
Am°
,
Fig. 4. (a) Schematic figure showing shear wave splitting due to anisotropy induced by a parallel alignment of vertical cracks. ~
A
1,
and A, are the vectors indicating the partide motions of the initial shear waves at the source point, the faster shear waves, and the slower split shear waves, respectively. (b) and (c) schematic figures showing our reconstruction procedure.0(b) E,Recorded and S20°horizontal W, which seismograms are, respectively, (top),parallel and seismograms to, and orthogonal rotated totoshow the faster the horizontal shear wave ground motions motion (bottom). in the (c) directions (left) Two Nibvectors showing how the
particle motions of the faster shear wave (A 1) and slower shear wave (A,) are added to recover the shear wave radiation before splitting at the source (A9,,). The particle motion is compared with Am (top right) which is calculated from the fault-plane solution (bottom right). Thin solid lines in the fault-plane solution represent the projection of shear wave polarization directions. The symbols P and T indicate the P-axis and the T-axis, respectively. Attenuation factors of faster and slower shear waves are assumed to be identical.
3.2. Reconstruction of shear wave radiation before splitting
Our waveform analysis comprises the four steps described below. First, the ground motion directions of the faster shear wave arrivals are inspected using diagrams of particle motions in the horizontal planeof(Fig. 3). waves The faster partide with motion directions shear are plotted arrows on equal area projection diagrams (Fig. 5). These equal area diagrams show that the faster shear waves are approximately polarized Nib0 E— Silo0 W regardless of their azimuths
and incident angles (Fig. 5). It is also obvious that most of the exceptions are deduced from unclear shear wave arrivals (dotted arrows in Fig. 5). Such aligned polarizations of faster shear waves are often interpreted as evidence for shear wave splitting (e.g. Booth et aL, 1985; Kaneshima et al., 1987). From now on, we call N110°Ethe 0 W: (posinegative) and fasterS20° shear directionslower (Sib shear wave tive) W wave the (positive) direction (N20 °E:negative). Second, the observed horizontal component seismograms (north—south and east—west) are rotated into the seismograms of the faster shear
245
EVIDENCE FOR SPLITFING OF SHEAR WAVES
(a)
KMO N=
4.0
(b) N= 30
Fig. 5. Equal area projections of faster shear wave particle ‘motion directions (indicated by solid and broken arrows) out to the incident angles of 350 (a) and 150 (b). Solid and broken arrows indicate reliable and less reliable data, respectively.
wave (Nib0 E— SilO0 W) and the slower shear wave (S20 0 W—N20°E) directions (Fig. 4b). Since both shear waveforms contain significant amplitudes of the vertical component, a 3-D rotation of the coordinate axes might be preferable. Nevertheless, in this case the short-term seismograph sta-
It should be emphasized that only relative amplitudes of the two shear waves, not absolute amplitudes, are considered here. Absolute amplitudes could be seriously affected by many factors, such as source intensity (magnitude), radiation pattern, and focusing and defocusing due to lateral hetero-
tion is located very close to the centre of the aftershock area, so that most of the shear waves have incident angles less than 150 at the surface. We believe that the 2-D rotation of the coordinates (in the horizontal plane) used in our analysis is meaningful as the first approximation and does not lead to erroneous results. In the third step, relative amplitudes of the faster (Af) and slower (AS) shear wave pulses (background noise level to first peak) are inspected on the rotated seismograms (Fig. 4b, bottom). For the events with sufficiently impulsive shear waveforms (classified as Type ‘i’ in DO column in Table 2), the measured amplitudes are reliable possibly with an error less than 20%. For the
geneity in the crust. On the other hand, relative amplitudes between faster and slower shear waves are expected to be insensitive to such factors, because both shear waves propagate along approximately the same ray path as long as anisotropy is weak. Finally, these two vectors are summed to reconstruct shear wave motion radiated from the source (A~in Fig. 4c), which will be termed ‘shear wave radiation before splitting’. Before summation of the two vectors, we should correct for the effects of seismic attenuation which can differ between the faster and slower shear waves. The contributions of an alignment of cracks to the inverse of quality factor (l/Q 1 and l/Q2 for faster shear wave and slower shear wave, respectively) have been evaluated by Hudson (1981) and Crampin (1984). The typical ray path length (L), the dominant frequency of shear waves (f~)~ and the average shear wave velocity (J’) for this study may be approximately taken 1. The values of as 1/Q15 km, 10 Hz, and 3.5 km s 1 and l/Q2 calculated
events with emergent shear waves (Type ‘e’ in Table 2), on the other hand, the amplitudes should involve a much larger error. Since the particle motion directions of faster and slower split shear waves have been presumed, we obtain two 2-D vectors showing particle motions in the horizontal plane of two split shear waves (Af, A~in Fig. 4c).
246
S. KANESHIMA aT AL.
from the formula by Hudson (1981) are about 0.0001 and 0.001, respectively, for the propagation of 10-Hz shear waves (V5 3.5 km s~)through
the initially radiated shear waves and we are not
an elastic medium containing thin cracks of 20 m radius and a crack density of 0.1. The attenuation coefficients of slower shear waves exp[ irf0 L/ Q2J’~] are 0.8—0.9 times those for faster shear waves exp[ I7f0L/Q1J’~].The difference in dissipation between the two waves, therefore, amounts to 10—20% at most. The difference may be overestimated, since, as will be discussed later, the crack density estimated for this area is smaller than 0.1. Consequently, it would be difficult to detect such small differences, even if the shear wave seismograms have sufficiently high signalto-noise ratios and focal mechanisms are well determined. In this study we assume that the difference between the attenuation factors of the two shear waves is negligible. It must be emphasised again that we examine only the polarization angles of
3.3. Numerical estimation of the fault-plane solutions
concerned with their absolute amplitudes.
=
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Fault-plane solutions of the aftershocks used in the shear waveform analysis are determined using the polarities (up and down) and amplitudes of P-wave first motions recorded at the telemetered stations of the Abuyama network (solid and open circles in Fig. 1) (Maeda, 1988). It is usually difficult to uniquely determine fault-plane solutions of micro—earthquakes (M < 2). We apply a numerical fault-plane solution determination method (Aoki, 1986; Maeda, 1988) to the aftershocks. This method uses Fourier analysis for a P-wave polarity distribution function on a focal sphere (for example, +1 for positive first motions, —1 for negative motions). A Null-axis is sought on the focal sphere. For each Null-axis supposed,
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Fig. 6. (a) Typical best-fit fault-plane solutions of the micro—earthquakes used in this study. Open and solid circles indicate dilatation and compression, respectively. F- and T-axes are shown as open squares and crosses, respectively. (b) Equal area projection of P-axes in the best-fit fault-plane solutions. The outer circle shows the dip of 900. (c) as (b) for the T-axes.
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EVIDENCE FOR SPLI1TING OF SHEAR WAVES
the focal sphere is rotated so that the Null-axis becomes vertical and the polarity should be a function of azimuth only. The polarity distribution is approximated by a periodical square function with a period of ~r.The direction of a nodal plane is constrained by the phase angle of the Fourier component at period i~. For the solutions which fit the observed P-wave polarities at all stations, the P-wave amplitudes are calculated using an empirical formula and are compared with the observations (Maeda, 1988). Any solution With a standard deviation of less than 0.4 of the residual logarithmic amplitudes, which represents the differences between the calculated and the observed logarithmic amplitudes, is considered as a feasible solution. Then we estimate the uncertainty involved in the fault-plane determination, considering the diversity of the feasible solutions. Fault-plane solutions of about 30 out of the ‘~ events used in the waveform analysis are well determined (Fig. 6). Both thrust and strike-slip earthquakes with P-axes striking nearly E—W have occurred. As shown in the equal area plots of P and T-axes (Fig. 6b and c), thrust-type earthquakes, similar to the main shock, are dominant (Maeda, 1988). There is no significant difference in the focal depths between the strike-slip events and the thrust events, We calculate the horizontal particle motion directions of shear waves radiated from a doublecouple point source (A’~m in Fig. 4c), using the formulae of Aid and Richards (1980). Here we assume the horizontally layered structure given in Table 1 as the velocity model beneath the temporary station. Although no information about detailed 3-D crustal structure is available at present, it may be reasonable to use such a layered model as the first approximation. We also assume
3.4. Effects of the uncertainty in hypocentre location
To estimate uncertainty of shear wave motions, location errors of the aftershocks should also be assessed. In this study the aftershocks are located using P- and S-wave arrival times recorded at the telemetered seismograph stations belonging to the Abuyama network (Fig. 1). Errors in the epicentre locations have been estimated to be <0.25 km in the aftershock area (Maeda and Watanabe, 1984). Focal depth errors have not been explicitly evaluated, but are expected to be less than twice those of the epicentres. We relocate the aftershocks used in the waveform analysis using a kind of master event technique, which is almost equivalent to the joint hypocentre determination (JHD) (Ito and Kuroiso, 1979). One of the aftershocks recorded at more than 10 telemetered stations is selected as the master event. Other events are located relative to the master event. The nominal absolute hypocentres of the aftershocks are calculated by adding the hypocentre coordinates of the master event to their relative coordinates. This process is repeated with each of 17 aftershocks being selected as the master event. For each aftershock, the standard deviations of the nominal hypocentre coordinates are considered as the error of the location. The result shows that, for most of the events, the errors of epicentral distances and focal depths are expected to be less than 0.15 km and 0.3 km, respectively. These correspond to the errors of azimuths and incident angles of 50 and 10, respectively. Such small errors are found to only slightly widen the uncertainty range of Ac,~and hardly affect the results.
that relative amplitudes of the split shear waves are not seriously affected by laterally heterogeneous structure beneath the station. Because of the non-uniqueness of the focal mechanisms, the orientations of ACm are scattered across a considerable range (the hatched fan shape in Fig. 7). The orientations of A~,,are compared with those of the
3.5. Evidence for shear wave splitting
shear wave radiation before splitting (At) (see Fig. 4c).
arrow), A95~ (thick solid arrow), and the range of ACm calculated from the solutions (hatched fan
Slower shear wave arrivals have been identified on the rotated seismograms of 27 out of the 40 aftershocks used (Table 2). Some examples are
shown in Fig. 7, together with feasible fault-plane solutions, A1 (thin solid arrow), A~(thin broken shape).
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S. KANESHIMA ET AL
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Fig. 7. Feasible fault-plane solutions, together with the P-wave first motions (open circle: dilatation, solid circle: compression), P-axes (squares) and T-axes (crosses), are shown in the top left diagrams in Fig 7(a)-(d) for four different events. The horizontal seismograms in the set of three component seismograms on the right of each figure are rotated so that one of the two traces indicate ground motion in the direction of Ni10°E—Sii0°W, which is the faster shear wave polarization direction, and the other is in the orthogonal direction S20°W—N20°E. The amplification of the vertical component seismograms is one fifth of those of the horizontal components. The thick solid arrow, thin solid arrow, thin dashed arrow in the bottom left diagrams indicate A°,,(shear wave radiation before splitting), A (faster shear wave particle motion), and A~(slower shear wave particle motion), respectively. The 0m calculated from the feasible focal mechanisms. hatched fan shape represents the range of the orientations of A
249
EVIDENCE FOR SPLITTING OF SHEAR WAVES
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Fig. 7 (continued).
Most of the events which show the A~direction approximately within the range of Am orientations have impulsive waveforms of faster and
slower shear waves (Fig. la—c; Type 0 in Table 2). For these events, the directions of Af do not coincide with those of A~even after considering
250
S. KANESHIMA ET AL.
non-uniqueness of the focal mechanisms. Inconsistency between faster shear wave particle motion and focal mechanism has already been reported by Kaneshima et al. (1987) and Peacock et al. (1988). The examples in this study not only show such inconsistency but also indicate that the shear wave radiation before splitting is consistent with the feasible fault-plane solutions. Significant mismatch between the directions of A~,and ACm tends to be observed for the events which show emergent arrivals of faster and slower shear waves (Type N, Table 2). The mismatch is, therefore, likely to result from misreading of shear wave arrivals. For four events of Type B, the A~ direction is poorly constrained (Table 2; Fig. 7d), since the temporal station is located near the T-axis or the Null-axis on the focal sphere. Consequently, both As,, and A have their orientations within the range of ACm directions. There is a case for which A rather than A~,,is consistent with the ACm direction regardless of its impulsive waveform (Type F, Table 2). Although we have no reasonable explanation of such an exception, it could be attributed to noise in the seismogram or errors involved in the focal mechanism determination, It is remarkable that most of the events showing consistency between the orientations of A~ and A’~m have incident angles smaller than 100 (Type 0, Table 2), while many of the events showing a poor match (Type N and Type F, Table 2) have incident angles larger than 100. For the former events, shear waves may suffer only minor waveform distortions owing to heterogeneity just beneath the station, and therefore, our reconstruction procedure has worked well.
-
-
4. Discussion Detailed analyses of earthquake focal mechanisms have been used in the study of shear wave splitting induced by crustal anisotropy. We believe that our results have confirmed the phenomenon of shear wave splitting. It should be repeated that we presume a parallel alignment of cracks as the cause of seismic anisotropy. For reasons discussed in a previous section, we also assume that the
difference between the attenuation factors of both shear waves is negligible. However, besides those treated by Hudson (1981) and Crampin (1984), there are other sources of relative attenuation between split shear waves in realistic fluid-filled cracked media, such as fluid movement in cracks. These so far unquantified effects may result in higher relative attenuation values. The results ohtamed in the present study may suggest that such effects are insignificant within the crust beneath KMO. For preferred alignments of minerals as the alternative cause of crustal anisotropy, no mechanism has been proposed so far which predicts attenuation factors significantly different between split shear waves. Therefore, the pattern of attenuation differences between two shear waves as well as that of traveltime differences cannot be used to distinguish which is the primary cause of crustal anisotropy, crack alignment or mineral orientation. At the present stage, there seems to be no effective method to resolve this problem. It would be necessary to analyse shear wave sesismograms of much higher frequency recorded in a borehole where shear waves are free from the large free surface effects. The direction of faster shear waves (WNW— ESE) slightly differs from that of the average P-axis direction (E—W). Around the temporary station, strike-slip earthquakes with P-axes nearly E—W have dominantly taken place (Ito and Watanabe, 1977), and the common fault-plane solution is shown in Fig. 8. Combining the focal mechanisms with the surface traces of active faults (Research Group for Active Faults, 1980), the upper crust in this region is inferred to be subject to the E—W compression. Provided that the crustal anisotropy is actually caused by crack orientation, the cracks should strike WNW—ESE. Thus, the simple dilatancy model which predicts stress-induced opening of tensile cracks parallel to the maximum compression and perpendicular to the minimum compression (Nur, 1971; Crampin, 1987) may have to be slightly modified. The estimated crack strike (WNW—ESE) appears to coincide with that of the surface trace of an active fault near KMO (Fig. 8). Kaneshima (1990) suggested that cracks in the vicinity of an active fault are aligned
251
EVIDENCE FORSPLITTING OF SHEAR WAVES
-
around the study location but possesses small local fluctuations. Delay times between faster and slower split
...~ ~
~
YG
shear waves were measured on the rotated seismograms as the difference in arrival times between 35°N ~
MYO2 MYO ~
/
/
\
.
10km
13~.5°E,—~
Fig. 8. Equal area rose diagrams showing the distributions of faster shear wave motion directions for KMO (this study), YGI, MYO (Kaneshima et aL, 1987), and MYO2 (Kaneshima, 1990) plotted on a map of the study area. Thin solid lines mdicate surface traces of Quaternary active faults (after Kaneshima, 1990). The typical focal mechanism of crustal earthquakes in this area is shown (Ito and Watanabe, 1977). Open and solid circles denote the 7’- and P-axes, respectively.
parallel, not to the maximum compression but, to the fault plane. The 1987 main shock and most of the aftershocks have thrust-type focal mechanisms with P-axes striking nearly E—W (Fig. 6) (Maeda, 1988). This suggests that the magnitudes of the intermediate and the minimum compression are similar to each other and much smaller than that of the maximum compression (OH >> ~ 0h~ where 0H’ 0h’ and ~ are the maximum horizontal compression, the minimum horizontal compression and the vertical compression, respectively). If the stress state actually has large effects on the cracks beneath KMO, the distribution of cracks striking in one direction and dipping randomly seems more likely to exist than the parallel alignment of vertical cracks. The randomly dipping parallel crack model can explain the observations of parallel alignments of faster shear waves (Kaneshima et al., 1988). The direction of faster shear wave polarizations is generally coincident with those observed at several stations in this region (Fig. 8) (Kaneshima et al., 1987; Kaneshima, 1990). However, there are small but noticeable differences in the directions from station to station. This implies that crustal anisotropy, possibly equivalent to the geometry of cracks, is almost uniform over an area of 15 km
the two shear waves (DT in Table 2). The delay times per unit kilometre of ray path lengths are found to be approximately 0.01 s km~, which corresponds to 3.5% velocity difference between split shear waves. Assuming that the anisotropy is generated by a parallel vertical crack alignment, the crack density (a3n, where a and n are the typical radius of circular cracks and the number density of cracks respectively) is expected to be 0.04. The degree of anisotropy is generally consistent with that observed at the station 15 km south of the aftershock area (Kaneshima et al., 1987) and other stations in Japan (Kaneshima, 1990).
5. Conclusions Shear wave splitting has been detected on three-component seismograms recorded during a short-term observation of aftershocks of an intermediate crustal earthquake, in Japan. Most of the faster shear waves are polarized WNW—ESE, and these polarizations differ significantly from those calculated from the fault-plane solutions of the aftershocks. Two 2-D vectors representing the polarizations of the faster and slower split shear waves in the horizontal plane are summed to recover the shear wave polarizations radiated from a point source and before splitting owing to anisotropy. For 10 aftershocks, the shear wave radiation before splitting is coincident with that generated by the fault-plane solutions. The results confirm that the observed splitting and polarization alignments in the aftershock area are the result of seismic anisotropy, rather than topographic effects or particular focal mechanisms.
Acknowledgements Our special thanks are given to Norio Hirano for his support on the aftershock observation. We
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also thank David Booth for critically reviewing this manuscript. This research was ~rti~ ported by the Grant-in-Aid for Encouragement of Young Scientist Research of the Ministry of Edu~
cation, Science and Culture.
References Aid, K. and Richards, P.G., 1980. Quantitative Seismology, Theory and Methods. Freeman, San Francisco, 932 pp. Ando, M., 1984. ScS polarization anisotropy around the Pacific ocean. J. Phys. Earth, 32: 179196. Ando, M., Ishikawa, Y. and Wada, H., 1980. S-wave ~ sotropy in the upper mantle under a volcanic area in Japan. Nature, 268: 43—46. Ando, M., Ishikawa, Y. and Yamazaki, F., 1983. Shear wave polarization anisotropy in the upper mantle beneath Honshu, Japan. J. Geophys. Res., 88: 5850—5864. Aoki, H., 1986. Focal mechanism computation by means of Fourier analysis. ZISIN, 39: 251—256 (in Japanese). Booth, D.C., Crampin, S., Evans, R. and Robert, 0., 1985. Shear-wave polarizations near the north Anatolian Fault: I, evidence for anisotropy-induced shear-wave splitting. Geophys. J. R. Astron. Soc., 83: 6173. Crampin, S., 1978. Seismic wave propagation through a cracked solid: polarization as a possible dilatancy diagnostic. Geophys. J. R. Astron. Soc., 53: 467496. Crampin, S., 1984. Effective anisotropic elastic constants for wave propagation through cracked solids. Geophys. J. R. Astron. Soc., 53: 135—145. Crampin, S., 1987. Geological and industrial implications of extensive-dilatancy anisotropy. Nature, 328: 491496. Crampin, S. and McGonigle, R., 1981. The variation of delays in stress-induced polarization anomalies. Geophys. J. R. Astron. Soc., 64: 1115—1131. Evans, R., 1984. Effects of the free surface on shear-wave trains. Geophys. J.R. Astron. Soc., 76: 165—172. Fukao, Y., 1984. Evidence from core-reflected shear waves for anisotropy in the Earth’s mantle. Nature, 309: 695—698. Hirano, N., 1986. A system for the temporary observation of earthquakes using a personal computer. Ann. Disas. Prey. Res. Inst., Kyoto Univ., 29, B-i: 29—37 (in Japanese).
Hudson, J.A., 1981. Wave speeds and attenuation of elastic waves in material containing cracks. Geophys. J. R. Astron. Soc., 64: 133—150. Ito, K. and Kuroiso, A., 1979. Detailed spatial distributions of foreshock and aftershock activities of small earthquakes. ZISIN, 32: 317—327 (in Japanese). Ito, K. and Watanabe, K., 1977. Focal mechanisms of very shallow earthquakes in the vicinity of Lake Biwa. ZISIN, 30: 43—54 (in Japanese). Kaneshima, S., 1990. OrigIn of crustal anisotropy: shear-wave splitting studies in Japan. J. Geophys. Res., in press. Kaneshima, S. and Ando, M., 1989. An analysis of split shear-waves observed above crustal and uppermost-mantle earthquakes beneath Shikoku, Japan: implications in effective depth extent of seismic anisotropy. J. Geophys. Res., 94: 14077—14092. Kaneshima, S., Ando, M. and Crampin, S., 1987. Shear-wave splitting above small earthquakes in the Kinki district of Japan. Phys. Earth Planet. Inter., 45: 45—58. Kaneshima, S., Ito, H. and Sugihara, M., 1988. Shear-wave splitting observed above small earthquakes in a geothermal area of Japan. Geophys. J., 94: 399—411. Maeda, N., 1988. Method for computing focal mechanisms for an earthquake cluster — aftershocks of the earthquake with M4.9 occurred in Kyoto.-Osaka Border Region on May 28, 1987. ZISIN, 41: 323—333 (in Japanese). Maeda, N. and Watanabe, H., 1984. Mode of activity of micro-earthquakes: in the case of the middle and northern parts of Kinki district, southwestern Japan. ZISIN, 37: 579—598 (in Japanese). Nur, A., 1971. Effects of stress on velocity anisotropy in rocks with cracks. J. Geophys. Res., 76: 2022—2034. Nuttli, 0., 1961. The effect of the Earth’s surface on the S wave particle motion. Bull. Seismol. Soc. Am., 51: 237—246. Oike, K. and Matsumura, K., 1985. A new recording system of seismic waves using audio recorder. ZISIN, 38: 359—364 (in Japanese). Peacock, S., Cramplin, S., Booth, D.C. and Fletcher, J.B., 1988. Shear-wave splitting in the Anza seismic gap southern California: temporal variations as possible precursors. J. Geophys. Res., 93: 3339—3356. Research Group for Active Faults, 1980. Active faults in Japan. University of Tokyo Press, 363 pp.