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Attenuation of seismic waves in the Trinidad and Tobago area
TECTONOPHYSICS ELSEVIER
Tectonophysics 253 (1996) I 11-127
Attenuation of seismic waves in the Trinidad and Tobago area Joan L. Latchman *, William B. Ambeh, Lloyd L. Lynch Seismic Research Unit, University of the West Indies, St. Augustine, Trinidad, Trinidad and Tobago
Received 25 October 1994; accepted 15 May 1995
Abstract
The attenuation of seismic waves from earthquakes located within the area bounded by 9-12°N and 60-63°W was estimated from short-period seismograms. Coda-Q, Qc, determinations were made for each of the six seismograph stations within the area, while spectral Q values from P-phases, Q~, were estimated for station TRN. The S - S single-scattering model was assumed for coda generation, and the to-2 source model was assumed for the spectral Q determinations. The Qc values show a strong frequency dependence in the frequency range 1.5-12 Hz. The value of Q at 1 Hz, Q0, was found to lie within the range 107-132, while the rate of frequency dependence, n, extends from 0.80 to 1.06 for shallow events. For intermediate-depth events, Qo varies from 101 to 173 and n from 0.80 to 1.02. The Q~ values obtained show a spatial variation within the region, the highest attenuation was obtained on land Trinidad.
1. I n t r o d u c t i o n In all real media, the amplitude of an oscillating system decays with time to zero. Such systems are described as damped systems. This usually results from the conversion of kinetic energy to heat, which occurs because of friction, the damping force. Earthquake waves propagating through the earth lose amplitude and are attenuated. The two mechanisms contributing to this phenomenon are (a) intrins i c / a n e l a s t i c attenuation and (b) apparent attenuation. Intrinsic/anelastic attenuation results from actual loss mechanisms such as damped resonance, static hysteresis, relaxation and viscosity, all of which are related to the "internal friction" o f the medium.
* Corresponding author.
K n o p o f f (1964), using terminology borrowed from electric circuit theory defined attenuation by Q, the quality factor, such that:
Q-l
AW
l =~,n- I,V
(1)
where W is the total amount o f elastic energy stored per unit volume per cycle and AW is the part of W that is dissipated per cycle. Anelastic characteristics of solids are controlled by the thermal and defect properties, which are influenced by the thermal conductivity, grain size, defect concentration and mobility, diffusion rate and relatively weak interatomic and interdefect bonds at grain boundaries. Many of the mechanisms are activated processes that are strongly dependent on temperature and to a small extent on pressure (Jackson and Anderson, 1970). Apparent attenuation may result from geometrical effects, such as refraction, reflection and scattering.
0040-1951/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0040- 1951(95)00050-X
112
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
Scattering of wave energy is believed to be caused by inhomogeneities comparable in scale to the wavelength of the elastic wave. This attenuation is linear and necessarily highly frequency dependent. Although, in principle, this is a geometric mechanism, its mathematical form is similar to anelastic attenuation and therefore cannot be removed from seismic amplitude data (Jackson and Anderson, 1970). The amplitudes of seismic body waves recorded at observing stations are also influenced by the local layering and velocity distribution. Arriving waves can travel along numerous paths. If the soil conditions modify the incoming seismic waves in a simple and significant way, then it would be expected that given frequencies w o u l d be p r e d i c t a b l y amplified/reduced, irrespective of the earthquake source mechanism or the direction from which seismic waves arrive. However, the effects due to geological discontinuities are strongly dependent on the three-dimensional nature of soil deposits and on the direction of arriving waves. Therefore, an amplifica-
tion pattern resulting from local site conditions and transmission path is unlikely to be repeated during any sequence of recorded earthquakes unless they occur on the same fault and have identical source mechanisms (Trifunac and Udwadia, 1974; Der and McElfresh, 1976). This study investigates the attenuation of seismic waves within the area enclosed by Trinidad, Tobago, Grenada and the Paria Peninsula (Fig. 1) by making use of earthquakes occurring within the area and recorded at stations TCE, TRN, TPP, GRW, TBH and TPR (Fig. 3). Following file broad site classification of soft, medium and hard, TCE, TBH and TPR fall under hard and TPP, TRN and GRW fall under medium.
2. Seismicity and tectonics of the area
The study area is located at the southeastern comer of the Caribbean Plate, within the boundary
I
I
N
CARIB BF /3N SEA
I
, ~ ~ TOBAGO li°N
A
N T
'++"+,,.+,.,o+.
o
3 f
~I "~
+"~+La"++,' e. '~?!,L Strike-slip fault
~ ORINOCO
Normal fault
62°W
~ -
~m~ '~,
61_'W
Fig. 1. Map showing significant fault traces (Speed, 1985; Morgan et al., 1988).
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
region between the Caribbean Plate and the South American Plate. Within this boundary region, the seismic and volcanic activity, resulting from the subduction of the oceanic lithosphere of the South American Plate beneath the Caribbean Plate, is manifested along the southern end of the Lesser Antillian island arc, from Grenada into the Paria Peninsula. The nature of the activity there changes to include the activity characteristic of the strike-slip boundary, the E1 Pilar fault, in northeastern Venezuela. The extent of the E1 Pilar is uncertain, there being various schools of thought. Vierbuchen (1984) defines the E1 Pilar fault as extending from the Gulf of Cariaco to a point 400 km east of Trinidad. However, Russo et al. (1990) found no evidence to support activity that
113
could be attributed to the E1 Pilar fault further west than 62.3°W. Molnar and Sykes (1969) postulate that the region in northeastern Venezuela, near Trinidad, marks the intersection of the transform fault with the Lesser Antillean arc. They suggest that hinge faulting, similar to the structure proposed by Isacks et al. (1969) for the northern end of the Tonga arc, may exist near Trinidad at the contact point of the transform fault and the subducting plate. It is generally held that the activity on the Venezuela side of the study area is not occurring aligned to any of the significant faults. On the other hand, foreshocks and aftershocks of an M b = 5.2 earthquake, which occurred on 20 September 1982 revealed a W- to WNW-trending zone of activity
MAGNITUDE
DEPTH
o.o-
0.9
0
I'0-
1'9
(kin) O--
69
0
Z.O-2-9
,,,,70--
r40
0
3.0-3.9
0
0
4.0-
0
> f40
4"9
% nJ
%
o C)
o c)
% o
o O~
62.5 °
62.0 °
6).5 °
61.0 °
60.5 °
Fig. 2. Events during the period 1 9 7 7 / 0 1 - 1 9 9 0 / 0 6 .
60.0 °
114
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
Table 1 Parameters of events used in coda-Q analysis Yr/mon/d
H/min/s
Lat (°N)
Long (°W)
Depth (km)
Mag
Stations
1992/12/21 1992/12/22 1992/12/22 1992/12/27 1992/12/28 1992/12/28 1992/12/28 1993/01/06 1993/01/08 1993/01/08 1993/01/09 1993/01/09 1993/01/10 1993/01/10 1993/01/10 1993/01/10 1993/01/12 1993/01/12 1993/01/18 1993/01/19 1993/01/21 1993/01/21 1993/01/23 1993/01/24 1993/01/28 1993/02/14 1993/02/14 1993/02/14 1993/02/15 1993/02/15 1993/02/16 1993/02/18 1993/02/22 1993/02/22 1993/03/01 1993/03/02 1993/03/02 1993/03/04 1993/03/05 1993/03/05 1993/03/08 1993/03/08 1993/03/08 1993/O3/O9 1993/03/11 1993/03/23 1993/03/29 1993/04/03 1993/04/04 1993/04/04 1993/04/04 1993/04/06 1993/04/11
07/51/29.83 04/40/09.47 16/13/I 1 . 9 6 09/45/11.17 05/14/33.03 10/01/31.29 17/45/31.51 18/24/01.11 05/00/12.95 12/43/06.96 12/44/07.02 19/45/23.31 11/09/20.55 13/45/31.04 17/41/53.99 20/14/12.31 12/46/48.09 19/36/41.71 09/13/56.21 08/05/26.64 06/24/49.43 10/47/52.89 09/44/36.63 00/25/43.89 13/07/30.39 05/04/15.01 05/09/25.25 12/38/40.75 14/20/53.83 20/43/20.43 20/58/28.56 05/30/18.86 04/36/38.86 07/11/39.19 15/40/23.49 12/41/53.41 19/30/45.72 23/51/24.40 02/46/50.92 09/33/17.56 07/18/40.33 09/48/45.12 10/32/33.18 01/34/59.14 19/27/10.98 13/11/42.30 10/13/33.77 06/17/34.73 04/08/11.69 16/40/46.41 18/11/50.03 16/38/08.85 13/03/37.27
10.9770 10.3460 11.4620 11.0250 10.6880 11.1100 11.2700 10.4140 10.9770 10.7570 10.5580 10.2640 11.1800 11.1350 11.1680 11.2100 10.5650 10.7440 10.3930 10.4410 10.5780 10.3790 10.3540 10.6690 11.2680 10.8120 10.9260 10.7120 9.7880 11.3430 10.2160 10.7590 10.8380 10.2500 10.8190 11.1100 11.1210 11.0990 11.2860 10.8910 11.0770 10.9450 10.9100 10.8320 10.9670 11.1870 10.9480 11.0190 10.8790 11.0360 10.4710 10.0410 10.2590
62.0170 62.3100 62.0640 62.0940 61.6290 60.6400 62.1120 62.8590 61.1580 62.4350 61.3280 60.8390 60.9440 60.6020 61.8960 60.2230 61.6770 62.4940 62.2750 62.0290 61.3050 62.1740 61.3280 61.1060 60.4230 60.0040 60.0360 60.1520 62.4650 61.4860 60.1290 62.3670 62.3490 61.5510 62.1950 62.1220 62.1950 61.7490 61.7930 62.4000 62.8860 61.5900 62.3130 62.1560 61.7570 61.7220 61.7580 62.1170 62.3970 61.9820 61.5350 61.1920 61.1970
97.24 5.00 124.27 29.63 5.00 8.00 100.35 1.14 10.00 10.00 32.96 43.74 t.51 31.01 64.81 13.01 15.06 87.62 10.00 42.95 5.00 5.00 50.80 23.95 33.21 17.55 24.45 13.01 33.00 86.26 82.34 73.53 86.80 46.05 73.04 9.23 8.40 9.86 10.10 53.25 5.00 21.21 106.61 23.21 111.67 43.76 67.34 73.89 30.36 111.91 28.36 48.99 54.33
3.1 3.7 3:4 3.3 2.8 2.7 3.2 3.4 2.1 3.0 2.5 3.1 3.2 3.4 2.5 3.0 2.6 3.5 3.5 2.9 3.1 3.5 2.2 2.9 3.4 3.6 3.3 2.9 3.2 2.8 3.4 3.9 3.0 2.5 3.0 2.8 2.9 2.3 2.5 3.5 3.0 2.9 3.2 3.0 2.9 3.0 3.9 3.1 3.8 3.5 2.8 3.5 2.6
TRN,GRW GRW TCE, TRN, TPP, TBH TCE, TPP, GRW TCE, TPP TRN TCE, TRN, GRW, TBH TCE, TRN, TPP, GRW TRN, TBH TCE, TRN, TPP TRN, TBH TRN, TPP, GRW TCE, TRN, TPP, GRW, TBH TCE TRN TCE, TRN TCE TRN, TBH TCE TRN, TBH TCE TRN, TPP, GRW, TBH TCE TRN, TPP, TBH TCE TRN, TPP TCE TRN, TPP, GRW, TBH TCE TRN, TPP, TBH TCE TRN TCE TRN, GRW, TBH TCE TRN, TPP, TBH TCE TRN, TPP, GRW, TBH TCE TRN, TBH, TPR TCE TRN TCE, TRN, TBH TCE, GRW TCE, TPR TCE, TRN, GRW TCE, TRN, TPP TCE, TRN, GRW GRW TCE TRN, GRW TCE TRN TCE TRN, GRW, TBH TCE TRN TPP, GRW, TBH, TPR TCE TRN TCE TBH TCE GRW, TBH, TPR TCE TRN TCE TRN TCE TRN, GRW, TBH TPR TCE. TRN, GRW TCE, TPR TCE, TPP, TBH TCE, TRN TCE, TRN TCE, TRN, TPP, TBH
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
I 15
Table 1 (continued) Yr/mon/d H/min/s
Lat (°N)
Long (°W)
Depth (km)
Mag
Stations
1993/04/11 1993/04/15 1993/04/16 1993/04/16 1993/04/18 1993/04/18 1993/04/21 1993/04/22 1993/04/22 1993/04/26 1993/05/01 1993/05/05 1993/05/08 1993/05/12 1993/05/22 1993/05/22 1993/05 /27 1993/05/29 1993/05/29 1993/05/31 1993/06/01 1993/06/01 1993/06/02 1993/06/03 1993/06/04 1993/06/04 1993/06/05 1993/06/13 1993/06/22 1993/06/23
11.1330 10.6480 11.3040 10.7890 10.7940 11.0580 11.1810 10.8440 10.5550 11.1160 10.9850 10.4320 11.1070 10.7490 10.7980 10.8670 11.5510 11.5880 11.1390 11.0800 10.8060 11.2390 11.3670 10.2060 11.3930 11.4630 9.9650 10.2150 11.9190 10.7070
62.5680 62.6520 61.2960 61.9540 62.4940 62.0100 62.8630 62.3740 62.4360 61.8390 60.0280 62.31O0 62.2030 62.3970 62.5700 62.2340 61.0310 61.9790 61.6640 62.2370 62.4450 61.8380 62.2150 60.5500 62.0940 61.5180 62.3460 62.3570 61.7640 60.7900
3.00 47.43 14.80 38.64 67.20 108.20 6.17 50.69 108.58 75.68 19.32 3.00 111.99 57.83 3.00 73.64 24.31 99.68 48.08 56.65 52.17 73.53 106.94 120.18 73.59 14.01 81.45 3.00 111.88 28.75
3.3 3.0 3.2 3.1 3.0 3.3 3.2 3.3 4.1 3.0 2.7 3.0 3.9 3.2 3.3 3.2 2.9 3.2 3.0 3.2 3.1 3.2 3.2 3.3 3.1 2.8 4.0 3.6 3.2 2.5
TCE, TRN, TPP, TBH TCE, TRN TCE, TPP, TBH, TPR TCE, TRN, TPP TCE, TRN, TBH TCE, TRN, TBH, TPR TCE, TRN TCE, TRN, TPP TCE TCE, TRN TCE, TRN, TBH TCE, TRN TCE TCE, TRN TCE, TRN, TPP TPP, GRW, TBH TRN, GRW TCE, TRN, GRW, TBH TCE, TRN, GRW, TBH TCE, TRN, GRW, TBH TCE, TRN, TBH TCE, TRN, GRW, TBH TCE, TRN, TPP, GRW, TBH TCE, TRN, TBH TCE, TRN, GRW TRN, GRW TCE, TRN, TBH TCE, TRN, GRW, TBH TCE, TRN TBH
17/49/00.47 12/37/35.81 11/43/14.14 22/51/57.76 00/14/52.50 02/16/37.28 09/45/59.15 09/38/41.18 l 2/31/57.15 12/09/40.73 03/23/11.57 23/40/50.53 18/38/13.91 09/40/45.83 05/03/14.80 10/29/55.01 04/37/31.32 00/16/05.33 14/32/03.56 07/58/21.45 03/34/31.80 12/44/08.26 08/22/03.77 16/47/41.30 05/39/53.88 11/52/21.91 18/09/49.09 07/48/15.69 02/35/14.87 12/20/12.69
southwest of Tobago. The focal mechanism of the main shock showed right-lateral strike-slip motion along an E - W - t r e n d i n g fault plane dipping steeply (71 °) to the north. This active fault appears to form part of the previously unrecognized Southern Tobago Fault System, for which there is evidence in the geology of the late Neogene rocks of the island (Morgan et al., 1988). On 10 March 1988 an M s = 6.4 (NEIC) earthquake and aftershocks, east of Trinidad, revealed the presence of a N W - S E - t r e n d ing active zone. The NEIC focal mechanism of the main shock is moderately well controlled and corresponds to strike-slip faulting with a large normal component. The preferred fault plane is undetermined. The depth of this event from pP phases given in the ISC Bulletin is 53 km. However, to date, the nature of the feature has not been formalised (Figs. 1 and 2). Besides these defined zones of activity,
earthquakes are routinely located throughout the region as shown in Fig. 2 and as can also be seen from even the limited period covered by the data used for the coda-Q analysis (Table 1; Fig. 3).
3. Data acquisition Instrumental eastern Caribbean earthquake data have been collected by the Seismic Research Unit since 1953. The collection system has progressed from photographic records delivered by mail, to analogue telemetered signals recorded on 24" magnetic tape in the 1970's, to digitised data recorded on IBM P C ' s in the 1980's. The network consists of a total of 30 stations, of which over 50% is operational at any given time. The sensor at each station is a single vertical-component short-period seismometer,
116
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127 HAGNITUDE
DEPTH
(kn) 1.0
-
1.9
(2)
0 -
69
02) 2 . 0
o
-
2.9
,,,, 70 -
140
E) 3.0 - 3.9
C-d~FA~IADA~ G F I W ¢'d
z~x
Ax :
(2)
AAx,~.
O
~ G O
t~
o
o
%
62.5 °
62.0 °
61.5 °
61.0 °
60.5 °
60.0 °
Fig. 3. Locations of events, 92/12/21-93/06/30, used in coda-Q analysis.
which is either a Marks Product L4C or a Kinemetrics Ranger SS1. The overall system transfer function for TRN is shown in Fig. 4. The signal from each seismometer is amplified, frequency modulated, then transmitted to the central recording site in St. Augustine, Trinidad, via VHF radio a n d / o r microwave links. The signals are then demodulated, fed into PC's (fifteen stations per computer) and digitized by a 12 bit analogue to digital converter at 100 samples/s. A triggering algorithm searches the resulting time series, from each station continuously, for possible earthquakes and stores the "'event", preceded by a selectable length of pre-triggering
time record, once preset triggering criteria are met. The data from each of the monitoring machines are transferred to another PC, on which there is interactive software for picking phase arrival times and routine hypocentral determination. The network detects over 1500 events annually.
4. Importance of attenuation The construction of buildings with adequate earthquake resistance requires the estimation of the poten-
J . L . L a t c h m a n et al. / T e c t o n o p h y s i c s 2 5 3 ( 1 9 9 6 ) 111 - 1 2 7
117
determine the attenuation parameter must consider these influences.
5. Determination of attenuation ~
rz
5,1. Coda method
e
w
u4
w o
~.00
-013~
°39 LOG
~.'0~
~.'70
FREQUENCY
Fig. 4, Amplitude response spectrum for station TRN.
tial ground motion in future earthquakes. The effects observed at a given site are influenced by the attenuation of the region, the characteristics of the source and the local site conditions. The attenuation parameter has been found to vary beneath the earth's surface. Estimates of Q in the earth are of the order 102 for the inner core, l04 for the outer core, l03 for the lower mantle, 102 for the upper mantle and 200 for the lithosphere (Fowler, 1990). Since the value of the attenuation parameter also varies from region to region within the crust, it is important to have a measure of the absorption of the intervening area in order to estimate the effects of an earthquake at any given distance from a specific source. The difference in felt area for earthquakes in the Western United States from comparable earthquakes in the Eastern United States, the latter extending to far greater distances, demonstrates the significance of differences in attenuation (Aki, 1982). Yet another facet of the attenuation of earthquake waves is that, in a given region, P-wave attenuation, Q,,, is usually different from S-wave attenuation, Q~. Qt~/Q,, varies regionally [e.g., Bakun et al. (1978); Rautian et al. (1978) found the ratio = 0.6, whereas Frankel (1982) found the ratio = 1.78]. A choice of method to
Coda waves, in this context, are the tail of a seismogram (after the arrival of major wave types such as P, S and surface waves) recorded at short distance from an earthquake. They have been explained by the backscattering of waves by heterogeneities distributed in a large region outside the zone of the direct wave path from the source to the station. Whereas it has been found that the spectral contents of the early part of a local earthquake seismogram depend strongly on the travel distance and the nature of the wave path to the station, the difference in spectrum among stations diminishes in the later part of the seismogram and disappears in the coda, a finding revealed by a common shape of coda amplitude decay curve (Aki and Chouet, 1975; Hermann, 1980). In this study we follow the techniques used by Ambeh and Lynch (1993). They made use of the single, backscattering model of Aki and Chouet (1975), extended by Sato (1977). The former assumes that the source and the receiver are coincident. This model gives the coda amplitude, A(flt) at frequency, f, and traveltime, t, as: - zrft
A( f l t ) = C( f ) t -~ e x p - -
(2)
Qc where C ( f ) represents the coda source factor, a is a constant that depends on geometrical spreading and takes values of 1.0, 0.5 and 0.75 for body wave, surface wave and diffusion scattering, respectively, and Qc is the coda quality factor. The extension of Sato (1977) allows for source-receiver offset, which permits the coda analysis to begin immediately after the shear wave arrival. For non-coincident source and receiver, the coda amplitude is given by: - zrft
A(rlt) = C ( f ) K ( r , a ) e x p - -
(3)
ac where a = t/t~, ts is the S-wave lapse time, r is the
I 18
J.L. Latchman et aL / Tectonophysics 253 (1996) 111-127
source-receiver distance, K(r,a) = (1/r){(1/a) In[ a + 1 ) / ( a - 1)]}0.5 and all the other symbols have the same meaning as in Eq. 2. Eq. 4 is obtained by taking natural logarithms of Eq. 3 and rearranging terms:
A(r,f]t)
In k ( , a )
r
lnC(f)-
( ¢rfl ,Qcl
t
(4)
For narrow-bandpass filtered seismograms, C(f) is constant and hence by performing a linear regression of the term on the left-hand side of Eq. 4 with respect to t, Qc can be found from the slope, which is the coefficient of t. If the S - S single scattering theory is correct, Qc should equal Qt~, shear wave attenuation, determined directly from the S-wave, and indeed Aki (1980a, b) has found good agreement between them.
where Q is the attenuation quality factor, V is the seismic wave velocity and the integral is over the ray path. Now if Q is assumed constant over the path then: t t* =
-
(8)
Q
where t is the travel time. Substituting Eq. 8 in Eq. 5 and taking natural logarithms of Eq. 6 yields: In
~rft
Z ( f ) = In A 0 - - -Q
(9)
which is the equation of a straight line having In A0 as the intercept and - ~ t / Q as gradient, from which Q can easily be determined (A1-Shukri et al., 1988).
5.2. Spectral decay method
6. Data for coda-Q analysis
Displacement spectra can be derived from the seismograms of one or more instruments that span the body-wave band. Spectra are normally determined by Fourier transforming a waveform mad smoothing the result. Source theories predict a constant long-period level, followed by a decay above a corner frequency that scales inversely with source size. A measure of seismic attenuation can be defined from the rate of high-frequency decay above the corner frequency (Cormier, 1982). The instrument-corrected acceleration spectrum observed at a station, a distance r from the epicentre is defined by Anderson and Hough (1984) as:
The active, i.e., not archived, database of the Seismic Research Unit was searched for all events located within 9-12°N and 60-63°W (Fig. 3). These data covered the period 1 9 9 2 / 1 2 / 2 1 - 1 9 9 3 / 0 6 / 3 0 . The most recent data were used because reliable station calibrations are available from 1993/01/19. Such information being required for the spectral method for Q determination (Table 2). For coda-Q analysis, waveforms recorded at stations TCE, TRN, TPP, GRW, TBH and TPR were sought. Those with good signal to noise ratio, free of clipping and spikes, were chosen. A total of 83 events met the criteria. The duration magnitudes of the events lie within the range 2.1 to 4.1 and their focal depths lie within 1 to 124 km. Of the total number of events, each station had the following number of acceptable records: T C E - - 7 0 ; TRN--66; T P P - - 2 6 ; G R W - - 3 0 ; T B H - - 3 9 ; and T P R - - t 0 .
a ( r , f ) =A oe ~f'*
(5)
such that:
A o = (27rf)Zs(f)G(r,f) (6) where G(r,f) is the geometric spreading, which, if assumed to be independent of frequency as in a homogeneous medium, is equal to 1/r for body waves, but which was not considered in this study, and S(f) is the source displacement spectrum, which is often assumed to be proportional to f--2 and is known as the w -2 model (Brune, 1970). t * is the attenuation time, and is given, for seismic phases by: dr t* = ]path QV (7)
7. Analysis
7.1. Coda method Each seismogram time series was bandpass filtered over five frequencies bands centred at 1.5, 3, 6, 12 and 24 Hz with bandwidths of 1, 2, 4, 8 and 16 Hz, respectively, using an eight-pole, phase-free Butterworth filter. Starting at the S arrival, the root-
119
J.L. Latchman et al./ Tectonophysics 253 (1996) 111-127
Table 2 Parameters of events used in the spectral analysis method and related Q values Yr/mon/d
H/min/s
Lat (°N)
Long (°W)
Depth (kin)
Mag
Q values
1993/01/23 1993/01/28 1993/02/14 1993/02/14 1993/02/22 1993/03/02 1993/03/04 1993/03/05 1993/03/08 1993/03/23 1993/04/03 1993/04/11 1993/04/16 1993/04/17 1993/04/17 1993/04/18 1993/04/18 1993/04/26 1993/05/01 1993/05/05 1993/05/12 1993/05/29
09/44/36.63 13/07/30.39 05/04/15.01 12/38/40.75 07/11/39.19 12/41/53.41 23/51/24.40 02/46/50.92 07/18/40.33 13/11/42.30 06/17/34.73 13/03/37.27 22/51/57.76 17/06/19.39 17/07/42.99 00/14/52.50 02/l 6/37.28 12/09/40.73 03/23/11.57 23/40/50.53 09/40/45.83 14/32/03.56
10.3540 11.2680 10.8120 10.7120 10.2500 11.1100 11.0990 11.2860 11.0770 11.1870 11.0190 10.2590 10.7890 10.3120 10.2380 10.7940 11.0580 11.1160 10.9850 10.4320 10.7490 11.1390
61.3280 60.4230 60.0040 60.1520 61.5510 62.1220 61.7490 61.7930 62.8860 61.7220 62.1170 61.1970 61.9540 62.2760 62.1440 62.4940 62.0100 61.8390 60.0280 62.31O0 62.3970 61.6640
50.80 33.21 17.55 13.01 46.05 9.23 9.86 10.10 5.00 43.76 73.89 54.33 38.64 3.00 3.00 67.20 108.20 75.68 19.32 3.00 57.83 48.08
2.2 3.4 3.6 2.9 2.5 2.8 2.3 2.5 3.0 3.0 3.1 2.6 3.1 3.4 3.3 3.0 3.3 3.0 2.7 3.0 3.2 3.0
211.62 +__8.79 736.02 __+55.48 191.36 __+3.22 414.6 +__17.19 238.19 __5.45 577.99 __+15.61 158.78 + 3,42 318.95 __+5.01 359.47 +__18.69 398.65 +__5,63 1080.73 __ 37.10 278.28 +__5.66 150.71 __+2.60 352.57 +__6.75 195.42 __+5.86 240.01 + 9.40 509.61 +__ 17.79 512.68 ::k 27.96 669.80 _+ 30.10 364.40 _ 5.54 443.58 _+ 17.52 302.47 +_6.12
mean-square (rms) amplitudes in each window were determined for the data in each frequency band, with the window sliding across the time series at 1 s intervals. Time-window lengths for the rms averaging of 8 s (for centre frequencies of 1.5, 3 and 6 Hz) and 5 s (for centre frequencies 12 and 24 Hz) were chosen so as to smooth out as much as possible irregularities in the amplitudes of the arrivals. The left-hand side of Eq. 4 was then evaluated and plotted against lapse time. From the plot, the linear portion, which had to be at least 25 s long, was visually selected and a least-squares straight line fitted to it. From the slope of the line, Qc was calculated. A sample plot is shown in Fig. 5. The 25 s window was chosen to allow the inclusion of many of the well-recorded smaller events. Qc determination was restricted to the best linear portion to minimize the effect of small-scale, temporal variations in coda amplitude influenced by interference, secondary arrivals, or site conditions. Because of the generally poor quality of the results in the 24-Hz band, they were not included. The poor quality of the 24-Hz band is expected considering the overall system response (Fig. 4).
7.2. Spectral m e t h o d
A specified window of the P-phase was fully cosine 2 tapered and Fourier transformed to produce a spectrum. Initially various window lengths were tested. Although the spectra for window lengths of 0.6, 0.9, 1.2 and 1.5 s were produced, only that obtained from the 0.6 s window was used for this study because, like AI-Shukri et al. (1988), we found that the most favourable portion of the waveform, from which to determine Q, is its onset. In all cases, window lengths greater than 2.0 s would include reflected/refracted phases and therefore window lengths greater than 1.5 s would not be useful. In many cases this phenomenon was observed for window lengths greater than 0.6 s. In all cases the window was opened at 0.3 s before the P-onset as given in the bulletin of the Seismic Research Unit. In one case, where there was a large P-residual, the window onset was revised. A noise sample, of length equal to that of the window, was taken 50 samples preceding the start of the window. This noise spectrum was removed from the P-phase spectrum, the resulting spectrum was smoothed with a running
J.L, Latchman et al. / Tectonophysics 253 (1996) 111-127
120
1.5Hz Q~ = 134
r:
o.o
+
.~-h-
~'~*~-.~+
,%
I
L
L
I
25.3
50,8
"/5,8
I01.I
3.0Hz
D 0.0
,.....,,
~H~+t"t~
~ 125.q
%
I
I
I
I
25.3
50.6
75.8
101.1
L
1
25.3
50,6
I 75.8
I 101.1
~" 125.q
6.0Hz Q~ = 579
.,,,.
p.
__=
0.0
"~,~ 126.q,
12.0Hz 4-
7:
0.0
I 25.6
24Hz
+ +
~ + +,#
0.0
~¢~
+÷
4-
I
I
I
25.6
51.2
75,7
LAPSE TIME
#%++
+ "~ 4-
~+ +
+ +~+
~
I
..i.+ +~ 4"
+~
I
I
I(~,3
127.9
(SEC)
Fig. 5. Example of coda-Q analysis as applied to station TCE seismogram for the event of 1993/02/14 05:04 UTC. The plot is for the quantity ha [ A ( r , f [ t ) / k ( r , a ) ] versus lapse time, t. The arrows indicate the portions chosen to determine Qc.
window, the width of which is a function of the above-mentioned window length. This was done five times to remove stochastic noise and so reveal the underlying spectrum shape. Spectra obtained for events located in the six source zones within the study area are shown in Fig. 6.
The spectra were visually examined for portions over at least a 10-Hz band, in which decay could be observed. There were five events with good spectra, for which decay occurred over 7.5 Hz. These were also included because of the clean spectrum shape. A least-squares method was then used to fit a straight
121
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127 0-0 I :
• coO 00
°°•°
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• • • 509
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-9.21
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°o° e 4 1 4 I I0"0
] 20"0
F R E Q U E N C Y
I 30-0
0-0
I I0-0
I 20"0
I 30-0
(Hz)
Fig. 6. Spectra obtained from events recorded by station TRN for the six zones in the study area. Qc values are shown with each spectrum.
line to this portion o f the spectrum. Q was determined from the gradient of the line by: T R A V T *7r Q =
(10) GRAD where T R A V T is the travel time to the P-onset and G R A D is the gradient of the fitted line.
8. R e s u l t s
The results shown in Table 3 suggest that the average Qc within the study area is relatively stable, for the given frequency bands, and does not vary significantly with depth. The ranges of Qc for shallow events are 180-218, 2 1 3 - 3 1 5 , 488-691 and 1141-1728 if the value of 2057 is not used since there is no intermediate-depth value for the 12-Hz
band for TPR. The ranges for intermediate-depth events are 162-347, 2 5 0 - 3 5 4 , 4 3 2 - 6 0 9 and 11061441. However, individual station results display some interesting differences. The results for TRN and TCE are, within error limits, the same except for the 1.5-Hz band, in which the value obtained for intermediate-depth events recorded at TCE display somewhat reduced attenuation. This result was not observed by A m b e h and Lynch (1993) because of the very limited data for TCE and TRN in the intermediate-depth range. Also the figures obtained for TBH(S) in the 1.5-3.0 Hz range display slightly higher attenuation values. Plots of Qc values by frequency are shown in Fig. 7, which display a zonal variation of Qc. This variation is more marked in the 3- and 12-Hz bands. There is also a suggestion that the attenuation on
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
122
o
(a)
z~x m
215
,,o
~e,.
,~,,
o
O
"
o
~,S'/m
181
o
8~ 0
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07
197
o
i
62.5
~
62.0
61.5
1
.,,,-
61.0
i
i
60.5
60.0
(b) z~
249 0
u~
o ~.~l~"~z~,,.~
~'
4,4
" - "
t,
i
62.5
i
62.0
e
L
61.5
~
i
6hO
60.5
i
60.0
Fig. 7. Qc values for events recorded at TRN for frequency b a n d s 1.5 (a), 3.0 Hz (b), 6.0 (c) and 12.0 Hz (d). Coordinates are °W long. and °N lat.
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
3~9 ~X491
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i
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Fig. 7 (continued).
if
i
60.5
i
60.0
124
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
Table 3 Average Qc values and their standard errors Station
1.5 Hz
3.0 Hz
6.0 Hz
TCE(S) TCE(I) TRN(S) TRN(I) TPP(S) TPP(1) GRW(S) GRW(1) TBH(S) TBH(1) TPR(S) TPR(1)
184 _+ 13 (27) 347 _ 35 (11) 218 ± 20 (32) 216 ± 18 (11) 211 ± 17 (15) 183 ± 17 (1) 176 ± 14 (9) 136 ± 12 (3) 180 ± 15 (10) 209 ± 23 (2) 205 ± 21 (4) 162 _+ 9 (1)
316 354 315 353 350 302 286 291 213 250 292 305
636 609 563 564 613 586 488 544 539 514 691 432
± 16 (45) ± 18 (22) ± 21 (45) ± 25 (16) ___22 (20) ± 19 (2) ± 15 (16) ± 15 (10) ___ 11 (26) ___9 (13) ± 15 (5) ± 26 (2)
± ± ± ± ± ± ± ± ± ± ± ±
12.0 Hz 36 (43) 24 (23) 27 (47) 27 (18) 41 (13) 43 (3) 20 (15) 23 (12) 35 (19) 25 (11) 52 (6) 19 (3)
1193 _+ 77 (27) 2591262 ± 69 (16) 1160 ± 73 (36) 1106 ± 58 (17) 1141 _+ 121 (1) 1454 ± 101 (1) 1728 ± 127 (13) 1441 + 77 (10) 2057 ± 200 (4) -
Bracketed values are the number of Q used in the average. (S) indicates events less than 70 km deep, (I) indicates events more than 70 km deep.
eastern Trinidad is significantly different from that on western Trinidad.
8.1. Variation of Qc with window length, average lapse time, epicentral distance, focal depth and magnitude The results from stations TCE and TRN for frequencies 6 and 12 Hz were examined for dependence on window length, average lapse time, epicentral distance, focal depth and magnitude. There is no striking correlation between Qc and any of these
1480
• • •
8.2. Qc variation and frequency dependence Coda-Q analysis in many regions has revealed a positive correlation between Qc and frequency (e.g., Aki and Chouet, 1975; Rautian et al., 1978). The form of the dependence is generally given by:
ID
a4o
variables. However, the TRN results show a slight negative correlation between Qc and focal depth and a slight positive correlation with average lapse time, file results for which are shown in Fig. 8. This observation is at variance with the interpretation of Roecker et al. (1982) and Rovelli (1984) that increasing coda Q with increasing lapse times is due to increasing Q with depth. This might be indicative of a regional peculiarity but would require further study for a firm conclusion.
See •
Qc = Qof n 200
I'0
50"6
100-2
FO
FOCAL
50"6
DEPTH
100- 2
(KM)
o~
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25-0
~'0
51"0
i • . • e •
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AVG.
LAPSE
TIME
where n has been found to lie mainly in the range 0.5 to 1.1. The Qc values of this study were fitted to Table 4 Qo and n values obtained for events at stations TCE, TRN and TPR Station
~ j 77"0
(SECS,)
Fig. 8. Variation of Qc with focal depth, showing slight negative correlation, and average lapse time, showing slight positive correlation, for station TRN at 6 Hz (left) and 12 Hz (right).
(11)
TCE TRN TPR
Shallow events
Intermediate events
All events
Qo
Qo
Qo
n
116 0.89_+0.04 132 0.80_+0.04 107 t.06_+0.13
n
173 0.74+_0.07 136 0.80_+0.06 101 0.92+-0.16
n
131 0.85_+0.04 133 0.80_+0.04 105 1.02_+0.11
125
LL. Latchman et aL / Tectonophysics 253 (1996) 111-12 7 MAGNITUOE
0 0
DEPTH (KM)
I-0-1.9
(~ 0 -
2.0-2.9
~" 7'0-140
69
0 3.0-3-9
tM %
--r 360±19
%
( 319±5 578±16 512±28 i ~ 399±6
(9
O~
J 1~ 736±55
~O-a,~ao2±6
lOeO ±37' "~510 ±18 1511±3 240±9 -- 443 ± 18 151:3
~ 0
s7o
30
(~415± 7 ~
~) 191
3
%
o %
%
¢lq
VENEZUELA
62.5 °
62.0 °
~
61.5 °
61.0 °
60.5 °
60.0 °
Fig. 9. Locationsof events used in Q,~ determination(with values shown).
the above equation. The results are given in Table 4. The results obtained in each frequency band were not uniformly abundant. For individual stations the bands with disproportionate numbers of results were excluded. The usable bands obtained for each station are as follows: TCE--1.5, 3.0, 6.0, 12.0; TRN--1.5, 3.0, 6.0, 12.0; TPP--1.5, 3.0, 6.0; G R W - - 3 . 0 , 6.0, 12.0; TBH--3.0, 6.0; and T P R - - I . 5 , 3.0, 6.0, 12.0. Only those stations with data in all four bands are here displayed.
8.3. Spectral Q for TRN The results from the limited data used in this study indicate a spatial variation of the attenuation
parameter. In general, the highest attenuation is observed on land Trinidad (Fig. 9).
9. Discussion and conclusions Of the 83 events used in the coda-Q analysis, 25 were of intermediate depth ( - - 3 0 % ) and of the 22 with usable P-wave spectra, there were three events ( = 14%) of intermediate depth. The average Q~ for the shallow events is 348 and 701 for the intermediate-depth events; 348 compares very well with the Frankel (1982) value of 380 found using arrivals to three stations in the northeastern Caribbean, for frequencies of 5 - 2 0 Hz. His data set
126
J.L. Latchman et aL / Tectonophysics 253 (1996) 111-127
consisted of events less than 50 km in depth. The values of Qc for TRN (see Table 2) are 218, 315, 563 and 1160 for shallow events at 1.5, 3.0, 6.0 and 12 Hz, respectively, and 216, 353, 564 and 1106 for intermediate depth events. Frankel's average from two stations for Qt3 is 400. In the determination of Q,, decay was usually observed above 5 Hz. Therefore, a comparison of Qt3 and Q~ made in the 6- and 12-Hz bands and using the average of 862 for Qt3 reveals that P-wave attenuation is greater than S-wave attenuation such that Q,~ = 0.40Q~. However, our observations suggest that simply averaging Q,~ and Qc for all the results may be misleading. In the S - S single scattering model, the scatterers responsible for the generation of coda waves are located on the surface of an ellipsoid whose surface projection is defined by the equation: X2
y2
( vt/2)----------~ + ( vt/2)2 _ ( R 2 / 4 ) = 1
(12)
for a surface source. Here R is the source-receiver distance, v is the velocity, t is the lapse time, and x and y are the surface coordinates (Putli, 1984). In the study area, Qc estimates at an average lapse time of 52 s correspond to sampling volumes of about 208 km in lateral extent, 137 km in depth and 16,500 km 2 in surface area (Ambeh and Lynch, 1993). Therefore, waves arriving at any station within the study area should have sampled largely overlapping volumes. A zonal variation in the Qc values obtained should not be apparent. However, our results suggest that such a variation exists. It is unlikely that the medium/hard station sites are responsible for this observation. This is not conclusive because an investigation of zonal variation of Qc was not one of the original objectives of this study and the techniques employed were not tailored to cater for it. The Q~ results prompted the Q~ plots. A future study would need to be done, restricting the lapse time to a constant value and so restricting the sampled volume to a fixed size. It should be noted that because 25 s was the minimum lapse time used, the extent of the ellipsoid for some events was as small as 100 km and 88 km in depth and, therefore, those events on land Trinidad, e.g., could have a sampled ellipsoid composed largely of on land scatterers. Clearly, a sampled surface as symmetrical as an ellipsoid, must assume a uniform distribution of
heterogeneities (Aki, 1969; Pulli and Aki, 1981). Although this may be a valid assumption for a tectonically stable region such as the Central United States, it is probably not applicable in an area as tectonically complex at the study area. It might be that the complex nature of the area reduces the expected overlap thus allowing genuine zonal variations to be revealed. The observation by Sutton et al. (1967) that attenuation appears to be affected by the orientation of the structural trend with respect to event location may also contribute to the observed differences in attenuation. Significant differences in attenuation at different frequencies observed at populated sites have important implications with regard to hazard/risk and should not be casually treated. The lessons learned from the Mexico City earthquake of 1985 forcefully demonstrate the potential for great disaster when various influences combine in time and place, e.g., the occurrence of an earthquake rich in 2 s energy, the efficient propagation of that energy to Mexico City and a site capable of greatly amplifying 2 s energy (Singh et al., 1988). In the determination of Q,~ geometric spreading was not taken into account and indeed the Q,, values obtained must incorporate this effect. Also, it was assumed that Q is constant over the travel path, which allowed Eq. 7 to be used. The results, however, indicate that Q does vary over the path and, therefore, the use of Eq. 7 is not strictly accurate.
Acknowledgements The authors deeply appreciate the time taken by Dr. Robin Adams of the International Seismological Centre and Prof. C. McCann of Reading University, UK to read and comment on this paper. Finally, thanks to the unknown editors, whose comments served to enhance the presentation.
References Aki, K., 1969. Analysis of seismic coda of local earthquakes as scattered waves. J. Geophys. Res., 74(2): 615-631. Aki, K., 1980a. Attenuation of shear waves in the lithosphere for frequency from 0.05 to 25Hz. Phys. Earth Planet. Inter., 21(I): 50-60.
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127 Aki, K., 1980b. Scattering and attenuation of shear waves in the lithosphere. J. Geophys. Res., 85(B11): 6496-6504. Aki, K., 1982. Scattering and attenuation. Bull. Seismol. Soc. Am., 72(6): $319-$330. Aki, K. and Chouet, B., 1975. Origin of coda waves: source, attenuation and scattering effects. J. Geophys. Res., 80(23): 3322-3342. AI-Shukri, H., Mitchell, B.J. and Ghalib, H.A., 1988. Attenuation of seismic waves in the New Madrid seismic zone. Seismol. Res. Lett., 59(4): 133-140. Ambeh, W.B. and Lynch, L., 1993. Coda Q in the eastern Caribbean, West Indies. Geophys. J. Int., 112: 507-516. Anderson, J.G. and Hough, S.E., 1984. A model for the shape of the fourier amplitude spectrum of acceleration at high frequencies. Bull. Seismol. Soc. Am., 74(5): 1969-1993. Bakun, W.H., Bufe, C.F. and Stewart, R.M., 1978. Body-wave spectra of Central California earthquakes. Bull. Seismol. Soc. Am., 66(2): 363-384. Brune, J., 1970. Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res., 75(26): 4997-5009. Cormier, V.F., 1982. The effect of attenuation on seismic body waves. Bull. Seismol. Soc. Am., 72(6): S169-$200. Der, Z.A. and McElfresh, T.W., 1976. Short-period P-wave attenuation along various paths in North America as determined from P-wave spectra of the SALMON nuclear explosion. Bull. Seismol. Soc. Am., 66(5): 1609-1623. Fowler, C.M.R., 1990. The Solid Earth. Cambridge Univ. Press, Canada, 472 pp. Frankel, A., 1982. The effects of attenuation and site response of the spectra of microearthquakes in the northeastern Caribbean. Bull. Seismol. Soc. Am., 72(4): 1379-1402. Hermann, R.B., 1980. Q estimates using the coda of local earthquakes. Bull. Seismol. Soc. Am., 70(2): 447-468. Isacks, B., Sykes, L.R. and Oliver, J., 1969. Focal mechanisms of deep and shallow earthquakes in the Tonga-Kermadec region and the tectonics of island arcs. Geol. Soc. Am. Bull., 80: 1443-1470. Jackson, D.D. and Anderson, D.L., 1970. Physical mechanisms of seismic wave attenuation. Rev. Geophys. Space Phys., 8(1): 1-63.
Knopoff, L., 1964. Q. Rev. Geophys., 2: 625-660. Molnar, P. and Sykes, L.R., 1969. Tectonics of the Caribbean and Middle America regions from focal mechanisms and seismicity. Geol. Soc. Am. Bull., 80: 1639-1684. Morgan, F.D., Wadge, G., Latchman, J., Aspinall, W.P., Hudson, D. and Samstag, F., 1988. The earthquake Hazard alert of
127
September 1982 in southern Tobago. Bull. Seismol. Soc. Am., 78(4): 1550-1562. Pulli, J.J., 1984. Attenuation of coda waves in New England. Bull. Seismol. Soc. Am., 74(4): 1149-1166. Pulli, J.J. and Aki, K., 1981. Attenuation of seismic waves in the lithosphere: comparison of active stable areas. In: Earthquakes and Earthquake Engineering. The Eastern Publishers, Ann Arbor, MI, pp. 129-141. Rautian, T.G., Khalturin, V.I., Martynov, V.G. and Molnar, P., 1978. Preliminary analysis of the spectral content of P and S waves from local earthquakes in the Garm, Tadjikistan region. Bull. Seismol. Soc. Am., 68(4): 949-971. Roecker, S.W., Tucker, B., King, J. and Hatzfeld, D., 1982. Estimates of Q in Central Asia as a function of frequency and depth using the coda of locally recorded earthquakes. Bull. Seismol. Soc. Am., 72: 129-149. Rovelli, A., 1984. Seismic Q for the lithosphere of the Montenegro region Yugoslavia: frequency, depth and time windowing effects. Phys. Earth Planet. Inter., 34: 159-172. Russo, R.M., Speed, R.C., Okal, E.A., Shepherd, J.B. and Rowley, K.C., 1990. Historical seismicity of the southeastern Caribbean and tectonic implications. Pure Appl. Geophys., 139: 87-120. Sato, H., 1977. Energy propagation including scattering effects. Single isotropic scattering approximation. J. Phys. Earth., 24: 27-41. Singh, S.K., Lenmo, J., Dominguez, T., Ordaz, M., Espinosa, J.M., Mena, E. and Quaas, R., 1988. The Mexico earthquake of September 19, 1985--A study of amplification of seismic waves in the valley of Mexico with respect to a hill zone site. Earthquake Spectra, 4: 653-673. Speed, R.C., 1985. Cenozoic collision of the Lesser Antilles Arc and continental South America and the origin of the El Pilar Fault. Tectonics, 4:41-69. Sutton, G.H., Mitronovas, W. and Pomeroy, P.W., 1967. Shortperiod seismic energy radiation patterns from underground nuclear explosions and small-magnitude earthquakes. Bull. Seismol. Soc. Am., 57(2): 249-267. Trifunac, M.D. and Udwadia, F.E., 1974. Variations of strong earthquake ground shaking in the Los Angeles area. Bull. Seismol. Soc. Am., 64(5): 1429-1454. Vierbucben, R.C., 1984. The geology of the El Pilar fault zone and adjacent areas in northeastern Venezuela. In: W.E. Bonini, R.B. Hargraves and R. Shagam (Editors), The CaribbeanSouth American Plate Boundary and Regional Tectonics. Geol. Soc. Am. Mem., 162: 189-212.
Tectonophysics 253 (1996) I 11-127
Attenuation of seismic waves in the Trinidad and Tobago area Joan L. Latchman *, William B. Ambeh, Lloyd L. Lynch Seismic Research Unit, University of the West Indies, St. Augustine, Trinidad, Trinidad and Tobago
Received 25 October 1994; accepted 15 May 1995
Abstract
The attenuation of seismic waves from earthquakes located within the area bounded by 9-12°N and 60-63°W was estimated from short-period seismograms. Coda-Q, Qc, determinations were made for each of the six seismograph stations within the area, while spectral Q values from P-phases, Q~, were estimated for station TRN. The S - S single-scattering model was assumed for coda generation, and the to-2 source model was assumed for the spectral Q determinations. The Qc values show a strong frequency dependence in the frequency range 1.5-12 Hz. The value of Q at 1 Hz, Q0, was found to lie within the range 107-132, while the rate of frequency dependence, n, extends from 0.80 to 1.06 for shallow events. For intermediate-depth events, Qo varies from 101 to 173 and n from 0.80 to 1.02. The Q~ values obtained show a spatial variation within the region, the highest attenuation was obtained on land Trinidad.
1. I n t r o d u c t i o n In all real media, the amplitude of an oscillating system decays with time to zero. Such systems are described as damped systems. This usually results from the conversion of kinetic energy to heat, which occurs because of friction, the damping force. Earthquake waves propagating through the earth lose amplitude and are attenuated. The two mechanisms contributing to this phenomenon are (a) intrins i c / a n e l a s t i c attenuation and (b) apparent attenuation. Intrinsic/anelastic attenuation results from actual loss mechanisms such as damped resonance, static hysteresis, relaxation and viscosity, all of which are related to the "internal friction" o f the medium.
* Corresponding author.
K n o p o f f (1964), using terminology borrowed from electric circuit theory defined attenuation by Q, the quality factor, such that:
Q-l
AW
l =~,n- I,V
(1)
where W is the total amount o f elastic energy stored per unit volume per cycle and AW is the part of W that is dissipated per cycle. Anelastic characteristics of solids are controlled by the thermal and defect properties, which are influenced by the thermal conductivity, grain size, defect concentration and mobility, diffusion rate and relatively weak interatomic and interdefect bonds at grain boundaries. Many of the mechanisms are activated processes that are strongly dependent on temperature and to a small extent on pressure (Jackson and Anderson, 1970). Apparent attenuation may result from geometrical effects, such as refraction, reflection and scattering.
0040-1951/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0040- 1951(95)00050-X
112
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
Scattering of wave energy is believed to be caused by inhomogeneities comparable in scale to the wavelength of the elastic wave. This attenuation is linear and necessarily highly frequency dependent. Although, in principle, this is a geometric mechanism, its mathematical form is similar to anelastic attenuation and therefore cannot be removed from seismic amplitude data (Jackson and Anderson, 1970). The amplitudes of seismic body waves recorded at observing stations are also influenced by the local layering and velocity distribution. Arriving waves can travel along numerous paths. If the soil conditions modify the incoming seismic waves in a simple and significant way, then it would be expected that given frequencies w o u l d be p r e d i c t a b l y amplified/reduced, irrespective of the earthquake source mechanism or the direction from which seismic waves arrive. However, the effects due to geological discontinuities are strongly dependent on the three-dimensional nature of soil deposits and on the direction of arriving waves. Therefore, an amplifica-
tion pattern resulting from local site conditions and transmission path is unlikely to be repeated during any sequence of recorded earthquakes unless they occur on the same fault and have identical source mechanisms (Trifunac and Udwadia, 1974; Der and McElfresh, 1976). This study investigates the attenuation of seismic waves within the area enclosed by Trinidad, Tobago, Grenada and the Paria Peninsula (Fig. 1) by making use of earthquakes occurring within the area and recorded at stations TCE, TRN, TPP, GRW, TBH and TPR (Fig. 3). Following file broad site classification of soft, medium and hard, TCE, TBH and TPR fall under hard and TPP, TRN and GRW fall under medium.
2. Seismicity and tectonics of the area
The study area is located at the southeastern comer of the Caribbean Plate, within the boundary
I
I
N
CARIB BF /3N SEA
I
, ~ ~ TOBAGO li°N
A
N T
'++"+,,.+,.,o+.
o
3 f
~I "~
+"~+La"++,' e. '~?!,L Strike-slip fault
~ ORINOCO
Normal fault
62°W
~ -
~m~ '~,
61_'W
Fig. 1. Map showing significant fault traces (Speed, 1985; Morgan et al., 1988).
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
region between the Caribbean Plate and the South American Plate. Within this boundary region, the seismic and volcanic activity, resulting from the subduction of the oceanic lithosphere of the South American Plate beneath the Caribbean Plate, is manifested along the southern end of the Lesser Antillian island arc, from Grenada into the Paria Peninsula. The nature of the activity there changes to include the activity characteristic of the strike-slip boundary, the E1 Pilar fault, in northeastern Venezuela. The extent of the E1 Pilar is uncertain, there being various schools of thought. Vierbuchen (1984) defines the E1 Pilar fault as extending from the Gulf of Cariaco to a point 400 km east of Trinidad. However, Russo et al. (1990) found no evidence to support activity that
113
could be attributed to the E1 Pilar fault further west than 62.3°W. Molnar and Sykes (1969) postulate that the region in northeastern Venezuela, near Trinidad, marks the intersection of the transform fault with the Lesser Antillean arc. They suggest that hinge faulting, similar to the structure proposed by Isacks et al. (1969) for the northern end of the Tonga arc, may exist near Trinidad at the contact point of the transform fault and the subducting plate. It is generally held that the activity on the Venezuela side of the study area is not occurring aligned to any of the significant faults. On the other hand, foreshocks and aftershocks of an M b = 5.2 earthquake, which occurred on 20 September 1982 revealed a W- to WNW-trending zone of activity
MAGNITUDE
DEPTH
o.o-
0.9
0
I'0-
1'9
(kin) O--
69
0
Z.O-2-9
,,,,70--
r40
0
3.0-3.9
0
0
4.0-
0
> f40
4"9
% nJ
%
o C)
o c)
% o
o O~
62.5 °
62.0 °
6).5 °
61.0 °
60.5 °
Fig. 2. Events during the period 1 9 7 7 / 0 1 - 1 9 9 0 / 0 6 .
60.0 °
114
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
Table 1 Parameters of events used in coda-Q analysis Yr/mon/d
H/min/s
Lat (°N)
Long (°W)
Depth (km)
Mag
Stations
1992/12/21 1992/12/22 1992/12/22 1992/12/27 1992/12/28 1992/12/28 1992/12/28 1993/01/06 1993/01/08 1993/01/08 1993/01/09 1993/01/09 1993/01/10 1993/01/10 1993/01/10 1993/01/10 1993/01/12 1993/01/12 1993/01/18 1993/01/19 1993/01/21 1993/01/21 1993/01/23 1993/01/24 1993/01/28 1993/02/14 1993/02/14 1993/02/14 1993/02/15 1993/02/15 1993/02/16 1993/02/18 1993/02/22 1993/02/22 1993/03/01 1993/03/02 1993/03/02 1993/03/04 1993/03/05 1993/03/05 1993/03/08 1993/03/08 1993/03/08 1993/O3/O9 1993/03/11 1993/03/23 1993/03/29 1993/04/03 1993/04/04 1993/04/04 1993/04/04 1993/04/06 1993/04/11
07/51/29.83 04/40/09.47 16/13/I 1 . 9 6 09/45/11.17 05/14/33.03 10/01/31.29 17/45/31.51 18/24/01.11 05/00/12.95 12/43/06.96 12/44/07.02 19/45/23.31 11/09/20.55 13/45/31.04 17/41/53.99 20/14/12.31 12/46/48.09 19/36/41.71 09/13/56.21 08/05/26.64 06/24/49.43 10/47/52.89 09/44/36.63 00/25/43.89 13/07/30.39 05/04/15.01 05/09/25.25 12/38/40.75 14/20/53.83 20/43/20.43 20/58/28.56 05/30/18.86 04/36/38.86 07/11/39.19 15/40/23.49 12/41/53.41 19/30/45.72 23/51/24.40 02/46/50.92 09/33/17.56 07/18/40.33 09/48/45.12 10/32/33.18 01/34/59.14 19/27/10.98 13/11/42.30 10/13/33.77 06/17/34.73 04/08/11.69 16/40/46.41 18/11/50.03 16/38/08.85 13/03/37.27
10.9770 10.3460 11.4620 11.0250 10.6880 11.1100 11.2700 10.4140 10.9770 10.7570 10.5580 10.2640 11.1800 11.1350 11.1680 11.2100 10.5650 10.7440 10.3930 10.4410 10.5780 10.3790 10.3540 10.6690 11.2680 10.8120 10.9260 10.7120 9.7880 11.3430 10.2160 10.7590 10.8380 10.2500 10.8190 11.1100 11.1210 11.0990 11.2860 10.8910 11.0770 10.9450 10.9100 10.8320 10.9670 11.1870 10.9480 11.0190 10.8790 11.0360 10.4710 10.0410 10.2590
62.0170 62.3100 62.0640 62.0940 61.6290 60.6400 62.1120 62.8590 61.1580 62.4350 61.3280 60.8390 60.9440 60.6020 61.8960 60.2230 61.6770 62.4940 62.2750 62.0290 61.3050 62.1740 61.3280 61.1060 60.4230 60.0040 60.0360 60.1520 62.4650 61.4860 60.1290 62.3670 62.3490 61.5510 62.1950 62.1220 62.1950 61.7490 61.7930 62.4000 62.8860 61.5900 62.3130 62.1560 61.7570 61.7220 61.7580 62.1170 62.3970 61.9820 61.5350 61.1920 61.1970
97.24 5.00 124.27 29.63 5.00 8.00 100.35 1.14 10.00 10.00 32.96 43.74 t.51 31.01 64.81 13.01 15.06 87.62 10.00 42.95 5.00 5.00 50.80 23.95 33.21 17.55 24.45 13.01 33.00 86.26 82.34 73.53 86.80 46.05 73.04 9.23 8.40 9.86 10.10 53.25 5.00 21.21 106.61 23.21 111.67 43.76 67.34 73.89 30.36 111.91 28.36 48.99 54.33
3.1 3.7 3:4 3.3 2.8 2.7 3.2 3.4 2.1 3.0 2.5 3.1 3.2 3.4 2.5 3.0 2.6 3.5 3.5 2.9 3.1 3.5 2.2 2.9 3.4 3.6 3.3 2.9 3.2 2.8 3.4 3.9 3.0 2.5 3.0 2.8 2.9 2.3 2.5 3.5 3.0 2.9 3.2 3.0 2.9 3.0 3.9 3.1 3.8 3.5 2.8 3.5 2.6
TRN,GRW GRW TCE, TRN, TPP, TBH TCE, TPP, GRW TCE, TPP TRN TCE, TRN, GRW, TBH TCE, TRN, TPP, GRW TRN, TBH TCE, TRN, TPP TRN, TBH TRN, TPP, GRW TCE, TRN, TPP, GRW, TBH TCE TRN TCE, TRN TCE TRN, TBH TCE TRN, TBH TCE TRN, TPP, GRW, TBH TCE TRN, TPP, TBH TCE TRN, TPP TCE TRN, TPP, GRW, TBH TCE TRN, TPP, TBH TCE TRN TCE TRN, GRW, TBH TCE TRN, TPP, TBH TCE TRN, TPP, GRW, TBH TCE TRN, TBH, TPR TCE TRN TCE, TRN, TBH TCE, GRW TCE, TPR TCE, TRN, GRW TCE, TRN, TPP TCE, TRN, GRW GRW TCE TRN, GRW TCE TRN TCE TRN, GRW, TBH TCE TRN TPP, GRW, TBH, TPR TCE TRN TCE TBH TCE GRW, TBH, TPR TCE TRN TCE TRN TCE TRN, GRW, TBH TPR TCE. TRN, GRW TCE, TPR TCE, TPP, TBH TCE, TRN TCE, TRN TCE, TRN, TPP, TBH
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
I 15
Table 1 (continued) Yr/mon/d H/min/s
Lat (°N)
Long (°W)
Depth (km)
Mag
Stations
1993/04/11 1993/04/15 1993/04/16 1993/04/16 1993/04/18 1993/04/18 1993/04/21 1993/04/22 1993/04/22 1993/04/26 1993/05/01 1993/05/05 1993/05/08 1993/05/12 1993/05/22 1993/05/22 1993/05 /27 1993/05/29 1993/05/29 1993/05/31 1993/06/01 1993/06/01 1993/06/02 1993/06/03 1993/06/04 1993/06/04 1993/06/05 1993/06/13 1993/06/22 1993/06/23
11.1330 10.6480 11.3040 10.7890 10.7940 11.0580 11.1810 10.8440 10.5550 11.1160 10.9850 10.4320 11.1070 10.7490 10.7980 10.8670 11.5510 11.5880 11.1390 11.0800 10.8060 11.2390 11.3670 10.2060 11.3930 11.4630 9.9650 10.2150 11.9190 10.7070
62.5680 62.6520 61.2960 61.9540 62.4940 62.0100 62.8630 62.3740 62.4360 61.8390 60.0280 62.31O0 62.2030 62.3970 62.5700 62.2340 61.0310 61.9790 61.6640 62.2370 62.4450 61.8380 62.2150 60.5500 62.0940 61.5180 62.3460 62.3570 61.7640 60.7900
3.00 47.43 14.80 38.64 67.20 108.20 6.17 50.69 108.58 75.68 19.32 3.00 111.99 57.83 3.00 73.64 24.31 99.68 48.08 56.65 52.17 73.53 106.94 120.18 73.59 14.01 81.45 3.00 111.88 28.75
3.3 3.0 3.2 3.1 3.0 3.3 3.2 3.3 4.1 3.0 2.7 3.0 3.9 3.2 3.3 3.2 2.9 3.2 3.0 3.2 3.1 3.2 3.2 3.3 3.1 2.8 4.0 3.6 3.2 2.5
TCE, TRN, TPP, TBH TCE, TRN TCE, TPP, TBH, TPR TCE, TRN, TPP TCE, TRN, TBH TCE, TRN, TBH, TPR TCE, TRN TCE, TRN, TPP TCE TCE, TRN TCE, TRN, TBH TCE, TRN TCE TCE, TRN TCE, TRN, TPP TPP, GRW, TBH TRN, GRW TCE, TRN, GRW, TBH TCE, TRN, GRW, TBH TCE, TRN, GRW, TBH TCE, TRN, TBH TCE, TRN, GRW, TBH TCE, TRN, TPP, GRW, TBH TCE, TRN, TBH TCE, TRN, GRW TRN, GRW TCE, TRN, TBH TCE, TRN, GRW, TBH TCE, TRN TBH
17/49/00.47 12/37/35.81 11/43/14.14 22/51/57.76 00/14/52.50 02/16/37.28 09/45/59.15 09/38/41.18 l 2/31/57.15 12/09/40.73 03/23/11.57 23/40/50.53 18/38/13.91 09/40/45.83 05/03/14.80 10/29/55.01 04/37/31.32 00/16/05.33 14/32/03.56 07/58/21.45 03/34/31.80 12/44/08.26 08/22/03.77 16/47/41.30 05/39/53.88 11/52/21.91 18/09/49.09 07/48/15.69 02/35/14.87 12/20/12.69
southwest of Tobago. The focal mechanism of the main shock showed right-lateral strike-slip motion along an E - W - t r e n d i n g fault plane dipping steeply (71 °) to the north. This active fault appears to form part of the previously unrecognized Southern Tobago Fault System, for which there is evidence in the geology of the late Neogene rocks of the island (Morgan et al., 1988). On 10 March 1988 an M s = 6.4 (NEIC) earthquake and aftershocks, east of Trinidad, revealed the presence of a N W - S E - t r e n d ing active zone. The NEIC focal mechanism of the main shock is moderately well controlled and corresponds to strike-slip faulting with a large normal component. The preferred fault plane is undetermined. The depth of this event from pP phases given in the ISC Bulletin is 53 km. However, to date, the nature of the feature has not been formalised (Figs. 1 and 2). Besides these defined zones of activity,
earthquakes are routinely located throughout the region as shown in Fig. 2 and as can also be seen from even the limited period covered by the data used for the coda-Q analysis (Table 1; Fig. 3).
3. Data acquisition Instrumental eastern Caribbean earthquake data have been collected by the Seismic Research Unit since 1953. The collection system has progressed from photographic records delivered by mail, to analogue telemetered signals recorded on 24" magnetic tape in the 1970's, to digitised data recorded on IBM P C ' s in the 1980's. The network consists of a total of 30 stations, of which over 50% is operational at any given time. The sensor at each station is a single vertical-component short-period seismometer,
116
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127 HAGNITUDE
DEPTH
(kn) 1.0
-
1.9
(2)
0 -
69
02) 2 . 0
o
-
2.9
,,,, 70 -
140
E) 3.0 - 3.9
C-d~FA~IADA~ G F I W ¢'d
z~x
Ax :
(2)
AAx,~.
O
~ G O
t~
o
o
%
62.5 °
62.0 °
61.5 °
61.0 °
60.5 °
60.0 °
Fig. 3. Locations of events, 92/12/21-93/06/30, used in coda-Q analysis.
which is either a Marks Product L4C or a Kinemetrics Ranger SS1. The overall system transfer function for TRN is shown in Fig. 4. The signal from each seismometer is amplified, frequency modulated, then transmitted to the central recording site in St. Augustine, Trinidad, via VHF radio a n d / o r microwave links. The signals are then demodulated, fed into PC's (fifteen stations per computer) and digitized by a 12 bit analogue to digital converter at 100 samples/s. A triggering algorithm searches the resulting time series, from each station continuously, for possible earthquakes and stores the "'event", preceded by a selectable length of pre-triggering
time record, once preset triggering criteria are met. The data from each of the monitoring machines are transferred to another PC, on which there is interactive software for picking phase arrival times and routine hypocentral determination. The network detects over 1500 events annually.
4. Importance of attenuation The construction of buildings with adequate earthquake resistance requires the estimation of the poten-
J . L . L a t c h m a n et al. / T e c t o n o p h y s i c s 2 5 3 ( 1 9 9 6 ) 111 - 1 2 7
117
determine the attenuation parameter must consider these influences.
5. Determination of attenuation ~
rz
5,1. Coda method
e
w
u4
w o
~.00
-013~
°39 LOG
~.'0~
~.'70
FREQUENCY
Fig. 4, Amplitude response spectrum for station TRN.
tial ground motion in future earthquakes. The effects observed at a given site are influenced by the attenuation of the region, the characteristics of the source and the local site conditions. The attenuation parameter has been found to vary beneath the earth's surface. Estimates of Q in the earth are of the order 102 for the inner core, l04 for the outer core, l03 for the lower mantle, 102 for the upper mantle and 200 for the lithosphere (Fowler, 1990). Since the value of the attenuation parameter also varies from region to region within the crust, it is important to have a measure of the absorption of the intervening area in order to estimate the effects of an earthquake at any given distance from a specific source. The difference in felt area for earthquakes in the Western United States from comparable earthquakes in the Eastern United States, the latter extending to far greater distances, demonstrates the significance of differences in attenuation (Aki, 1982). Yet another facet of the attenuation of earthquake waves is that, in a given region, P-wave attenuation, Q,,, is usually different from S-wave attenuation, Q~. Qt~/Q,, varies regionally [e.g., Bakun et al. (1978); Rautian et al. (1978) found the ratio = 0.6, whereas Frankel (1982) found the ratio = 1.78]. A choice of method to
Coda waves, in this context, are the tail of a seismogram (after the arrival of major wave types such as P, S and surface waves) recorded at short distance from an earthquake. They have been explained by the backscattering of waves by heterogeneities distributed in a large region outside the zone of the direct wave path from the source to the station. Whereas it has been found that the spectral contents of the early part of a local earthquake seismogram depend strongly on the travel distance and the nature of the wave path to the station, the difference in spectrum among stations diminishes in the later part of the seismogram and disappears in the coda, a finding revealed by a common shape of coda amplitude decay curve (Aki and Chouet, 1975; Hermann, 1980). In this study we follow the techniques used by Ambeh and Lynch (1993). They made use of the single, backscattering model of Aki and Chouet (1975), extended by Sato (1977). The former assumes that the source and the receiver are coincident. This model gives the coda amplitude, A(flt) at frequency, f, and traveltime, t, as: - zrft
A( f l t ) = C( f ) t -~ e x p - -
(2)
Qc where C ( f ) represents the coda source factor, a is a constant that depends on geometrical spreading and takes values of 1.0, 0.5 and 0.75 for body wave, surface wave and diffusion scattering, respectively, and Qc is the coda quality factor. The extension of Sato (1977) allows for source-receiver offset, which permits the coda analysis to begin immediately after the shear wave arrival. For non-coincident source and receiver, the coda amplitude is given by: - zrft
A(rlt) = C ( f ) K ( r , a ) e x p - -
(3)
ac where a = t/t~, ts is the S-wave lapse time, r is the
I 18
J.L. Latchman et aL / Tectonophysics 253 (1996) 111-127
source-receiver distance, K(r,a) = (1/r){(1/a) In[ a + 1 ) / ( a - 1)]}0.5 and all the other symbols have the same meaning as in Eq. 2. Eq. 4 is obtained by taking natural logarithms of Eq. 3 and rearranging terms:
A(r,f]t)
In k ( , a )
r
lnC(f)-
( ¢rfl ,Qcl
t
(4)
For narrow-bandpass filtered seismograms, C(f) is constant and hence by performing a linear regression of the term on the left-hand side of Eq. 4 with respect to t, Qc can be found from the slope, which is the coefficient of t. If the S - S single scattering theory is correct, Qc should equal Qt~, shear wave attenuation, determined directly from the S-wave, and indeed Aki (1980a, b) has found good agreement between them.
where Q is the attenuation quality factor, V is the seismic wave velocity and the integral is over the ray path. Now if Q is assumed constant over the path then: t t* =
-
(8)
Q
where t is the travel time. Substituting Eq. 8 in Eq. 5 and taking natural logarithms of Eq. 6 yields: In
~rft
Z ( f ) = In A 0 - - -Q
(9)
which is the equation of a straight line having In A0 as the intercept and - ~ t / Q as gradient, from which Q can easily be determined (A1-Shukri et al., 1988).
5.2. Spectral decay method
6. Data for coda-Q analysis
Displacement spectra can be derived from the seismograms of one or more instruments that span the body-wave band. Spectra are normally determined by Fourier transforming a waveform mad smoothing the result. Source theories predict a constant long-period level, followed by a decay above a corner frequency that scales inversely with source size. A measure of seismic attenuation can be defined from the rate of high-frequency decay above the corner frequency (Cormier, 1982). The instrument-corrected acceleration spectrum observed at a station, a distance r from the epicentre is defined by Anderson and Hough (1984) as:
The active, i.e., not archived, database of the Seismic Research Unit was searched for all events located within 9-12°N and 60-63°W (Fig. 3). These data covered the period 1 9 9 2 / 1 2 / 2 1 - 1 9 9 3 / 0 6 / 3 0 . The most recent data were used because reliable station calibrations are available from 1993/01/19. Such information being required for the spectral method for Q determination (Table 2). For coda-Q analysis, waveforms recorded at stations TCE, TRN, TPP, GRW, TBH and TPR were sought. Those with good signal to noise ratio, free of clipping and spikes, were chosen. A total of 83 events met the criteria. The duration magnitudes of the events lie within the range 2.1 to 4.1 and their focal depths lie within 1 to 124 km. Of the total number of events, each station had the following number of acceptable records: T C E - - 7 0 ; TRN--66; T P P - - 2 6 ; G R W - - 3 0 ; T B H - - 3 9 ; and T P R - - t 0 .
a ( r , f ) =A oe ~f'*
(5)
such that:
A o = (27rf)Zs(f)G(r,f) (6) where G(r,f) is the geometric spreading, which, if assumed to be independent of frequency as in a homogeneous medium, is equal to 1/r for body waves, but which was not considered in this study, and S(f) is the source displacement spectrum, which is often assumed to be proportional to f--2 and is known as the w -2 model (Brune, 1970). t * is the attenuation time, and is given, for seismic phases by: dr t* = ]path QV (7)
7. Analysis
7.1. Coda method Each seismogram time series was bandpass filtered over five frequencies bands centred at 1.5, 3, 6, 12 and 24 Hz with bandwidths of 1, 2, 4, 8 and 16 Hz, respectively, using an eight-pole, phase-free Butterworth filter. Starting at the S arrival, the root-
119
J.L. Latchman et al./ Tectonophysics 253 (1996) 111-127
Table 2 Parameters of events used in the spectral analysis method and related Q values Yr/mon/d
H/min/s
Lat (°N)
Long (°W)
Depth (kin)
Mag
Q values
1993/01/23 1993/01/28 1993/02/14 1993/02/14 1993/02/22 1993/03/02 1993/03/04 1993/03/05 1993/03/08 1993/03/23 1993/04/03 1993/04/11 1993/04/16 1993/04/17 1993/04/17 1993/04/18 1993/04/18 1993/04/26 1993/05/01 1993/05/05 1993/05/12 1993/05/29
09/44/36.63 13/07/30.39 05/04/15.01 12/38/40.75 07/11/39.19 12/41/53.41 23/51/24.40 02/46/50.92 07/18/40.33 13/11/42.30 06/17/34.73 13/03/37.27 22/51/57.76 17/06/19.39 17/07/42.99 00/14/52.50 02/l 6/37.28 12/09/40.73 03/23/11.57 23/40/50.53 09/40/45.83 14/32/03.56
10.3540 11.2680 10.8120 10.7120 10.2500 11.1100 11.0990 11.2860 11.0770 11.1870 11.0190 10.2590 10.7890 10.3120 10.2380 10.7940 11.0580 11.1160 10.9850 10.4320 10.7490 11.1390
61.3280 60.4230 60.0040 60.1520 61.5510 62.1220 61.7490 61.7930 62.8860 61.7220 62.1170 61.1970 61.9540 62.2760 62.1440 62.4940 62.0100 61.8390 60.0280 62.31O0 62.3970 61.6640
50.80 33.21 17.55 13.01 46.05 9.23 9.86 10.10 5.00 43.76 73.89 54.33 38.64 3.00 3.00 67.20 108.20 75.68 19.32 3.00 57.83 48.08
2.2 3.4 3.6 2.9 2.5 2.8 2.3 2.5 3.0 3.0 3.1 2.6 3.1 3.4 3.3 3.0 3.3 3.0 2.7 3.0 3.2 3.0
211.62 +__8.79 736.02 __+55.48 191.36 __+3.22 414.6 +__17.19 238.19 __5.45 577.99 __+15.61 158.78 + 3,42 318.95 __+5.01 359.47 +__18.69 398.65 +__5,63 1080.73 __ 37.10 278.28 +__5.66 150.71 __+2.60 352.57 +__6.75 195.42 __+5.86 240.01 + 9.40 509.61 +__ 17.79 512.68 ::k 27.96 669.80 _+ 30.10 364.40 _ 5.54 443.58 _+ 17.52 302.47 +_6.12
mean-square (rms) amplitudes in each window were determined for the data in each frequency band, with the window sliding across the time series at 1 s intervals. Time-window lengths for the rms averaging of 8 s (for centre frequencies of 1.5, 3 and 6 Hz) and 5 s (for centre frequencies 12 and 24 Hz) were chosen so as to smooth out as much as possible irregularities in the amplitudes of the arrivals. The left-hand side of Eq. 4 was then evaluated and plotted against lapse time. From the plot, the linear portion, which had to be at least 25 s long, was visually selected and a least-squares straight line fitted to it. From the slope of the line, Qc was calculated. A sample plot is shown in Fig. 5. The 25 s window was chosen to allow the inclusion of many of the well-recorded smaller events. Qc determination was restricted to the best linear portion to minimize the effect of small-scale, temporal variations in coda amplitude influenced by interference, secondary arrivals, or site conditions. Because of the generally poor quality of the results in the 24-Hz band, they were not included. The poor quality of the 24-Hz band is expected considering the overall system response (Fig. 4).
7.2. Spectral m e t h o d
A specified window of the P-phase was fully cosine 2 tapered and Fourier transformed to produce a spectrum. Initially various window lengths were tested. Although the spectra for window lengths of 0.6, 0.9, 1.2 and 1.5 s were produced, only that obtained from the 0.6 s window was used for this study because, like AI-Shukri et al. (1988), we found that the most favourable portion of the waveform, from which to determine Q, is its onset. In all cases, window lengths greater than 2.0 s would include reflected/refracted phases and therefore window lengths greater than 1.5 s would not be useful. In many cases this phenomenon was observed for window lengths greater than 0.6 s. In all cases the window was opened at 0.3 s before the P-onset as given in the bulletin of the Seismic Research Unit. In one case, where there was a large P-residual, the window onset was revised. A noise sample, of length equal to that of the window, was taken 50 samples preceding the start of the window. This noise spectrum was removed from the P-phase spectrum, the resulting spectrum was smoothed with a running
J.L, Latchman et al. / Tectonophysics 253 (1996) 111-127
120
1.5Hz Q~ = 134
r:
o.o
+
.~-h-
~'~*~-.~+
,%
I
L
L
I
25.3
50,8
"/5,8
I01.I
3.0Hz
D 0.0
,.....,,
~H~+t"t~
~ 125.q
%
I
I
I
I
25.3
50.6
75.8
101.1
L
1
25.3
50,6
I 75.8
I 101.1
~" 125.q
6.0Hz Q~ = 579
.,,,.
p.
__=
0.0
"~,~ 126.q,
12.0Hz 4-
7:
0.0
I 25.6
24Hz
+ +
~ + +,#
0.0
~¢~
+÷
4-
I
I
I
25.6
51.2
75,7
LAPSE TIME
#%++
+ "~ 4-
~+ +
+ +~+
~
I
..i.+ +~ 4"
+~
I
I
I(~,3
127.9
(SEC)
Fig. 5. Example of coda-Q analysis as applied to station TCE seismogram for the event of 1993/02/14 05:04 UTC. The plot is for the quantity ha [ A ( r , f [ t ) / k ( r , a ) ] versus lapse time, t. The arrows indicate the portions chosen to determine Qc.
window, the width of which is a function of the above-mentioned window length. This was done five times to remove stochastic noise and so reveal the underlying spectrum shape. Spectra obtained for events located in the six source zones within the study area are shown in Fig. 6.
The spectra were visually examined for portions over at least a 10-Hz band, in which decay could be observed. There were five events with good spectra, for which decay occurred over 7.5 Hz. These were also included because of the clean spectrum shape. A least-squares method was then used to fit a straight
121
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127 0-0 I :
• coO 00
°°•°
05Jo o o
• • • 509
•
• ~,o+o + •÷•++0 0
-2-30 •
oOOo
¢#o+* 4 4 4
%
o
o o 0 eoB°ll° ° • • e
° o o o o o o ••ol080 o o* e ÷ +÷ + +÷ +
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o o• oOoO
- 4 "61
~
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+
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0000353 + .364
*
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--;5
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I
OF PARIA
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PARIA PENINSULA
NORTH OF PARIA PENINSULA
rr
I
I
I
I
I
n (/) Z
C)
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•
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.J
I.IJ -4-61
E OF TRINIDAD
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++÷.1.,÷÷
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....
+ ~+
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ON LAND TRINIDAD
-9.21
0-0
I I0"0
I 20"0
I 30"0
÷ ÷ + 0"0
*+
•
,302 +
000
O°o
°
o
o
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o °
o 0"- O~l
:
÷ +
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ee
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o "o
e•
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NW OF TRINIDAD
°o° e 4 1 4 I I0"0
] 20"0
F R E Q U E N C Y
I 30-0
0-0
I I0-0
I 20"0
I 30-0
(Hz)
Fig. 6. Spectra obtained from events recorded by station TRN for the six zones in the study area. Qc values are shown with each spectrum.
line to this portion o f the spectrum. Q was determined from the gradient of the line by: T R A V T *7r Q =
(10) GRAD where T R A V T is the travel time to the P-onset and G R A D is the gradient of the fitted line.
8. R e s u l t s
The results shown in Table 3 suggest that the average Qc within the study area is relatively stable, for the given frequency bands, and does not vary significantly with depth. The ranges of Qc for shallow events are 180-218, 2 1 3 - 3 1 5 , 488-691 and 1141-1728 if the value of 2057 is not used since there is no intermediate-depth value for the 12-Hz
band for TPR. The ranges for intermediate-depth events are 162-347, 2 5 0 - 3 5 4 , 4 3 2 - 6 0 9 and 11061441. However, individual station results display some interesting differences. The results for TRN and TCE are, within error limits, the same except for the 1.5-Hz band, in which the value obtained for intermediate-depth events recorded at TCE display somewhat reduced attenuation. This result was not observed by A m b e h and Lynch (1993) because of the very limited data for TCE and TRN in the intermediate-depth range. Also the figures obtained for TBH(S) in the 1.5-3.0 Hz range display slightly higher attenuation values. Plots of Qc values by frequency are shown in Fig. 7, which display a zonal variation of Qc. This variation is more marked in the 3- and 12-Hz bands. There is also a suggestion that the attenuation on
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
122
o
(a)
z~x m
215
,,o
~e,.
,~,,
o
O
"
o
~,S'/m
181
o
8~ 0
l§~S
07
197
o
i
62.5
~
62.0
61.5
1
.,,,-
61.0
i
i
60.5
60.0
(b) z~
249 0
u~
o ~.~l~"~z~,,.~
~'
4,4
" - "
t,
i
62.5
i
62.0
e
L
61.5
~
i
6hO
60.5
i
60.0
Fig. 7. Qc values for events recorded at TRN for frequency b a n d s 1.5 (a), 3.0 Hz (b), 6.0 (c) and 12.0 Hz (d). Coordinates are °W long. and °N lat.
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
3~9 ~X491
-
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or,
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60.5
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i
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61.5
i
61.0
Fig. 7 (continued).
if
i
60.5
i
60.0
124
J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127
Table 3 Average Qc values and their standard errors Station
1.5 Hz
3.0 Hz
6.0 Hz
TCE(S) TCE(I) TRN(S) TRN(I) TPP(S) TPP(1) GRW(S) GRW(1) TBH(S) TBH(1) TPR(S) TPR(1)
184 _+ 13 (27) 347 _ 35 (11) 218 ± 20 (32) 216 ± 18 (11) 211 ± 17 (15) 183 ± 17 (1) 176 ± 14 (9) 136 ± 12 (3) 180 ± 15 (10) 209 ± 23 (2) 205 ± 21 (4) 162 _+ 9 (1)
316 354 315 353 350 302 286 291 213 250 292 305
636 609 563 564 613 586 488 544 539 514 691 432
± 16 (45) ± 18 (22) ± 21 (45) ± 25 (16) ___22 (20) ± 19 (2) ± 15 (16) ± 15 (10) ___ 11 (26) ___9 (13) ± 15 (5) ± 26 (2)
± ± ± ± ± ± ± ± ± ± ± ±
12.0 Hz 36 (43) 24 (23) 27 (47) 27 (18) 41 (13) 43 (3) 20 (15) 23 (12) 35 (19) 25 (11) 52 (6) 19 (3)
1193 _+ 77 (27) 2591262 ± 69 (16) 1160 ± 73 (36) 1106 ± 58 (17) 1141 _+ 121 (1) 1454 ± 101 (1) 1728 ± 127 (13) 1441 + 77 (10) 2057 ± 200 (4) -
Bracketed values are the number of Q used in the average. (S) indicates events less than 70 km deep, (I) indicates events more than 70 km deep.
eastern Trinidad is significantly different from that on western Trinidad.
8.1. Variation of Qc with window length, average lapse time, epicentral distance, focal depth and magnitude The results from stations TCE and TRN for frequencies 6 and 12 Hz were examined for dependence on window length, average lapse time, epicentral distance, focal depth and magnitude. There is no striking correlation between Qc and any of these
1480
• • •
8.2. Qc variation and frequency dependence Coda-Q analysis in many regions has revealed a positive correlation between Qc and frequency (e.g., Aki and Chouet, 1975; Rautian et al., 1978). The form of the dependence is generally given by:
ID
a4o
variables. However, the TRN results show a slight negative correlation between Qc and focal depth and a slight positive correlation with average lapse time, file results for which are shown in Fig. 8. This observation is at variance with the interpretation of Roecker et al. (1982) and Rovelli (1984) that increasing coda Q with increasing lapse times is due to increasing Q with depth. This might be indicative of a regional peculiarity but would require further study for a firm conclusion.
See •
Qc = Qof n 200
I'0
50"6
100-2
FO
FOCAL
50"6
DEPTH
100- 2
(KM)
o~
"'° zoo
i -"- -;"-'1
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JlITel-•
2.~)'0
25-0
~'0
51"0
i • . • e •
?7"0
AVG.
LAPSE
TIME
where n has been found to lie mainly in the range 0.5 to 1.1. The Qc values of this study were fitted to Table 4 Qo and n values obtained for events at stations TCE, TRN and TPR Station
~ j 77"0
(SECS,)
Fig. 8. Variation of Qc with focal depth, showing slight negative correlation, and average lapse time, showing slight positive correlation, for station TRN at 6 Hz (left) and 12 Hz (right).
(11)
TCE TRN TPR
Shallow events
Intermediate events
All events
Qo
Qo
Qo
n
116 0.89_+0.04 132 0.80_+0.04 107 t.06_+0.13
n
173 0.74+_0.07 136 0.80_+0.06 101 0.92+-0.16
n
131 0.85_+0.04 133 0.80_+0.04 105 1.02_+0.11
125
LL. Latchman et aL / Tectonophysics 253 (1996) 111-12 7 MAGNITUOE
0 0
DEPTH (KM)
I-0-1.9
(~ 0 -
2.0-2.9
~" 7'0-140
69
0 3.0-3-9
tM %
--r 360±19
%
( 319±5 578±16 512±28 i ~ 399±6
(9
O~
J 1~ 736±55
~O-a,~ao2±6
lOeO ±37' "~510 ±18 1511±3 240±9 -- 443 ± 18 151:3
~ 0
s7o
30
(~415± 7 ~
~) 191
3
%
o %
%
¢lq
VENEZUELA
62.5 °
62.0 °
~
61.5 °
61.0 °
60.5 °
60.0 °
Fig. 9. Locationsof events used in Q,~ determination(with values shown).
the above equation. The results are given in Table 4. The results obtained in each frequency band were not uniformly abundant. For individual stations the bands with disproportionate numbers of results were excluded. The usable bands obtained for each station are as follows: TCE--1.5, 3.0, 6.0, 12.0; TRN--1.5, 3.0, 6.0, 12.0; TPP--1.5, 3.0, 6.0; G R W - - 3 . 0 , 6.0, 12.0; TBH--3.0, 6.0; and T P R - - I . 5 , 3.0, 6.0, 12.0. Only those stations with data in all four bands are here displayed.
8.3. Spectral Q for TRN The results from the limited data used in this study indicate a spatial variation of the attenuation
parameter. In general, the highest attenuation is observed on land Trinidad (Fig. 9).
9. Discussion and conclusions Of the 83 events used in the coda-Q analysis, 25 were of intermediate depth ( - - 3 0 % ) and of the 22 with usable P-wave spectra, there were three events ( = 14%) of intermediate depth. The average Q~ for the shallow events is 348 and 701 for the intermediate-depth events; 348 compares very well with the Frankel (1982) value of 380 found using arrivals to three stations in the northeastern Caribbean, for frequencies of 5 - 2 0 Hz. His data set
126
J.L. Latchman et aL / Tectonophysics 253 (1996) 111-127
consisted of events less than 50 km in depth. The values of Qc for TRN (see Table 2) are 218, 315, 563 and 1160 for shallow events at 1.5, 3.0, 6.0 and 12 Hz, respectively, and 216, 353, 564 and 1106 for intermediate depth events. Frankel's average from two stations for Qt3 is 400. In the determination of Q,, decay was usually observed above 5 Hz. Therefore, a comparison of Qt3 and Q~ made in the 6- and 12-Hz bands and using the average of 862 for Qt3 reveals that P-wave attenuation is greater than S-wave attenuation such that Q,~ = 0.40Q~. However, our observations suggest that simply averaging Q,~ and Qc for all the results may be misleading. In the S - S single scattering model, the scatterers responsible for the generation of coda waves are located on the surface of an ellipsoid whose surface projection is defined by the equation: X2
y2
( vt/2)----------~ + ( vt/2)2 _ ( R 2 / 4 ) = 1
(12)
for a surface source. Here R is the source-receiver distance, v is the velocity, t is the lapse time, and x and y are the surface coordinates (Putli, 1984). In the study area, Qc estimates at an average lapse time of 52 s correspond to sampling volumes of about 208 km in lateral extent, 137 km in depth and 16,500 km 2 in surface area (Ambeh and Lynch, 1993). Therefore, waves arriving at any station within the study area should have sampled largely overlapping volumes. A zonal variation in the Qc values obtained should not be apparent. However, our results suggest that such a variation exists. It is unlikely that the medium/hard station sites are responsible for this observation. This is not conclusive because an investigation of zonal variation of Qc was not one of the original objectives of this study and the techniques employed were not tailored to cater for it. The Q~ results prompted the Q~ plots. A future study would need to be done, restricting the lapse time to a constant value and so restricting the sampled volume to a fixed size. It should be noted that because 25 s was the minimum lapse time used, the extent of the ellipsoid for some events was as small as 100 km and 88 km in depth and, therefore, those events on land Trinidad, e.g., could have a sampled ellipsoid composed largely of on land scatterers. Clearly, a sampled surface as symmetrical as an ellipsoid, must assume a uniform distribution of
heterogeneities (Aki, 1969; Pulli and Aki, 1981). Although this may be a valid assumption for a tectonically stable region such as the Central United States, it is probably not applicable in an area as tectonically complex at the study area. It might be that the complex nature of the area reduces the expected overlap thus allowing genuine zonal variations to be revealed. The observation by Sutton et al. (1967) that attenuation appears to be affected by the orientation of the structural trend with respect to event location may also contribute to the observed differences in attenuation. Significant differences in attenuation at different frequencies observed at populated sites have important implications with regard to hazard/risk and should not be casually treated. The lessons learned from the Mexico City earthquake of 1985 forcefully demonstrate the potential for great disaster when various influences combine in time and place, e.g., the occurrence of an earthquake rich in 2 s energy, the efficient propagation of that energy to Mexico City and a site capable of greatly amplifying 2 s energy (Singh et al., 1988). In the determination of Q,~ geometric spreading was not taken into account and indeed the Q,, values obtained must incorporate this effect. Also, it was assumed that Q is constant over the travel path, which allowed Eq. 7 to be used. The results, however, indicate that Q does vary over the path and, therefore, the use of Eq. 7 is not strictly accurate.
Acknowledgements The authors deeply appreciate the time taken by Dr. Robin Adams of the International Seismological Centre and Prof. C. McCann of Reading University, UK to read and comment on this paper. Finally, thanks to the unknown editors, whose comments served to enhance the presentation.
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J.L. Latchman et al. / Tectonophysics 253 (1996) 111-127 Aki, K., 1980b. Scattering and attenuation of shear waves in the lithosphere. J. Geophys. Res., 85(B11): 6496-6504. Aki, K., 1982. Scattering and attenuation. Bull. Seismol. Soc. Am., 72(6): $319-$330. Aki, K. and Chouet, B., 1975. Origin of coda waves: source, attenuation and scattering effects. J. Geophys. Res., 80(23): 3322-3342. AI-Shukri, H., Mitchell, B.J. and Ghalib, H.A., 1988. Attenuation of seismic waves in the New Madrid seismic zone. Seismol. Res. Lett., 59(4): 133-140. Ambeh, W.B. and Lynch, L., 1993. Coda Q in the eastern Caribbean, West Indies. Geophys. J. Int., 112: 507-516. Anderson, J.G. and Hough, S.E., 1984. A model for the shape of the fourier amplitude spectrum of acceleration at high frequencies. Bull. Seismol. Soc. Am., 74(5): 1969-1993. Bakun, W.H., Bufe, C.F. and Stewart, R.M., 1978. Body-wave spectra of Central California earthquakes. Bull. Seismol. Soc. Am., 66(2): 363-384. Brune, J., 1970. Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res., 75(26): 4997-5009. Cormier, V.F., 1982. The effect of attenuation on seismic body waves. Bull. Seismol. Soc. Am., 72(6): S169-$200. Der, Z.A. and McElfresh, T.W., 1976. Short-period P-wave attenuation along various paths in North America as determined from P-wave spectra of the SALMON nuclear explosion. Bull. Seismol. Soc. Am., 66(5): 1609-1623. Fowler, C.M.R., 1990. The Solid Earth. Cambridge Univ. Press, Canada, 472 pp. Frankel, A., 1982. The effects of attenuation and site response of the spectra of microearthquakes in the northeastern Caribbean. Bull. Seismol. Soc. Am., 72(4): 1379-1402. Hermann, R.B., 1980. Q estimates using the coda of local earthquakes. Bull. Seismol. Soc. Am., 70(2): 447-468. Isacks, B., Sykes, L.R. and Oliver, J., 1969. Focal mechanisms of deep and shallow earthquakes in the Tonga-Kermadec region and the tectonics of island arcs. Geol. Soc. Am. Bull., 80: 1443-1470. Jackson, D.D. and Anderson, D.L., 1970. Physical mechanisms of seismic wave attenuation. Rev. Geophys. Space Phys., 8(1): 1-63.
Knopoff, L., 1964. Q. Rev. Geophys., 2: 625-660. Molnar, P. and Sykes, L.R., 1969. Tectonics of the Caribbean and Middle America regions from focal mechanisms and seismicity. Geol. Soc. Am. Bull., 80: 1639-1684. Morgan, F.D., Wadge, G., Latchman, J., Aspinall, W.P., Hudson, D. and Samstag, F., 1988. The earthquake Hazard alert of
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September 1982 in southern Tobago. Bull. Seismol. Soc. Am., 78(4): 1550-1562. Pulli, J.J., 1984. Attenuation of coda waves in New England. Bull. Seismol. Soc. Am., 74(4): 1149-1166. Pulli, J.J. and Aki, K., 1981. Attenuation of seismic waves in the lithosphere: comparison of active stable areas. In: Earthquakes and Earthquake Engineering. The Eastern Publishers, Ann Arbor, MI, pp. 129-141. Rautian, T.G., Khalturin, V.I., Martynov, V.G. and Molnar, P., 1978. Preliminary analysis of the spectral content of P and S waves from local earthquakes in the Garm, Tadjikistan region. Bull. Seismol. Soc. Am., 68(4): 949-971. Roecker, S.W., Tucker, B., King, J. and Hatzfeld, D., 1982. Estimates of Q in Central Asia as a function of frequency and depth using the coda of locally recorded earthquakes. Bull. Seismol. Soc. Am., 72: 129-149. Rovelli, A., 1984. Seismic Q for the lithosphere of the Montenegro region Yugoslavia: frequency, depth and time windowing effects. Phys. Earth Planet. Inter., 34: 159-172. Russo, R.M., Speed, R.C., Okal, E.A., Shepherd, J.B. and Rowley, K.C., 1990. Historical seismicity of the southeastern Caribbean and tectonic implications. Pure Appl. Geophys., 139: 87-120. Sato, H., 1977. Energy propagation including scattering effects. Single isotropic scattering approximation. J. Phys. Earth., 24: 27-41. Singh, S.K., Lenmo, J., Dominguez, T., Ordaz, M., Espinosa, J.M., Mena, E. and Quaas, R., 1988. The Mexico earthquake of September 19, 1985--A study of amplification of seismic waves in the valley of Mexico with respect to a hill zone site. Earthquake Spectra, 4: 653-673. Speed, R.C., 1985. Cenozoic collision of the Lesser Antilles Arc and continental South America and the origin of the El Pilar Fault. Tectonics, 4:41-69. Sutton, G.H., Mitronovas, W. and Pomeroy, P.W., 1967. Shortperiod seismic energy radiation patterns from underground nuclear explosions and small-magnitude earthquakes. Bull. Seismol. Soc. Am., 57(2): 249-267. Trifunac, M.D. and Udwadia, F.E., 1974. Variations of strong earthquake ground shaking in the Los Angeles area. Bull. Seismol. Soc. Am., 64(5): 1429-1454. Vierbucben, R.C., 1984. The geology of the El Pilar fault zone and adjacent areas in northeastern Venezuela. In: W.E. Bonini, R.B. Hargraves and R. Shagam (Editors), The CaribbeanSouth American Plate Boundary and Regional Tectonics. Geol. Soc. Am. Mem., 162: 189-212.