REGIONAL VARIATION OF Qscs BY STUART A. …Bulletin of the Seismological Society of America, Vol....

Bulletin of the Seismological Society of America, Vol. 70, No. 4, pp. 1071-1102, August 1980

REGIONAL VARIATION OF Qscs

BY STUART A. SIPKIN* AND THOMAS H. JORDAN

ABSTRACT

The ScSn phase-equalization and stacking algorithm of Jordan and Sipkin (1977) has been applied to an extensive set of HGLP and ASRO data to obtain regionalized estimates of Qs~s. Tests of the algorithm using synthetic data reveal no signif icant sources of bias. The low value of Qs~s previously obtained for the western Pacific (156 -+ 13) is corroborated by additional data, and Qs~s observations in other regions correlate with variations in crustal age and tectonic type. A representative value for the ocean basins sampled by our data is 150, with the best estimates being somewhat lower (135 to 142) for younger oceanic regions and somewhat higher (155 to 184) for older regions. The two subduction zones sampled here, KuriI-Japan and western South America, are characterized by la rger Qscs estimates than the ocean basins (197 -+ 31 and 266 --. 57, respectively), and the difference between them is qualitatively consistent with the contrasts in upper-mantle attenuation structure proposed by Sacks and Okada (1974). Continental regions are poorly sampled in this study because the signal-generated noise in the vicini ty of the ScS, phases is generally larger for continental paths, but a representative value is inferred to be Qs~s -- 225. For paths crossing China, Qscs is observed to be lower (~180), providing additional evidence for a high-temperature upper mantle previously inferred from surface- wave and travel-time measurements. Our best estimate for the average Earth is Qscs -- 170 (__.20 per cent), which appears to be signif icantly lower than that predicted by normal mode data, suggesting some frequency dependence. Q~ I correlates with ScS,-ScS~_ 1 travel t ime along a line given by

Qscs (4.4 x 10-4)4 Ts~s + 4.88 x 10 -3,

where &Tscs is the JB residual in seconds; this correlation favors a thermal control on the ATscs variations. It is inferred from the tectonic correlations that much, if not most, of the heterogeneity expressed in the Qs~s and & Tscs variations is confined to the upper mantle. Substantial differences in the attenuation structures underlying continents and oceans are implied. In fact, the average quality factor for the upper mantle beneath stable cratons may not be much less than that for the lower mantle.

INTRODUCTION

The quality factor for ScS waves, Qscs', is a parameter diagnostic of terrestrial anelasticity, averaging the anelastic properties of the entire mantle. Numerous estimates of this quantity have been derived from the spectral ratios of multiple ScS phase pairs (Press, 1956; Steinhart et al., 1963; Kovach and Anderson, 1964; Sato and Espinosa, 1967; Yoshida and Tsujiura, 1975). In a previous paper (Jordan and Sipkin, 1977; hereafter referred to as Paper I), the problem of ScS attenuation has been formally posed in the frequency domain as an inverse problem for a linear, complex-valued ScS attenuation operator, and its solution has been derived by standard least-squares techniques. The algorithm based on this analysis has a

* Present address: U.S. Geological Survey, Denver, Colorado 80225. 1071

1072 S T U A R T A. S l P K I N AND THOMAS H. J O R D A N

number of advantages over the classical spectral-ratio method. The spectral products and cross-products for various ScSn phase pairs from different sources are phase- equalized and summed (stacked) prior to taking ratios. Stacking increases the signal- to-noise ratio (SNR), stabilizes the estimates, and helps to average out the effects of local heterogeneities and source variability. Moreover, measures of the SNR for individual phases are used to weight the signals in the stacks and to estimate noise- induced uncertainties in the model parameters.

In Paper I, this algorithm was applied to a set of 17 multiple ScS phase pairs digitally recorded by High-Gain Long-Period (HGLP) stations at Kipapa, Hawaii (KIP), and Matsushiro, Japan (MAT) from deep-focus events in the western Pacific. Stable estimates of the amplitude and phase responses of the ScS attenuation operator were derived in the frequency interval 6 to 60 mHz. Within this band, the apparent Q of SCSn waves multiply reflected beneath the western Pacific was estimated to be 156 + 13, and no significant frequency dependence of Qscs was observed. The estimate of Qscs for the western Pacific was considerably less than the values published for other regions. Kovach and Anderson (1964), for example, obtained Qs~s = 600 for South America, and Yoshida and Tsujiura (1975) obtained Qs~s = 290 for the Sea of Japan. Taken at face value, these observations require very large geographical differences in the attenuation structure of the mantle.

In this study, the techniques of Paper I have been applied to a more extensive data set to assess the lateral variations of Qscs. Substantial regional differences in Qs~s do exist, as shall be seen, but these do not appear to be as extreme as the discrepancies among the published estimates imply. This article is organized into four parts. The first discusses some numerical experiments that validate the approximations intrinsic to the method of analysis. The second presents the Qs~s estimates derived by stacking subsets of data grouped by geographic and tectonic regions. The third discusses our interpretation of these data, and the fourth outlines some of their implications.

N U M E R I C A L E X P E R I M E N T S

Various approximations are made in formulating the estimation algorithm employed here and in Paper I. The operator describing the differential attenuation of two ScS phases on the same seismogram, ScSm and ScSn (m < n), is assumed to be linear and to depend on the reflection numbers m and n only through an exponential dependence on the ScSn-ScSm differential travel time; i.e., the apparent Q of an ScSn phase is assumed to be independent of n and epicentral distance. These approximations should be good for the source-receiver geometries considered here, providing that Q~, the local quality factor for shear, varies slowly with radius at the base of the mantle and that the core-mantle boundary is a simple fluid-solid interface. Some data relevant to the structural assumptions are discussed in a later section.

Two additional approximations are important. First, the source excitation ratios for the correlated ScSn/ScSm phase pairs are assumed to be samples from a distribution with unit mean and small variance, such that any spatial modulation of the wave field by the source radiation pattern introduces into the cross-correlation functions only small random variations which can be suppressed by stacking. This approximation is reasonable because the maximum difference in take-off angles for any two phases correlated in the experiments is only about 8 ° (ScS4/ScS2 from a deep-focus event at 72°). Second, all propagation effects other than attenuation and geometrical spreading by a spherically symmetric Earth structure are also assumed to contribute only small random variations to the cross-correlation functions and

REGIONAL VARIATION OF Qscs 1073

to be suppressible by stacking. In particular, any frequency dependence of the reflection coefficients caused by sphericity and fine structure at the surface or at the core-mantle boundary is neglected.

To test these approximations and other components of the algorithm, a series of numerical experiments have been performed using synthetic data. In the first, a set of SH-polarized seismograms were synthesized corresponding to those analyzed in Paper I, duplicating the source and receiver geometry as accurately as possible. Using a code written by R. Buland (Buland, 1976), the synthetics were calculated by summing the contributions from all toroidal modes with frequencies less than 50 mHz. Poloidal contributions to the S H components were neglected. Buland has shown that these modify the multiple ScS amplitudes by less than 10 per cent at the distances (44 ° to 72 °) and frequencies (>5 mHz) relevant to this experiment. However, the poloidal contributions increase with horizontal phase velocity and therefore with n introducing, as shall be seen, some positive bias into the apparent value of Qscs. The toroidal eigenfunctions and eigenfrequencies were computed for Gilbert and Dziewonski's (1975) model 1066A, and the mode quality factors were derived from the Q model given on p. 199 of their paper; for this model, Qscs = 231. The excitation parameter for each mode was calculated assuming a double-couple source mechanism with a step-function time history. The fault-plane solutions for the specific events used in Paper I were unknown to us, thereby making it necessary

] .2E '04

Uh I-- Z 0 (D (D

- I . 2 E * 0 4

TIME (HR)

z C) ¢Y ~_)

: ~ 0.

p - z t . J

w ¢.) <~ . . J o_

- 8 . 0 E . 0 1 0 'I ~'

TIME (HR) FIG. 1. Observed and synthetic seismograms at station KIP. HGLP SH-polarized seismogram from a

deep-focus earthquake south of Fiji (Table 1, event 9) (top). Synthetic for this event computed by toroidal-mode summation out to 50 mHz (bottom). Synthetic has been convolved with HGLP instrument response, and both records have been low-passed through a six-pole Butterworth filter whose corner i s 25 mHz.

1074 S T U A R T A . S I P K I N A N D T H O M A S H . J O R D A N

to approximate the mechanisms by solutions for nearby earthquakes (Isacks and Molnar, 1971).

Figure 1 compares a seismogram synthesized by this procedure with an HGLP record used in Paper I. The synthetic has been passed through the HGLP instrument response, and both seismograms have been low-passed by a zero-phase filter with a corner at 25 mHz to suppress ringing in the synthetic due to the spectral truncation at 50 mHz. At this distance (50 °) and source depth (517 km) the ScS, and sScSn phases for n -- 2, 3, 4 are clearly evident in the interval following the S, ScS, and multiple-S wave groups {terminating at -25 min) and prior to the long-arc arrivals (beginning at ~75 min). Several discrepancies between the synthetic and the

2 3 - 1 " 0

0

c -

-2

-3

T

Q = 268 -*6

Synthetic L

~ 0

g_

• tL •

-1

I i i

0 20 40 60

Frequency (mHz) FIG. 2. Modulus and phase of an attenuation operator derived by stacking synthetic data. Synthetics

were computed to duplicate the geometry of western Pacific stack I using an Ear th model by Gilbert and Dziewonski (1975). Qscs found from a weighted least-squares fit to the modulus estimates is 286 + 6 (solid line); model value is 231 (dashed line). Error bars, most less than the size of the plotting symbols, represent +1 standard deviation (+__la). Phase units are radians.

observed seismograms are notable. Within the large wave groups following S, there are obvious phase differences; most of these result from an incorrect source model. Between the ScSn groups, the signal levels on the observed seismogram exceed those on the synthetic by about a factor of 5; these signals probably represent energy scattered by structural features not included in the 1066A model (e.g., upper-mantle discontinuities and lateral heterogeneities). Finally, the observed ScSn and sScSn phases appear to decay with n more rapidly than the synthetic wave groups. This discrepancy is attributed to the fact that the apparent Qscs for this western Pacific path is less than that of the Earth model.

The synthetics replicating the seismograms of Paper I were processed in a manner


exactly analogous to the original data, yielding the spectral est imates of the S c S a t tenua t ion opera tor shown in Figure 2. Between 5 and 40 mHz (the useful band for the synthet ic S c S pulses), the logarithms of the modulus est imates decrease approximate ly l inearly with frequency, and the phase est imates are nearly zero. This behavior conforms to the constant-Q, zero-phase a t tenuat ion model assumed in the calculations. A variance-weighted, least-squares fit to the modulus est imates of Figure 2 yields Qscs = 286 _ 6. The s tandard error of the est imate was calculated f rom the (signal-generated) noise power in an interval immediate ly preceding the later-arriving signal of each phase pair, as described in Paper I. This power is low in the synthetics, for reasons discussed above; hence, the relative uncer ta in ty of the Qscs est imate is only 2.2 per cent. In comparison, the relative error computed

0.0

A - 0 . 5 ¸ (D

" O

t ~

E -1.0

-1.5

-2.0 2'o 4'0 6'o 8o lbo

0 2'0 4'0 go 8'0 160 Frequency (mHz)

FIG. 3. Experiment with synthetic data showing the effects of crustal layering o n ScSn/ScSn l spectral ratios. Light solid lines represent the ScS2/ScS differential attenuation operator for an LCCQ model with Qscs = 156 and ScS2 ray parameter of 4 sec/deg. Dashed lines are modulus and phase of complex-valued ScS2/ScS ratio obtained after convolving ScS2 with the crustal transfer function of the SOD-1 model (Spudich et al., 1978). Heavy solid lines are the spectra obtained by smoothing the spectral products with a 10-mtIz running-mean filter before dividing. A least-squares fit to the latter modulus spectrum over the interval 6 to 60 mHz yields Qscs = 149.

direct ly f rom the misfit of the modulus est imates to the exponential decay curve is 2.7 per cent. T h e two methods of estimating uncertainties, one a priori and one a posteriori , are thus in reasonable agreement. Th e derived value of Qscs is greater than the model value of 231 by 16 per cent, however; this discrepancy substantially exceeds tha t expected from random errors and therefore indicates the presence of some positive bias. Calculations by Buland demonst ra te tha t this discrepancy is almost ent irely a t t r ibutable to the exclusion of the poloidal contr ibutions from the SH-polar ized seismograms; the bias is in t roduced in the computa t ion of the synthetics and not by the est imation algorithm. Thus, for the geometry of Paper I, the approximations intrinsic to the algori thm appear to be justified.

One potent ia l source of bias in regional est imates of Qscs not adequate ly tested in the mode summat ion exper iment is the spectral variability caused by near-surface

1076 S T U A R T A. SIPKIN A N D T H O M A S H. J O R D A N

(crustal) stratification. To examine its influence on the attenuation estimate, synthetics of ScSn pulses reflected through realistic crustal and upper-mantle models were generated. Geometrical optics approximations were made except in the vicinity of the surface-reflection points, where frequency-dependent, plane-wave reflection coefficients were calculated by the HaskeU-Thompson method. Attenuation was modeled by an LCCQ operator. In Figure 3, the ScSJScS spectral ratio is shown for the SOD-1 oceanic crustal model (Spudich et al., 1978); the bias in the estimate of Qscs introduced by crustal interactions within this structure is less than 4 per cent. Similar results were obtained using the continental crustal and upper-mantle model of Massd (1973). Since these discrepancies are small compared to the errors in Qscs computed from real data (10 to 40 per cent in this study) and small compared to the regional variations documented below, it is concluded that any bias introduced by crustal variations is probably negligible.

TABLE 1

EARTHQUAKES USED IN THIS STUDY*

No. Location Date Origin Time Lat i tude Longitude Depth rnb (UTC) (deg.) (deg.) (kin)

1 Fox Island 21 Apr. 1972 01:28:08.2 53.95 N 166.82 W 91 5.8 2 N. Fiji 9 May 1972 12:20:22.3 17.83 S 178.79 W 565 5.8 3 Sea of Okhotsk 21 Aug. 1972 06:23:48.6 49.47 N 147.08 E 573 5.9 4 Argentina 1 Feb. 1973 05:14:19.9 22.53 S 66.19 W 214 6.0 5 Hawaii 26 Apr. 1973 20:26:27.0 20.05 N 155.16 W 9 5.9 6 N. Korea 10 Sept. 1973 07:43:32.3 42.48 N 131.05 E 552 5.8 7 Argentina 25 Oct. 1973 14:08:58.5 21.96 S 63.65 W 517 6.1 8 N. Fiji 19 Dec. 1973 12:55:51.1 20.60 S 176.32 W 191 5.9 9 S. Fiji 28 Dec. 1973 05:31:03.8 23.88 S 180.00 E 517 6.2

10 Kuril Island 11 Mar. 1974 11:37:31.6 48.31 N 153.16 E 154 5.8 11 S. Fiji 23 Mar. 1974 14.28:33.0 23.93 S 179.88 E 504 6.0 12 Hindu Kush 30 July1974 05:12:40.4 36.42 N 70.76 E 209 6.3 13 N. Fiji 21 Oct.1974 04:12:28.7 17.97 S 178.49 W 596 5.9 14 Hokkaido 8 Nov. 1974 21:23:22.2 42.53 N 141.75 E 125 5.9 15 Kamchatka 23 Aug. 1975 13:51:23.0 54.71 N 160.07 E 131 5.7 16 Hawaii 29 Nov.1975 14:47:41.1 19.46 N 155.14 W 11 5.9 17 New Hebrides 9 Jan. 1976 23:54:36.3 15.80 S 167.85 E 173 5.7 18 Kuril Island 21 Jan. 1976 10:05:19.0 44.74 N 149.15 E 5 6.2 19 New Hebrides 4 Mar. 1976 02:50:01.5 14.77 S 167.12 E 98 6.3 20 N. Fiji 10 Apr. 1976 17:12:08.3 17.70 S 178.46 W 548 5.7 21 Solomon Island 5 June 1976 08:20:09.2 10.08 S 161.06 E 79 6.0 22 Sea of Okhotsk 10 July 1976 11:37:12.8 47.36 N 145.72 E 387 5.8 23 N. Fiji 25 Nov. 1976 14:06:35.4 19.50 S 177.70 W 442 6.0 24 Chile-Argentina 17 Jan. 1977 21:27:16.3 24.92 S 68.68 W 44 6.0 25 N. Fiji 21 Jan. 1977 06:11:05.3 18.06 S 178.37 W 601 5.7

* Source parameters from the Bulletin of the International Seismological Centre (ISC).

REGIONAL ESTIMATES OF Qscs

The procedures of Paper I have been applied to an extensive set of multiple ScS data digitally recorded by six HGLP stations and one Abbreviated Seismic Research Observatory (ASRO). The 25 intermediate-magnitude earthquakes used in this study are listed with their source parameters in Table 1. The horizontal-component seismograms were rotated, and the ScSn phases were identified on the transversely polarized (SH) components. Those isolated from other arrivals and characterized by good waveforms were selected for further processing. The data were grouped by geographic and tectonic regions, and estimates of the regional ScS attenuation

R E G I O N A L V A R I A T I O N OF Qsc8 1 0 7 7

operators were derived by the phase equalization and stacking algorithm of Paper I. The only modification to this algorithm was to double the estimates of noise power and thereby increase the standard error of Qscs by about a factor of~/2. (This estimate of noise power more appropriately describes the observed seismograms, where the noise is primarily signal generated and approximately proportional in amplitude to ScSn). In Figures 4 to 25 are shown the maps of sources, stations, ScSn surface-reflection points, and the graphs of the regional attenuation spectra. The tectonic regionalization used on the maps is from Jordan (1979b).

Additional products of the data analysis are precise estimates of the differential travel times between phase pairs, computed by maximizing the time-domain, cross- correlation functions. The differential times, reduced to equivalent ScSn-ScSn-1 times, are displayed in Figure 26 as residuals with respect to the Jeffreys and BuUen

& /

, rn F

L ~

.--15, ab'25' 11 ~'9[

I ,i

KIP ~ QD

~" # ,

r

/ /

/ \ \ \

\

FIG. 4. Map of the western Pacific showing epicenters (solid triangles), stations (solid circles), and ScS, surface-reflection points (crosses for n = 2, open triangles for n = 3, and open squares for n = 4). Event numbers are from Table 1. Dashed contour encloses the region with oceanic crustal ages greater than 100 m.y.

(1940} tables, corrected for source depth, eUipticity and elevations of the stations, and surface-reflection points. The median residuals and their 95 per cent confidence intervals are tabulated for each region in Table 2. A detailed analysis of ScS,-ScS,n travel times from HGLP and ASRO stations can be found in Sipkin and Jordan (1980).

Western Pacific. The western Pacific Basin constitutes the greatest expanse of thermally mature oceanic lithosphere now in existence; mapping the seismic velocity and attenuation structure beneath it is a seminal problem for mantle dynamics. The favorable source-receiver geometries of the region have been extensively utilized in our previous work on ScS, travel times and attenuation (Paper I; Sipkin and Jordan, 1975, 1976, 1979, 1980).

The HGLP data set comprises a number of paths from deep-focus events crossing the western Pacific; all paths have bounce points in crust whose ages exceed 100 m.y. (Figure 4). Various stacking experiments with these data have yielded the spectra in Figures 5 to 9. In the first, the 17 ScSn/ScSm pairs from Paper I were

1078 S T U A R T A. S I P K I N A N D T H O M A S H . J O R D A N

" 0 0

r"

-2

-5 W. Pocific # 1

I I I I

Q) 0 U'/

r" Ck

T r r r T ~

1 0 2o 4o 6o

Frequency (mHz) FIG. 5. Modulus and phase of the attenuation operator for the western Pacific (Table 2, stack 1).

Data are identical to those of Paper I. Error bars are +la. Weighted least squares-fit to modulus data (Qs¢s = 157 + 17) shown by solid line (top panel); phase spectrum for LCCQ operator with center frequency at 34 mHz and Qs¢s = 157 shown by dashed line (bottom panel}.

reanalyzed using the modif ied S N R es t imates (stack 1, Figure 5). As before, a 180- sec t ime window was employed, entirely excluding contr ibut ions f rom the sScSn phases. T h e s tandard error of the new Qscs es t imate was higher t han the old (+_17 versus _ 13), as expected, whereas the es t imates themselves were essentially identical (157 versus 156}. T h e addit ion of four high-quali ty ScSn/ScSm pairs to the s tack gave a compat ib le value: Qscs = 150 +_ 14 (stack 2, Figure 6). In a third experiment , these 21 ScSn/ScSm pairs were combined into a s tack with the corresponding 21 sScSn/sScSm pairs, yielding Qscs = 155 _ 11 (stack 3, Figure 7). T h e es t imates der ived f rom the three stacking exper iments are thus mutua l ly consistent. The stabi l i ty of these es t imates provides fur ther evidence tha t the formal uncertaint ies der ived f rom the a lgor i thm are realistic and, therefore, tha t the appa ren t Qs~s of the western Pacific is de te rmined to a precision of about 10 per cent.

T h e phase funct ion of an LCCQ opera tor has a factor logari thmical ly dependent on a normal ized f requency [Paper I, equat ion {6}]. For definition of the a t tenua t ion operator , the zero-phase point defining the normalizat ion occurs a t the appa ren t center f requency of the ScSn pass band, a consequence of the phase-equal izat ion


procedure. Taking this reference frequency to be 34 mHz, as in Paper I, it is found that the phase data are compatible with the LCCQ model, although the assertion that the data really resolve the attenuative dispersion is not statistically justified. The phase spectra for other regions are generally more uncertain than those for the western Pacific, so the phase observations are of limited utility in rigorously testing the LCCQ model (see Sipkin and Jordan, 1980, for travel-time observations related to attenuative dispersion). Instead, the phase spectrum can be employed to assess the quality of the modulus estimates within a specified band. It was found that significant deviations of the empirical phase spectrum from the LCCQ model are often diagnostic of spurious interferences which corrupt the modulus spectrum (cf. Paper I, Figure 3). Therefore, in this study, phase stability was used as a criterion for selecting the spectral interval from which the apparent Qscs is determined.

i

Q : 150-+14

" 0

0

- 2

W. Pacific # 2 - 3 I i i

~0 O r -

n

T i

i h i i i i

2 0 4 0 6 0

Frequency (mHz)

FIG. 6. Attenuation operator for the western Pacific from augmented data set (Table 2, stack 2). Conventions same as in Figure 5.

For the western Pacific stacks, the interval of phase stability and good SNR is 6 to 61 mHz. Within this band, the logarithmic modulus decreases approximately linearly with frequency, and no significant frequency dependence of Qscs can be discerned. However, a comparison of these results with the spectra of higher frequency signals recorded over similar paths by the World Wide Standardized Seismograph Network (WWSSN) indicates a rapid rise of Qscs with frequency above about 100 mHz (Sipkin and Jordan, 1979).

The investigations of ScSn-ScSm travel times have revealed systematic path variations in the western Pacific basin not obviously related to crustal age or other surface tectonic features (Sipkin and Jordan, 1980). To look for similar variations in Qscs, data for the Fiji-KIP and Fiji-MAT paths were stacked separately, obtaining estimates of 141 __. 16 and 176 ___ 37, respectively (Figures 8 and 9). Based on their

1 0 8 0 S T U A R T A. SIPKIN A N D T H O M A S H. J O R D A N

formal uncertainties, these Qscs values are not significantly different at the 95 per cent confidence level. However, the median travel-time residuals for these two paths (+4.7 and +2.0 sec, respectively) correlate inversely with the Qscs estimates, suggesting that the Qs¢s difference is real and reinforcing our speculation that the travel-time variations in the western Pacific are caused by mantle temperature fluctuations.

Central Pacific (Hawaii). The ScS attenuation spectrum for the H a w ~ a n Island region has been estimated from the HGLP seismograms of the 1973 Hawaiian earthquake recorded at KIP (Figure 10). A stack comprising the six paired combi- nation of (ScS,: n = 1, . . . , 4) yields Qs~s = 184 _ 48 (Figure 11), somewhat greater than the western Pacific average but similar to the Fiji-MAT value. The phase pairs are few, so the SNR for the stack is poor, the spectra in Figure 11 are noisy, and the

0

¢ -

- 2

- 3

Q = I 5 5 +-- 11

W. Pacific #5 i i i i

0

~0 o

E_ r

k r L i i

2O 4O 6 0

Frequency (rnHz) FIG. 7. Attenuation operator for the western Pacific from set containing both ScS,/ScSm and sScSn/

sScSm data (Table 2, stack 3). Conventions same as in Figure 5.

standard error of the Qscs estimate is large. As in the case of the Fiji-MAT paths, however, the higher value of Qscs is supported by the travel times, which are generally lower than the western Pacific median.

Clearly, there is no evidence in the data for a large-scale low-velocity or low-Q anomaly in the upper mantle beneath the surface-reflection points, which extend from the northern tip of Hawaii to western Molokai. If anything, the region is characterized by slightly higher velocities and lower attenuation than some older regions of the western Pacific despite the fact that the reflection points lie atop the Hawaiian swell and near the Hawaiian hotspot. Models of the swell which attribute its existence to convective upwelling beneath the Hawaiian Islands (Dietz and Menard, 1953) or simple lithospheric thinning (Detrick and Crough 1978) do not explain these results. Perhaps, as speculated by Jordan (1979a), the swell is underlain


by a low-density depleted residue of hotspot vulcanism, forming a high-velocity, high-Q root zone beneath the archipelago.

Eastern Pacific. A lack of well-placed sources made it difficult to extend the study into the eastern Pacific. Four ScSn/ScSm phase pairs recorded at Albuquerque (ALQ), three from the 1975 Hawaiian earthquake and one from a Fox Island event, were the only data obtained of sufficient quality to be analyzed (Figure 12). For the intermediate-depth (91 km) Fox Island earthquake, the waveforrns were complicated by the presence of sScS~ phases. The energy from these depth phases was included in the stack by using a 180-sec time window. Corrections to the cross-correlations for the slight differential move-out of sScS,, relative to ScS~ were not applied since they are negligible at the distances (A _ 45 °) and frequencies relevant to this experiment. Because the stack comprised so few phase pairs, the SNR was low and

0

- 2

- 3

O : 141 ±16

Fiji to KIP _ _ i i i I

~ 0 o

f_ T t T'- '--r-... t. "

J r i 4 1 0 I i ' 0 2 0 6 0

Frequency (mHz) FIG. 8. Attenuation operator for Fiji-KIP paths (Table 2, stack 4). Conventions same as in Figure 5.

the phase spectrum of the attenuation operator displayed instabilities at frequencies above 33 mHz. From the variance-weighted fit to the modulus estimates in the band, 6 to 33 mHz, it was found that Qscs = 135 ___ 31 (Figure 13).

This value is the least obtained for any region examined in our survey. A lower Qscs for the eastern Pacific relative to the central and western Pacific is hardly surprising. Dispersion and travel-time studies have demonstrated that the shear velocities in the oceanic upper mantle increase coherently with crustal age as predicted by thermal decay models (Leeds et al., 1974; Forsyth, 1975; Sipkin and Jordan, 1976; Duschenes and Solomon, 1977). Furthermore, age variations of surface- wave attenuation parameters consistent with these models have been recently documented (Canas and Mitchell, 1978). The low Qscs found for the eastern Pacific could therefore be another manifestation of lithospheric aging, at least in part.

Despite its plausibility, this hypothesis is contradicted by the travel times. The

1082 STUART A. SIPKIN AND THOMAS H. JORDAN

0

-2

-3

Fiji to M A T

Q = 176 +-37

[

o

~ 0 ¢-

&.

L

20 40 60

Frequency (mHz)

FIG. 9. Attenuation operator for Fiji-MAT paths (Table 2, stack 5). Conventions same as in Figure 5.

I

5 ~ I P

A

- 20 ° N ~-'~-~T~

160 ° W 155 ° I I

FIG. 10. Map of the Hawaiian Islands showing epicenter, station, and ScS,~ surface-reflection points. Symbols same as in Figure 4.

median residual of the eastern Pacific paths is less than those of bo th the western Pacific and Hawaii, a relat ionship opposite to tha t found in previous studies of ScS2- ScS t imes (Okal and Anderson, 1975; Sipkin and Jordan, 1976}. Th e travel- t ime discrepancy may be caused by large lateral variations along these part icular ScSn paths. T h e ScS3 pa th of event 1, for example, has a surface-reflection point in the Nor th American continent, whereas the ScS2 reflection point is s i tuated on the very young oceanic crust of the Juan de Fuca Rise. Such a geometry is expected to bias negatively the ScS3-ScS2 t ravel time, and, in fact, the observed residual is among

R E G I O N A L V A R I A T I O N O F Qscs 1083

the lowest found for any path classified as oceanic, only +0.9 sec. The similar geometry of event 16 could perhaps explain its low ScS4-ScS2 and ScS4-ScS3 residuals as well. If lateral variations of this type do exist, however, they should bias the Qscs value to a high value. Why then is the Qscs estimate for the eastern Pacific so low?

The poor correlation between Qscs and travel time casts suspicion on the modulus estimate at 33 mHz, which lies considerably below the least-squares line in Figure 13. Deleting this point from the modulus spectrum raises the Qscs estimate to 164 + 50, bringing the eastern Pacific into better agreement with the dashed correlation line in Figure 27. Clearly, additional data are required to resolve the question more ful ly .

" O

0

-2

i : i

Hawaii i

I i,

i i

- 3

i

Q = 184+_48 I

! i i ! ,

i

~ o c -

a _

0 2O 40 60

Frequency (rnHz) FIG. 11. At tenuat ion operator for Hawai i (Table 2, stack 6). Conventions same as in Figure 5.

Trans-Pacific. The SCSn surface-reflection points for Fiji events recorded at ALQ span the Pacific basin over intermediate-age (25 to 100 m.y.) oceanic crust {Figure 14). To avoid shallow angles of incidence at the core-mantle boundary and to minimize the radiation-pattern modulation at these large distances (h -~ 90°), analysis was restricted to ScS4/ScS3 phase pairs, for which the ray parameters are less than 5 sec/deg, and the differences in take-off are only about 5 °. Energy from sScSn phases was excluded by using a 150 sec window. The amplitude spectrum of Figure 15 yields a Qscs of 150 +_ 34, and the median ScS4-ScS3 residual is +5.7 sec. Thus, the results for these trans-Pacific paths are similar to those found for the older regions of the western Pacific.

Coral Sea. Multiple ScS waveforms recorded at Charters Towers, Australia (CTA) from three intermediate-focus earthquakes in the Solomon and New He- brides arcs provide good sampling of the Coral Sea Basin (Figure 16). According to


- - \ :Lc

[] A , % ~ .

16

FIG. 12. Map of the eastern Pacific showing epicenters, station, and ScS, surface-reflection points. Symbols same as in Figure 4. Dot-dashed contour is approximately 25-m.y. isochron.

0

~:-2

-3

J

E. Pacific J ~ i J i i

£ ~ 0

a.

-I

20 40 60 Frequency (m Hz)

FIG. 13. Attenuation operator for the eastern Pacific (Table 2, stack 7). Conventions same as in Figure 5. Deleting the modulus estimate at 33 mHz raises the estimate to Qscs = 164 + 50.

Weissel and Watts (1979), the primary crustal ages within the basin vary from 56 to 62 m.y. The ScS attenuation spectra of Figure 17 were computed with a 180-sec window, which includes the sScSn phases. A fit to the amplitude data in the band 6 to 50 mHz gives a low value of Qscs (142) with a fairly small standard error (+22) that is less than, but not inconsistent with, results for the Pacific Basin. The median travel-time residual of _+3.7 sec is also consistent with the Pacific estimates.

Kuril-Japan. The subduction zones of the northwest Pacific differ in tectonic regime, and presumably in upper-mantle structure, with the ocean basins discussed thus far. The data set for this region comprised 15 ScSn/ScSm phase pairs recorded at MAT from four events with epicenters extending from Hokkaido to Kamchatka (Figure 18). As in the previous case, spectra were computed with a 180-sec window


to include the sScSn phases from the three intermediate-focus earthquakes. The spectral amplitudes from 6 to 56 mHz yielded Qscs ffi 197 +_ 31 (Figure 19). This estimate is greater than the ocean basin values, and the corresponding travel times are less.

South America. Qscs estimates have also been derived for the continental subduction zone of western South America. The signals were recorded at La Paz, Bolivia (ZLP/ZOBO) from three earthquakes in northwestern Argentina (Figure 20). Two stacking experiments were then performed. In the first, 7 ScSJScSm phase pairs from the two deeper events (4 and 7) were processed with a 132-sec time window, excluding all sScS~ energy. (Recording problems restricted analysis to one ScS2/ScS phase pair from event 7.) This gave Qscs = 285 + 111 (Figure 21). In the second, 12 phase pairs were used, and the sScS~ energy was included by extending the window length to 240 sec, yielding Qscs -- 266 + 57 (Figure 22). Clearly, Qs~s for western South America is significantly greater than the values recovered for other regions, although it does not appear to be as high as the estimates of previous workers, such as Kovach and Anderson (1964). The higher Qscs estimates obtained here correlate with the travel times, which generally show negative residuals (Figure 26).

\

\ \ \

\ \

f~

%

\

C ~

G~

~ t !

11 I' 9/ r~ / \\\

I fJ \~

[.X

\

.3

FIG. 14. Map of epicenters, station, and ScS, surface-reflection points for trans-Pacific paths. Symbols same as in Figure 4. Dot-dashed contour is approximately 25-m.y. isochron; dashed contour encloses oceanic crust with ages greater than 100 m.y.

China. Ideally, a global study of 8cS attenuation should include estimates from a variety of continental regions with differing tectonic regimes. A lack of adequate data has prevented achievement of this goal. HGLP and SRO records were examined for a number of continent-crossing paths, but the SNR for the multiple ScS phases was generally poor. Part of the difficulty is attributable to unfavorable source- receiver geometries, but, in many cases, the ScS, waveforms were obscured by complex, low-group velocity arrivals. Evidently, energy multiply reflected within the upper mantle can propagate more efficiently beneath the continents than beneath the oceans, probably because Q~ in the continental upper mantle is high. This interpretation is supported by the high Qscs estimates for western South America.

Some data were obtained for paths that cross China (Figure 23). An analysis of five ScSn/ScSm phase pairs recorded at Chiengmai, Thailand (CHG) from events 6 and 22 gave Qscs = 168 + 58 (Figure 24), and three (ScSn + sScSn)/(ScSm + sScSm)


-2

-3

Trans-Pacific

O : 150 +-54

[

2D

0 o~ O c-

a_

' ' T

i ~ i J i i

0 20 40 60

Frequency (mHz) Fro. 15. Attenuation operator for trans-Pacific paths (Table 2, stack 8). Conventions same as in

Figure 5.

~ 2 19 [] T, V l 7

\

Fro. 16. Map of the Coral Sea region showing epicenters, station, and ScS, surface-reflection points. Symbols same as in Figure 4.

phase pairs from a single Hindu Kush earthquake (event 12) recorded at MAT gave Qscs = 186 + 73 (Figure 25). Neither of the attenuation spectra is of high quality, as indicated by the large uncertainties. Both, however, yield Q's significantly lower than were found for western South America and only insignificantly greater than the nominal values for the western Pacific. The travel times show a corresponding relationship.

Compared with stable continental regions, the Chinese mainland appears to be underlain by an upper mantle characterized by anomalously low shear velocities {Pines e t al . , 1980; Sipkin and Jordan, 1980). This anomalous velocity structure is presumably a manifestation of high upper-mantle temperatures related to the active

R E G I O N A L VARIATION OF Qscs 1087

orogenesis within China being driven by peripheral plate convergence (e.g., Tappon- nier and Molnar, 1977). Therefore, it is suspected that the attenuation structure of the region is also anomalous with respect to stable continental platforms.

I N T E R P R E T A T I O N

Our experimental results are summarized in Table 2. The Qscs values listed here are apparent quality factors; to interpret them in terms of terrestrial anelasticity requires a careful assessment of the modeling assumptions and an evaluation of the possible sources of bias.

Qscs measurements have been made on different data sets using a variety of stacking parameters. Those pertaining to the same tectonic or geographic province (e.g., stacks 1 to 3, 11 and 12, and 13 and 14) display an internal consistency that

.g,-I o

-2

-5

O =142-'22

Cor(]l Se(] i , J

v 0

o . .c rl

2O 4O 60

Frequency (mHz)

FIG. 17. A t t enua t ion operator for Coral Sea pa ths (Table 2, s tack 9). Convent ions same as in Figure 5.

supports estimates of the observational uncertainties due to signal interference, radiation-pattern variability, localized heterogeneities, and other sources of random or quasi-random noise. Numerical experiments with synthetic data, described in a previous section, have revealed no significant bias in the stacking algorithm. In particular, bias is not introduced by the frequency dependence of the reflection and transmission coefficients due to the sphericity of the core-mantle interface or the fine structure of the crust and upper mantle, at least for the models we have tested.

These models may be inadequate in two respects. First, as noted in the discussion of Figure 1, the normal-mode synthetics for model 1066A underestimate the observed signal levels between the ScSn wave groups, suggesting that some energy is scattered out of ScSn by structural features not included in the 1066A model, such as upper- mantle discontinuities and small-scale lateral heterogeneities. Scattering could bias


the Qscs measurements to low values. It was shown in Paper I, however, that the bias in Qscs caused by the scattering from upper-mantle discontinuities is rather small, less than 5 per cent for even extreme models such as Jordan and Anderson's (1974) B1. Also, the increase in Qscs observed at frequencies above 100 mHz suggests that the scattering losses from small-scale random heterogeneities are probably negligible in the HGLP band (Sipkin and Jordan, 1979). Therefore, it is unlikely that the bias due to scattering is comparable in magnitude to the observational uncertainties, and such bias will be neglected in further discussions.

Second, the models used in the numerical experiments may not adequately represent the elastic or anelastic structure in the vicinity of the core-mantle interface. A low-Q zone, for example, might exist at the base of the mantle (Mikumo and Kurita, 1968; Teng, 1968; Anderson and Hart, 1978a), vitiating the approximation that the differential attenuation between two multiple ScS phases depends on the epicentral distance only through an exponential dependence on their differential travel time. Other effects could also give rise to a more complex variation with distance; the shear modulus of the outermost core might not be zero (Sato and

FIG. 18. Map of epicenters, station, and ScSn surface-reflection points for Kuril-Japan paths. Symbols same as in Figure 4.

Espinosa, 1967; Ibrahim, 1973) or the basal layer of the mantle, Bullen's Region D", might be internally stratified (Cleary, 1969; Berzon et al., 1972; Buchbinder and Poupinet, ~.973), perhaps in association with a solidified chemical boundary layer at the top of the core (Jordan, 1979b). In an attempt to limit the bias potentially introducible by these complications, the ray parameters for the ScSn waves used in this study were restricted to less than 5.5 sec/deg, which corresponds to surface- focus ScS at 35 °. This criterion appears to be satisfactory on both theoretical and empirical grounds. The amplitudes and waveforms of long-period body phases that interact strongly with the core-mantle boundary, such as SINKS, can be adequately modeled without invoking nonzero rigidity in outer core or complex interface structures (Choy, 1977), and, although layering of the interface is suggested by other data, the radial scale lengths over which it occurs are probably small, roughly comparable to those of crustal stratification (Phinney and Alexander, 1969; Jordan, 1979b). Our numerical experiments show that layering on this scale does not appreciably bias the Qscs estimates. For the low values of the ray parameters

REGIONAL VARIATION OF 08c8 1089

D

" 5 - I "0 0

C

-2

-5

Q : 197-+31

t -+ - T . . . . . .

Kuril-dapan I I I

£

~ o O .£:

-1

I I I I I I

0 20 40 60

Frequency (mHz) FIO. 19. At tenuat ion operator for Kuri l -Japan paths (Table 2, stack 10). Conventions same as in

Figure 5.

considered here, the (negative) bias in Qscs introduced by a basal low-Q zone would be less than 4 per cent even if the structure were as pronounced as that in Anderson and Hart 's (1978a) model SL1. However, the most direct justification for our assumptions is empirical: no dependence of Qscs on ray parameters less than 5.5 sec/deg was observed, either in individual spectral ratios or in the stacking results. For example, within their observational errors, the Qs~s values for the Hawaiian stack and the western Pacific stacks are not distinguishable, despite the differences in the average ray parameters, which, in fact, bracket the range for all stacks. Thus, although the possibility of significant bias due to structural complexities near the core-mantle boundary cannot be completely discounted, no evidence is seen for such effects in the data.

Given these considerations, the data shall be tentatively interpreted to be unbiased estimates of the intrinsic quality factor for vertically traveling SCSn waves localized within a geographic or tectonic province. That is, if Q~(r) and vjr) specify the radial variations of the local quality factor and velocity for shear waves at frequencies within the HGLP band, then

2La Q~s =- ~ v,-'(r)Q,-'(r) dr

TScS (1)


where 0 Tscs is the vertical ScS travel time, and the range of integration extends from the core-mantle boundary at radius b to the surface at radius a.

Comparison with previous studies. In regions where comparisons are available, the Qscs values found in this study are generally lower than those derived by previous workers. For example, the best estimate for western South America is 266 _ 57 (stack 12). Using similar geometries, Press (1956), Anderson and Kovach (1964), and Kovach and Anderson (1964) obtained values between 440 and 600. Sato and Espinosa (1967) extended the range of epicentral distances to include stations in eastern Canada (h = 80°). They estimated Qscs = 581 _ 33 at short epicentral distances and Qscs = 181 + 5 as an average for all distances; they interpreted the apparent decrease in Qs~s with epicentral distance to be an indication of appreciable viscosity in the outer core. Each of these studies used hand-digitized, unrotated seismograms from Press-Ewing instruments; spectral ratios were calculated for individual phase pairs before averaging.

Z L P / Z O B O

[]

z~

[]

[]

r7

24

v 4

66°1 W 6rO ~

FIG. 20. Map of the central Andes, South America, showing epicenters, station, and ScS, surface- reflection points. Symbols same as in Figure 4. Hatchured area delimits the continental region tectonically quiescent during the Phanerozoic.

Okal (1978; data listed by Anderson and Hart, 1978) applied the spectral-ratio method to rotated seismograms from WWSSN stations in South America and found Qscs values of 330 and 360. He also derived estimates for a number of Pacific- crossing paths, all of which feU in the range 230 to 380.

Yoshida and Tsujiura (1975) calculated ScSn/ScSm and sScSn/sScS,, spectral ratios for two deep-focus events in eastern Russia recorded on magnetic tape at the Dodaira Observatory in Japan. Their estimate of Qscs = 290, for the Sea of Japan is consistent with values previously obtained by Otsuka (1963) from the spectral decay of high-frequency ScS pulses, but it is considerably greater than the estimate of 197 _+ 31 for Kuril-Japan paths (stack 10).

Because the instrumental pass-bands of these earlier studies were centered at higher frequencies than the HGLP pass-band, the apparent inconsistencies could arise from an increase of Qscs with frequency of the sort documented by Sipkin and Jordan (1979). For example, Press' (1956) measurements for South America were centered at about 90 mHz, whereas ours span the interval 6 to 63 mHz. This explanation is unsatisfactory, however, since the bandwidths used here overlap or entirely contain the frequency range for the other observations that were cited.


It is suspected that at least some of the discrepancies between earlier studies and this work stem from different methodologies. Best et al. (1974) computed spectral ratios for ScSn waves recorded at the HGLP station at KIP from the April 4, 1973 Hawaiian earthquake and found Qscs = 300 +_ 30; using the same records in the phase-equalization and stacking procedure produced Qscs = 184 +_ 48 (stack 6). On the other hand, Nakanishi (1979} applied a spectral stacking technique similar to ours to HGLP data from station MAT and obtained Qscs = 160 _ 33 for the Sea of Japan and Qscs = 212 + 18 for Kuril-Japan paths, in excellent agreement with our results (stack 10).

It is not always clear from the published reports exactly which procedures have been followed, but it appears that in most applications of the spectral-ratio method, the quantities actually divided are the smoothed power spectra of two ScS , signals.

0

c

- 2

- 5

S. America # 1 i i h i i

~o o

2O 4 O 6O

Frequency (mHz) FIG. 21. Attenuation operator for South America from a reduced data set using a 132-sec time window

(Table 2, stack 11). Conventions same as in Figure 5.

Therefore, the incoherent parts of the two spectra contribute to the ratio, as well as the coherent parts. Since the SNR usually decreases with increasing reflection number and increasing frequency, this procedure can lead to a positive bias in the Qscs estimates. Furthermore, because the ratios are always positive, their distribu- tions at high frequencies where the scatter is large tend to be strongly skewed to positive values, and simple averaging of such ratios (e.g., Kovach and Anderson, 1964; Yoshida and Tsujuira, 1975) can enhance the bias. In the phase-equalization and stacking algorithm, on the other hand, the spectral products and complex- valued cross products are summed before dividing, and the incoherent noise contributions tend to average out.

In any case, no source of bias has been identified that could raise the estimates in Table 2 by more than 5 to 10 per cent. These low values of Qscs corroborate the


n~ o

-2

-3

Q = 266 -+ 5"7

S. America # 2 L J J i

go c - (3-

l i

i h I h i I 0 2 0 4 0 6

Frequency (mHz)

F io . 22. A t tenua t i on opera to r for South Amer ica f rom the complete data set using a 240-sec t ime w indow (Tab le 2, stack 12). Convent ions same as in Figure 5.

22

-- 12 --E3 =_A I~_ ~_~ +~"~IV] ATE

Fie . 23. Map of southeast Asia showing epicenters, stations, and SoS. surface-reflection points for Chinese paths. Symbols same as in Figure 4. Hatehured areas are continental regions tectonieally quiescent in the Phanerozoic.

results of Paper I, and they are consistent with Brune's (1977) work on SS/S ratios, Burdick's (1978) study of t~*, and Nakanishi's (1979) Qscs observations.

Correlation with travel times. The coherence between the regional variations of - 1 Qscs and those of the ScS travel times is documented in Figure 27. The data fit a

correlation line given by

Q ~ s = (4.4 x lO-4)ATscs + 4.88 x 10 -a (2)

R E G I O N A L V A R I A T I O N OF Qscs 1093

where ATscs is the ScS, - ScS,-1 residual, in seconds, with respect to the Jeffreys- Bullen (1940) tables. Only the point for the eastern Pacific (stack 7) lies away from the correlation line by more than 4-1 S.E. in -1 Qs~s, and as previously noted, this point's location may be biased by strong lateral inhomogeneities along the eastern Pacific paths. Because both -1 Qscs and hTs~s are observed to be frequency dependent (Sipkin and Jordan, 1979, 1980), we emphasize that equation (2) pertains only to ScS signals in the HGLP band.

The good positive correlation between Qs~s and hTs~s favors certain hypotheses regarding the source of the hTscs variations over others. In particular, distortions of the core-mantle interface or deep-mantle chemical heterogeneities do not readily account for this correlation, but a thermal control on the hTscs and Qscs variations does.

4 -2

-3

° , Q = 1 6 8 - + 5 8

E. China ; i

I

~o

- I

' 2 o ' 4 o ' 6 o Frequency (mHz)

FIG. 24. Attenuation operator for paths crossing eastern China to station CHG (Table 2, stack 13). Conventions same as in Figure 5.

Tectonic correlations. The Qscs observations also correlate with variations in crustal age and crustal type, a fact established previously for ScSn travel times (Sipkin and Jordan, 1975, 1976, 1980; Okal and Anderson, 1975; Jordan, 1979b). A representative value of Qscs for the ocean basins sampled by the data is 150, which equals the observed value from trans-Pacific paths (Table 2, stack 8). The estimation uncertainties make the regional variations within ocean basins difficult to resolve, but, taken at face value, the observations suggest that younger oceanic regions (eastern Pacific, Coral Sea) have values somewhat lower than 150 and older regions (central and western Pacific) somewhat higher. If real, these differences are most plausibly explained as another consequence of lithospheric thickening and cooling with age, predicted by the thermal-boundary layer models and confirmed by surface- wave dispersion and attenuation measurements (Leeds et al., 1974; Forsyth, 1975;

1 0 9 4 STUART A. SIPKIN A N D THOMAS H. J O R D A N

Yoshii, 1975; Canas and Mitchell, 1978) and shear-wave travel-time studies (Sipkin and Jordan, 1976; Duschenes and Solomon, 1977).

It is noted, however, that variations of comparable magnitude, but not obviously correlated with crustal age or other lithospheric properties, are observed within the older regions of the western Pacific (stacks 4 and 5), and these path differences are also corroborated by the travel times (Figure 27). A more detailed study of S c S , - ScSm residuals in this region suggests the existence of mesoscale heterogeneities (~ 103 kin) which apparently trend in a northwesterly direction and which may be manifestations of upper-mantle convective circulation (Sipkin and Jordan, 1980).

Both subduction zones sampled here, Kuril-Japan and western South America, are characterized by higher values of Qscs than the ocean basins. Of course, lower attenuation is not unexpected for regions occupied by cold, detached, and rapidly

i J T i i

t ~ t Q = 186±73

N. China i i i i h i

o

- 2

- 3

1

~0

0 _

- 1

i i i J i i

0 20 40 60

Frequency (mHz) FIG. 25. Attenuation operator for paths crossing northern China to station MAT (Table 2, stack t4).

Conventions same as in Figure. 5.

sinking thermal-boundary layers. The significant difference between the two estimates (197 ___ 31 versus 266 ___ 57, respectively) is not surprising, either; the former pertains to an oceanic-type subduction zone overlain by marginal basins with high- heat flow (Karig, 1971), whereas the latter pertains to a continental-type subduction zone abutting a stable continental platform. The data are qualitatively consistent with the contrasts in upper-mantle attenuation between these two regions proposed by Sacks and Okada (1974), although the Qscs values suggest a somewhat lower average Q, for the upper mantle than their models imply (200 to 500). Because the measurements upon which their models are based were made at relatively short periods (<10 sec), the discrepancies in absolute Q, values may constitute further evidence that Q, increases rapidly at high frequencies.

Continental cratons removed from the active plate margins have not been sampled

5[ 0

o 51-

0 I

c- O

. D

{D 0

tD - ~ 0 ©

O

o

E 5 Z

o

0

0 -4

REGIONAL VARIATION OF Qscs

~ r-lN N

Western Pacific @2 FI M m

Hawaii

1095

r~ [] Eastern Pacific

R R ÷

Trans-Pacific

Coral Sea

F~ Kur i l - Japan

~ ScSz-ScS ScSs- ScS2 ScS4-ScS3

ScSs-ScS ScS4-ScSz ScS4-ScS

S o . A m e r i c a ~ 2

Eastern China

Northern China

o 2 6 ' 16't 'i JB ScSn-ScSn_lResidual (sec)

I I

Fro. 26. Histogram summary of ScS.-ScSm residuals for all regions sampled. Residuals are computed with respect to Jeffreys-Bullen tables, corrected for source depth, ellipticity, stat ion elevation, and elevation of surface-reflection points, and normalized to equivalent ScS.-ScSn 1 residuals. Arrows indicate medians.

in this study due to the difficulties outlined previously, but indirect estimates of Qscs can still be made. According to Sacks and his coworkers (Sacks, 1969; Sacks and Okada, 1974; Sacks et al., 1976), the upper-mantle attenuation structure of western South America is similar to that beneath the stable craton to the east. This hypothesis is consistent with the travel-time observations for western South Amer- ica, which, like those for the cratons, have negative residuals (Sipkin and Jordan, 1976, 1980). If it is correct, then Qscs for stable continental areas is appreciably greater than 200.

Qscs and Constraints can also be derived from the empirical relation between -1 hTscs, equation (2). The median ScSn - ScSn-1 residual for all continental paths found in the previous study of HGLP and SRO data is -1.0 sec (Sipkin and Jordan, 1980), which corresponds to Qscs = 225. Travel-time residuals for paths confined to the shields and stable platforms are generally more negative than this median; hence, their associated Qs~s values are predicted to be larger than 225.

Besides South America, the only other continental region sampled by our data is China (stacks 13 and 14), where Qs~s is observed to be low. Our measurements

1 0 9 6 S T U A R T A. S I P K I N A N D T H O M A S I-I. J O R D A N

p r o v i d e a d d i t i o n a l e v i d e n c e for t h e ex i s t ence of a h i g h - t e m p e r a t u r e u p p e r m a n t l e b e n e a t h C h i n a p r e v i o u s l y i n f e r r ed f rom s u r f a c e - w a v e a n d t r a v e l - t i m e o b s e r v a t i o n s (P ines et al., 1980; S i p k i n a n d J o r d a n , 1980).

ScS parameters for the average Earth. R e p r e s e n t a t i v e ocean ic a n d c o n t i n e n t a l v a l u e s o f Qs~s and hTscs c o n s i s t e n t w i t h e q u a t i o n (2) a r e g iven in T a b l e 3. T h e t r a v e l - t i m e r e s i d u a l s a r e t h e ocean ic a n d c o n t i n e n t a l m e d i a n s f o u n d b y S i p k i n a n d J o r d a n (1980). A s s u m i n g t h e E a r t h to be 65 p e r c en t ocean , we o b t a i n Qscs ~- 170 a n d ATs~s ~- +2.4 sec, w h e r e t h e o v e r b a r d e n o t e s p a r a m e t e r s for t h e a v e r a g e E a r t h . B e c a u s e a l l ScSn-ScSm t r a v e l t i m e s u sed to de r ive t h e s e va lue s h a v e b e e n c o r r e c t e d for foca l d e p t h s a n d for e l e v a t i o n s o f t h e r e c e i v e r s a n d t h e su r f a c e - r e f l e c t i on po in ts , t h e r e s i d u a l s c o r r e s p o n d to an E a r t h w h o s e o u t e r so l id b o u n d a r y is a t a = 6371 kin. A l l v a l u e s a r e a v e r a g e s ove r a f r e q u e n c y b a n d w h o s e c e n t e r is a p p r o x i m a t e l y 30 m H z .

TABLE 2 REGIONALIZED ESTIMATES OF Qscs AND S c S ~ - S c S ~ TRAVEL TIMES

Number of Phase Pairs ~T,~s* Time Frequency

No. Region ScS~ sScSn ScSn + sScS~ Window Band Qscs Median 95% C.I.t (sec) (mHz)

ScSm sScS~ ScSm + sScSm (sec) (sec)

1 Western Pacific 1 17 - - - - 180 6-61 157 _+ 17 +3.1 (+1.9, +4.9) 2 Western Pacific 2 21 - - - - 180 6-61 150 + 14 +4.1 (+2.0, +6.1) 3 Western Pacific 3 21 21 - - 180 6-61 155 _ 11 - - - - 4 Fiji-KIP 12 - - - - 180 6-61 141 + 16 +4.7 (+3.9, +8.6) 5 Fiji-MAT 6 - - - - 180 6-50 176 +_ 37 +2.0 (+0.4, +6.1) 6 Hawaii - - - - 6 180 11-56 184 + 48 +1.6 (+1.0, +4.1) 7 Eastern Pacific 4 180 6-33 135 _+ 31 +1.5 (+0.0, +3.7) 8 Trans-Pacific 5 - - - - 150 7-53 150 _+ 34 +5.7 (+4.2, +7.2) 9 Coral Sea 15 180 6-50 142 + 22 +3.7 (+1.8, +4.0)

10 Kurfl-Japan 15 180 6-56 197 +_ 31 -0.4 (-1.2, +0.7) 11 South America 1 7 - - - - 132 15-45 285 + 111 -0.6 (-1.9, +1.1) 12 South America 2 12 240 8-63 266 __. 57 -1.1 (-1.3, -0.6) 13 Eastern China 3 - - 2 180 6-33 168 + 58 +0.8 {-1.4, +3.2) 14 Northern China 3 240 4-33 186 + 73 +1.0 {+0.6, +2.4)

* Residuals with respect to Jeffreys and BuUen (1940) tables, corrected for source depth, ellipticity, receiver elevation, and elevation of surface-reflection points; all ScS,-ScS,, residuals expressed as equivalent ScS,-ScS,_I residuals.

t Thompson-Savur 95% confidence interval for the median (Hollander and Wolfe, 1973).

T h e a b s o l u t e a c c u r a c y of t h e p a r a m e t e r s in T a b l e 3 is d i f f icul t to a ssess b e c a u s e t h e s a m p l i n g e r ro r s a r e n o t known. B a s e d on t h e s c a t t e r in t h e t r a v e l - t i m e obse r - va t ions , t h e p r e c i s i o n of t h e ATscs e s t i m a t e s is a b o u t +1 sec. I f t h e Paci f ic is r e p r e s e n t a t i v e of o t h e r o c e a n bas ins , t he~ t h e a v e r a g e Qscs for o c e a n s is fa i r ly wel l c o n s t r a i n e d a n d p r o b a b l y l ies w i t h i n 10 to 15 p e r c en t of t h e n o m i n a l va lue o f 150.

S i n c e t h e s a m p l i n g o f t h e c o n t i n e n t a l m a n t l e is poor , t h e a c c u r a c y of i ts a v e r a g e

Qscs v a l u e d e p e n d s l a rge ly on t h e p r e d i c t i o n e r ro r s a s s o c i a t e d w i t h e q u a t i o n (2),

w h i c h cou ld be as h igh as 20 to 30 p e r cent . F o r t u n a t e l y , t h e c o n t i n e n t s o c c u p y on ly o n e - t h i r d o f t h e E a r t h ' s sur face , so t h a t t h e e s t i m a t e o f Qscs s h o u l d be good to 20 p e r c e n t o r less.

T h e r e f o r e , w i t h i n t h e H G L P f r e q u e n c y b a n d (6 to 60 mHz) Qscs for t h e a v e r a g e E a r t h is p r o b a b l y less t h a n 200. C o m p a r a b l e v a l u e s d e r i v e d b y t h e i nve r s ion of lower f r e q u e n c y (0.2 to 10 m H z ) n o r m a l m o d e d a t a l ie in t h e i n t e r v a l 200 to 240, w i t h t h e b e s t m o d e l s {those c h a r a c t e r i z e d b y nonze ro b u l k d i s s ipa t ion ) y i e ld ing e s t i m a t e s a t t h e h i g h e n d o f t h i s r a n g e (Sa i lo r a n d Dz iewonsk i , 1978; A n d e r s o n a n d H a r t , 1978b).


These facts have been used to infer that Qscs may actually decrease with frequency in the vicinity of 10 mHz (Sipkin and Jordan, 1979).

IMPLICATIONS

This study has documented significant regional variations in Qscs that are coherent with variations in ATscs (Table 2; Figure 27). The linear relationship between ScS attenuation and travel-time residuals, equation (2), can be conveniently reparame- terized in the following form

.010

I

.008 ! Q-I

ScS

.006

.0 04

- - 1 Qs~s = Q~s + 7(T°cs/~s~s - 1).

i i i i i i i i i

/

/ /

/ /

/ /

/

, 100

(3)

125

Qs~s

150

175

200

250

300

350 I I I I I i I I I l I I

-2 0 2 4 6 8 JB ScSn-ScSn-, Residual (sec)

FIG. 27. Correlation of Q~s and median ScS,-ScSm_I residual. Stack numbers are from Table 2. Vertical error bars are + l a for Q~s; horizontal error bars are 95 per cent confidence intervals for the residual medians, calculated by the Thompson-Savur method. Dashed correlation line corresponds to Qsc½ = (4.4 × lO-4)hTscs + 4.88 × 10 -3, where ATscs is the ScS,-ScS,_I residual in seconds.

Here, as in equation (1), T°cs is the surface-focus ScS travel time for a vertical (zero distance) ray path whose attenuation factor is Q~I. The overbar again denotes parameters for the average Earth, and y is a dimensionless constant. The data have yielded the numerical values

----1 Qscs = 5.88 × 10 -3 (4a)

T~cs = 938.1 sec (4b)

7 = 0.40. (4c)

These quantities provide constraints on phenomenological models of mantle rheol- ogy.

To illustrate this point, consider a very simple absorption-band model of weak dissipation in shear (Liu et al., 1976; Anderson et al., 1977), one whose density of


strain retardation times, D(r), varies as - 1 over some interval Zm ----< T --<__ TM and is zero elsewhere [follow the notation and conventions of Minster (1978); e.g., T has the dimensions of seconds per radian]. It is postulated that the variations of both

-1 0 Ts~s (3) are Qs~s and in equation due solely to spatial variations of the absorption- band parameters, and two additional assumptions are made: (1) that the center frequency ~0o of the HGLP band is far from the end points of the absorption band,

--1 TM << ~o << Tm -1, rendering Q-1 << 1 nearly a constant function of frequency in the vicinity of O~o; and (2) that, although TM is allowed to be an arbitrary function of position, T~ is spatially invariant. Under these conditions, it is not difficult to show

Ts~s is required to be independent of that this model can satisfy equation (3) if o position above an upper cutoff frequency specified by

~m -1 = ~0oe ~/~. (5)

(All terms of order Q-2 have been neglected in this derivation.) Using the value of given by (4c), this upper cutoff frequency is calculated to be 486 rad/sec (80 Hz).

Tscs is nearly frequency independent and The absorption-band model implies that o that Qscs ~ ~ above the cutoff.

TABLE 3 ScS PARAMETERS FOR OCEANS, CONTINENTS, AND THE

AVERAGE EARTH AT 30 m H z

Region Qscs ATs~s (sec)

Oceans 150 +4.2 Continents 225 -1.0 Average Earth 170 +2.4

Of course, it cannot be assumed that this contrived model has any physical basis. Because shear dissipation is probably governed by thermally activated processes, any corner frequencies should vary exponentially with inverse temperature, and the assumption of a single, high-frequency cutoff independent of geographic position is probably unrealistic. Moreover, the observations of high-frequency ScS phases in the western Pacific imply the existence of a corner somewhere in the vicinity of 0.2 to 0.8 Hz (Sipkin and Jordan, 1979), which is at least two orders of magnitude less than the cutoff derived in the above exercise.

The data alone do not constrain the range of mantle depths over which the Vs and Q, heterogeneities occur. It may be inferred, however, that much, if not most, of this inhomogeneity is confined to the upper mantle where large temperature gradients are known to exist. The predominance of upper-mantle heterogeneities is implied by the global correlation of ScS parameter variations with crustal age and tectonic history, as well as by a considerable body of previous seismological experience. Two examples ae given: (1) the low upper-mantle shear velocities inferred for China from surface-wave dispersion data (Pines et al., 1980) are consistent with the large ScSn- SCSm residuals and low Qscs values obtained here for China-crossing paths. (2) The contrasting attenuation structures in the mantle wedges above the northwestern and southeastern Pacific subduction zones, delineated by Sacks and Okada (1974) using P waves, are also evident in the Qscs data (cf. stacks 10 and 12).

Define Qg~ and -1 QLM to be the slowness-weighted radial integrals of Q- I for the mantle layers above and below a depth of 670 km, respectively, and T°M and TOLM to be the corresponding two-way vertical travel times; e.g.,

R E G I O N A L V A R I A T I O N OF Qscs

2 ~6.371 km v~-l(r)Q~-l(r) dr

1099

(6)

To explore the consequences of confining the lateral variations to the upper mantle, any aspherical heterogeneities in the lower mantle are completely neglected; QLM is thus taken to be a parameter independent of geographical position. Table 4 gives two models conforming to this assumption and also satisfying the estimates of Table 3. Model A is based on the specification that QLM ---- 350, the value for Sailor and Dziewonski's (1978) normal mode model QMU, which is a frequency-independent model derived from normal mode data assuming no dissipation in compression. The actual value of QLM in the mode band (0.3 to 10 mHz) cannot be much less than this, because introducing any bulk dissipation tends to increase the QLM estimate. For example, Sailor and Dziewonski's models QBS and QKB and Anderson and Hart 's (1978b) model SL8, all characterized by nonzero bulk dissipation and yielding better fits to the mode data, have QLM = 403, 395, and 360, respectively.

Since QLM for model A is much greater than the Qscs estimates the QUM values are forced to be small, only 77 for the average Earth. In fact, this QUM is substantially less than the average quality factor for the upper mantle inferred from surface-wave and higher-mode measurements made in the same frequency band as the ScS

TABLE 4 TWO MODELS OF Q~ AVERAGES CONSISTENT WITH Qscs DATA

Model A Model B

Parameter Average Oceans Continents Average Oceans Continents

Earth Earth

QUM 77 64 122 108 84 225 QLM 350 350 350 225 225 225 Qscs 170 150 225 170 150 225

measurements (Roult, 1975; Deschamps, 1977; Canas and Mitchell, 1978; Sailor and Dziewonski, 1978; Anderson and Hart, 1978b). For example, global averages of the Q observations for the modes oTt, 1Tl and oSt at frequencies greater than 6 mHz are invariably above 100 (see summaries by Anderson and Hart, 1978b), which imply QUM values on the order of 105 to 130 (Sailor and Dziewonski, 1978; Anderson and Hart, 1978b).

This discrepancy may be another consequence of a decrease in Q, with frequency in the mode band previously inferred from the Qscs comparisons. In the derivation of normal mode models, QLM is constrained primarily by the low-order modes, so the assumption of frequency independence could bias the ratio QLM/QuM to high values.

However, the hypothesis that the upper mantle is more attenuating than the lower mantle is corroborated by seismological evidence spanning the entire teleseis- mic band, including studies of sScS,/ScSn ratios (Kovach and Anderson, 1964; Yoshida and Tsujiura, 1975) and high-frequency ts* observations (Burdick, 1978). We have, therefore, constructed another model by maximizing the QUM values under the assumption that QUM <= QLM in all regions (Table 2, model B). This model has the particular features that Qui = QLM ---- 225 for continents and that QuM/QLM = 0.48. Model B yields QUM = 108, which is more consistent with the surface-wave and higher-mode data relevant to the HGLP band. It is also noted that QUM ---- 84 for oceans, which is nearly identical to the upper-mantle average given by Lee and

1100 STUART A. SIPKIN A N D THOMAS H. J O R D A N

S o l o m o n ' s (1979) mode l S21P for the cen t r a l Pacific. Thus , the hypo thes i s a d v a n c e d by th i s model , t h a t the u p p e r m a n t l e b e n e a t h the c o n t i n e n t s is n o t m u c h more a t t e n u a t i n g t h a n the lower man t l e , deserves fu r the r cons idera t ion .

T h e heur i s t i c pu rpose of the a r g u m e n t s c o n t a i n e d in these las t p a r a g r a p h s m u s t

be emphas ized . T h e a s s u m p t i o n s u p o n which t hey are based, in pa r t i cu l a r the pos tu l a t e of l o w e r : m a n t l e homogene i ty , have in no way b e e n confnzned by a d e q u a t e

se ismological exper imen t s . Clearly, all of the h y p o t h e s e s a n d specu la t ions s t a t ed here r equ i r e t e s t ing by the app l i ca t ion of fo rmal i nve r s ion t e c h n i q u e s to m o r e

ex tens ive da t a sets before t h e y can be l e n d e d m u c h credence .

I t is obv ious f rom T a b l e 4, however , t h a t the Qscs es t ima te s in T a b l e 3 imp ly

s u b s t a n t i a l d i f ferences in the a t t e n u a t i o n s t ruc tu r e s u n d e r l y i n g the c o n t i n e n t s a n d the oceans. Mode l s of the u p p e r man t l e , charac te r ized by th ick c o n t i n e n t a l root s t r u c t u r e s (e.g., J o rdan , 1975; 1978), are therefore cons i s t en t wi th our observa t ions .

ACKNOWLEDGMENTS

We gratefully acknowledge the cheerful assistance of R. Buland, whose codes were used to generate the normal-mode synthetics, and we thank I. Nakanishi and T.-L Teng for preprints of their papers. This research was sponsored by the National Science Foundation under Grants EAR77-00897 and EAR78- 12962.

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SCRIPPS INSTITUTION OF OCEANOGRAPHY UNIVERSITY OF CALIFORNIA LA JOLLA, CALIFORNIA 92093

Manuscript received December 4, 1979

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