Bulletin of the Seismological Society of America, Vol. 81, No. 2, pp. 592-610, April 1991

PROPAGATION OF Lg WAVES IN THE NORTH AUSTRALIAN CRATON: INFLUENCE OF CRUSTAL VELOCITY GRADIENTS

BY J. ROGER BOWMAN AND B. L. N. KENNETT

ABSTRACT

Aftershocks of three large earthquakes near Tennant Creek in the Northern Territory of Australia provide a unique opportunity to study regional seismic phases in the North Australian Craton. Three portable digital seismographs were operated near the source zone to provide control on earthquake locations, and seven recorders formed a line between Tennant Creek and the seismic array at Alice Springs, which is 430 km to the south. Eleven earthquakes of sufficient size for analysis were recorded during a one week deployment two months following the main shocks. The group velocity observed for Lg waves along this profile of 3.7 kmlsec is at the high end of the normal range and appropriate for a stable continental interior. We estimate attenuation in discrete frequency bands by measuring the decay of amplitude as a function of distance from the source and assuming the common r-s~s relationship for geometrical spreading. However, this assumption leads to frequency dependent Q values: Q -- (230 ± 36) f(0.66±0.12) that are abnormally low for a stable continental region. The apparent Q is also not consistent with other observations, such as the high Lg group velocity, the positive bias in M L estimates obtained for other parts of Australia using standard attenuation relations, the size of felt areas for large central Australian earthquakes, nor with the high frequency con- tent of seismic reflection data collected near our profile. Some crustal models for northern Australia derived from seismic refraction work show a gradient zone between 30 and 55 km rather than a sharp Moho discontinuity. We therefore investigate the effect of gradient zones at the crust-mantle transition on the decay of Lg amplitudes using syn- thetic seismograms calculated with the wavenumber integral method. The modeling suggests that some of the S-wave energy that would be trapped in a crustal wave guide with a sharp lower boundary can leak out in the presence of a gradient and so enhance the attenuation. In addition, there are focusing effects due to the formation of caustics from the gradient zones which cannot be represented by a single analytic amplitude correction.

INTRODUCTION

Lg waves are the dominant feature of seismograms at regional distances and are therefore quite useful for estimating ear thquake magnitudes and for the detection and estimation of the yields of nuclear explosions. However, the accuracy of magnitude and yield estimates is dependent on the correct estima- tion of Lg amplitude decay with distance. In this article, we present results of a study of Lg at tenuat ion in the Precambrian shield in central Austral ia that demonstrate the effect of regional crustal structure on the rate of Lg amplitude decay.

Aftershocks of the 22 January 1988 Tennant Creek, Northern Territory, ear thquakes provide a localized source of radiation for an analysis of regional

592

Lg WAVES IN THE NORTH AUSTRALIAN CRATON 593

phases recorded by a 430-km l inear a r r ay of por table se i smographs be tween T e n n a n t Creek and Alice Spr ings (Fig. 1). The th ree T e n n a n t Creek main- shocks ( M s 6.3, 6.4, and 6.7) produced two scarps of 32 k m combined leng th (Bowman, 1988) and were followed by thousands of af tershocks in a 10 by 40 k m zone (Bowman et al., 1990) displaying complex geomet ry t h a t suggests f au l t ing on conjugate p lanes (Choy and Bowman, 1990).

Most previous s tudies of Lg propaga t ion have rel ied on broadly d i s t r ibu ted sources and rece ivers and, as a consequence, es t imates of group veloci ty and a t t e n u a t i o n r ep re sen t averages over the region sampled by the pa ths avai lable . Moreover , t he r e is seldom r e d u n d a n t da t a for the same paths , so no direct measu re of e r rors in the es t imates is avai lable . We t ake advan tage of the a b u n d a n t af tershocks of the T e n n a n t Creek e a r t h q u a k e s to examine Lg propa- gat ion a long a single, s imple pa th in the N o r t h Aus t r a l i an Craton.

Severa l l ines of evidence suggest t ha t the a rea of s tudy has low to modera t e a t t enua t ion . The se i smograph profile lies in a c ra ton where the re has been l i t t le tectonic ac t iv i ty in the past bi l l ion years . Also, the group veloci ty of Lg waves observed in this s tudy is high, which is charac ter i s t ic of o ther s table con t inen ta l regions exh ib i t ing low a t t enua t ion . Next , the isoseismal a reas of A u s t r a l i an e a r t h q u a k e s are l a rger t h a n those for tectonic areas . Moreover , local magni - tudes e s t ima ted us ing Richter ' s (1958) a t t en u a t i o n re la t ionsh ip are b iased to h igher magni tudes . F ina l ly , deep seismic ref lect ion da ta f rom cent ra l Aus t r a l i a are u n u s u a l l y r ich in h igh- f requency ene rgy imply ing low a t t e n u a t i o n (Goleby et al., 1989).

19 I I l s

Tennant N 1 0 Creek

2o wR' '

5 2

~ 1 AH2 21 8 ,310 AH3

,.,'44

,LH5

22 AH6

~,H7

23 AH8

MSPA Alice Springs

24 t I t 133 '134 E 135 136

FIG. 1. Map of the source (diamonds) and receiver (triangles) locations used for studying Lg propagation. Portable stations (N1 and H1 to H8) recorded the vertical component only at 25.6 samples/sec and the Alice Springs array recorded three-component data at 20 samples/sec. Stations of the Warramunga (WRA) seismic array are shown as plus signs. Station B2 at the intersection of the two arms of the WRA array recorded three-component data at 16 samples/sec. The inset on the right shows the location of the temporary receiver array within Australia, and the inset on the left shows the locations of the aftershocks used in this study, with symbols corresponding to event numbers in Table 1, and of the thrust fault scarps (Bowman et al., 1990), as heavy lines with hatch marks on the upper plate.

594 J. R. B O W M A N AND B. L. N. K E N N E T T

However, in the present study, we find that estimates of at tenuat ion are anomalously high when we correct the observed Lg wave amplitudes for geometrical spreading with a factor commonly used in North America and Western Europe. Crustal studies in the northern part of central Austral ia suggest that the crust-mantle transition consists of a gradient zone ra ther than an abrupt discontinuity (Finlayson, 1982). We have therefore investigated the effect of the character of the crust-mantle transition on the apparent at tenua- tion of Lg waves using synthetic seismogram modeling. Incomplete trapping of Lg waves in the presence of a gradient zone is likely to be responsible for the relatively rapid decrease in Lg amplitude with distance from the source.

DATA AND GEOLOGICAL SETTING

Eight portable seismographs were operated on a profile between Tennant Creek and Alice Springs for one week in March 1988 (Fig. 1). These stations consisted of vertical-component Willmore Mark III seismometers with 1 sec natural periods and nine-track digital instruments recording continuously at 25.6 samples/sec. A triparti te array consisting of station N1 situated west of the fault zone, three-component station B2 at the Warramunga (WRA) array, and the northernmost station H1 of the linear array was used for determination of aftershock epicenters. Data from station H2, which had a partially clamped seismometer, and station H4, which had numerous tape errors, were not used for the at tenuat ion analysis, but data from H2 were retained in the record section displays. In addition to the portable stations, we use data from the three-component, short-period station (SZ, SN, and SE for vertical, north-south and east-west components) of the Alice Springs array (ASPA, Fig. 1)

The propagation path from Tennant Creek to Alice Springs is in the North Austral ian Craton, which has formed a single relatively stable crustal block for 1700 m.y. (Plumb, 1979). The Tennant Creek fault zone is near the boundary between the Early Proterozoic Tennant Creek "inlier" and the thin Paleozoic Wiso Basin to the west. The inlier is a basement outcrop of a much larger feature and consists of sediments and metasediments of the Warramunga Group, which are intruded by lower Proterozoic granites. Station H1 to H3 were located on the Proterozoic Davenport geosyncline, which is often considered to be part of the Tennant Creek inlier; stations H7, H8, and ASPA were on the igneous and metamorphic rocks of the Archean Arunta block; and stations H5 and H6 were on late-Proterozoic consolidated sediments of less that 260-m thickness overlying the Arunta block (Smith and Milligan, 1964). All seis- mometers were buried in Cenozoic eolean and residual sand and gravel deposits that blanket most of the region with a thickness generally less than 20 m. In the absence of thick, young sedimentary basins, we do not expect large varia- tions in site response.

Because of the high level of aftershock activity, we were able to select 11 ear thquakes for analysis of sufficient size to be recorded at the most distant stations during the brief recording period (inset, Fig. 1; Table 1). Aftershock locations were determined using arrival t ime data from stations N1, B2, and H1, a velocity model (Table 2) simplified from results of refraction surveys (Finlayson, 1981, 1982), and the program HYOELLIPSE (Lahr, 1980). Addi- tional arrival t imes were available from triggered recorders in the source area for several of the larger events. Because only three stations were generally used in the solutions and no station was located within two or three focal depths, all

Lg WAVES IN THE NORTH AUSTRALIAN CRATON 595

TABLE 1 EARTHQUAKES USED IN THIS STUDY

Origin Time Latitude Longitude Depth Number (m/d/y) (h m s) (°S) (°E) (km)* M L

1 3/27/88 8 51 45.1 19.853 133.933 4.0 2 3/27/88 12 51 1.2 19.785 133.894 4.0 3.2 3 3/28/88 0 27 12.6 19.908 134.030 6.7 5.0 (mb 4.9) 4 3/28/88 0 58 14.0 19.913 134.028 4.0 3.5 5 3/28/88 2 6 35.8 19.795 133.878 4.0 6 3/28/88 19 1 10.7 19.858 133.934 4.0 3.0 7 3/29/88 13 22 40.3 19.824 133.923 4.0 8 3/30/88 15 54 39.5 19.880 134.004 4.0 3.1 9 3/31/88 7 33 14.5 19.827 133.980 4.0

10 3/31/88 10 46 52.6 19.899 134.046 4.0 11 4/01/88 5 9 58.1 19.864 134.101 4.0

*Constrained to 4 km unless additional local data were available.

TABLE 2 CRUSTAL VELOCITY MODEL*

Depth (kin) Vp (km/sec)

0.00 4.5O 0.17 5,00 0.34 5.50 2.14 6.06 6.00 6.20

13.00 6.27 27.00 6.85 40.00 7.30 47.50 7.40 50.50 8.16 58.00 8.18 61.00 8.29

*Modified from Finlayson (1981, 1982).

bu t one of the dep ths were f ixed a t 4 k m , which is h a l f the m a x i m u m focal dep th found in de ta i led a f t e r shock s tudies (B ow man et al., 1990). U n c e r t a i n t i e s in ep icen te r a re gene ra l l y less t h a n 3 km.

For even t 5 (Table 1) a s am p l e record sect ion of the reg iona l d a t a is shown in F igu re 2 and a t h r ee - com ponen t record f rom Alice Spr ings is shown in F i g u r e 3. In bo th d i sp lays each t r ace is no rma l i zed to i ts m a x i m u m ampl i tude . A t Alice Spr ings the no r th - sou th c o m p o n e n t (SN) is ve ry close to r ad i a l and the eas t -wes t componen t (SE), to t r a n s v e r s e . The ver t i ca l componen t da te in F igu re 2 shows the evolu t ion of the wavef i e ld f rom 10 k m to 430 k m f rom the source. A t r a n g e s beyond 120 kin, t he s e i s m o g r a m s consis t of impu l s ive c rus t a l P w a v e s fol lowed by e m e r g e n t Lg w a v e t ra ins . The Lg a r r i va l a t s t a t ion H6 is more impu l s ive and s t ronge r t h a n a t ne ighbo r ing s ta t ions . Record sect ions for the 11 even t s se lected are r e m a r k a b l y s imi la r , a l t hough the re is some v a r i a t i o n in the re la- t ive s t r e n g t h s of P and Lg, probab ly caused by differences in focal m e c h a n i s m . The s m a l l e r e a r t h q u a k e s h a v e the h ighes t s ignal- to-noise ra t io b e t w e e n 1.5 and 5 Hz.

596 J. R. B O W M A N A N D B. L. N. K E N N E T T

607080 _~-~---~- -"~ ~ 607080

50 .=.- 50 o ~i oo "i 40

~:3 ":; ~: ~ '5. " 3oi 3o t-L 20 : ~. = 20

10. j ~ B ~ ~ ~ ~ _-.4 10 O- ~: = ~ = ~ ~: ~ ~: ~ 0

I I r I 1 ~ I r i I I i i I I i i i I r I q I r r

0 100 200 300 400 D i s t a n c e [ k m ]

FIG. 2, Seismograms [or event 5 at stations on the line between Tennant Creel{ and Alice Springs. Each trace is normalized to its max imum amplitude. Locations of stations are shown in Figure 1, and station SZ is the short-period, vertical-component of s tat ion ASPA. The Lg arr ival is the largest phase at regional distances.

SZ ~ 8 8 328 2293

88 328 ~ 7-/zi

s n ~ e ' " ' r . . . . . . . . . . . ~ - , ' ~ p q l ~ , ' ~ e , , ~ ' , , , l , , , ' , - , - ' , ' . . . . . . , . r . . . . . . . . . . 2 : 7 : 2 0 . 0 "[ I '~'''''~"~''~'.~I"'''''''~'''''''''I''''~'~''~"'''''''~''''~'''~'''''''~'~''''''''~'''~''''~'''''''''t'''''''''~""'''''~''~''~`~' ........ 88 328 ~ 3955

i

j I L , . , . ~ I J , , ~ L . . . . . . . . . . . . . . . . . . . . . . . .

2 : 7 : 2 0 . 0

.......... T ......... I ......... i ......... I ......... i ......... ~ ......... i,,,,,,,I,I ......... i ......... I ......... i ......... M ......... i ......... i ......... i

02:08 02:09

FIG. 3. Three-component, short-period seismograms for event 5 recorded at the Alice Springs array. Each trace is normalized to its maximum amplitude, which is shown on the r ight in digital counts.

The P-wave first arrivals have an apparent velocity of 7.7 to 7.8 km/sec, which suggests that they are refractions from the lower crust. Finlayson (1982) used data from mine blasts near Tennant Creek recorded along a line extending 500 km to the east to interpret a Moho depth of 50 km and Pn velocity of 8.2 km/sec. The crossover distance where Pn becomes a first arrival in Finlayson's model TCMI-2 is about 350 km for a surface source, and only stations H8 and ASPA lie beyond this distance. However, the differences between arrival times at these stations in our data are consistent with the velocities of 7.7 to 7.8

Lg WAVES IN THE NORTH AUSTRALIAN CRATON 597

km/sec observed at closer ranges. This suggests that the crust is thicker along this profile extending south of Tennant Creek than along a profile to the east, or that the Pn velocity is anomalously low. The apparent velocity of 7.7 to 7.8 km/sec observed here is intermediate between the lower crustal (7.4 km/sec) and Pn (8.2 km/sec) velocities of TCMI-2.

On the vertical components along the profile (Fig. 2), the initial P wave is followed by a coda of ra ther uniform amplitude without prominent, discrete phases such o as Pg or Sn (except for a clear early arrival at H8). On the radial (SN) component at ASPA (Fig. 3), on the other hand, the first P is followed by 11 sec by a Pg phase, and on both the horizontal components the Lg is preceded by a smaller pulse that may be an S counterpart to the initial P arrival. It should be noted that trace normalization exaggerates the strength of the Pg on the radial (SN) component.

The Lg phase dominates the seismograms at distances beyond 120 km with an average amplitude 3.3 + 1.4 t imes that of the P wave in the group velocity window from 8 to 7 km/sec (for seismograms filtered in a 3 to 8 Hz passband). Unless otherwise specified, amplitudes refer to the maximum sustained ampli- tude defined by Nuttl i (1980), that is the amplitude equaled or exceeded by the three largest amplitude peaks in the wave train. The L g / P ratio in northern Austral ia falls between that observed for ear thquakes in eastern North Amer- ica (10) and for ear thquakes and explosions in the western USSR (1) (Pomeroy et al., 1982). At ASPA the ratios of radial and transverse components to the vertical component amplitudes are 0.8 + 0.2 and 1.3 + 0.3, respectively, some- what lower than the ratio of 2 between maximum horizontal and vertical sometimes assumed (e.g., Street, 1978).

GROUP VELOCITY

The Lg group velocity is est imated as 3.7 km/sec by fitting a line to the maximum amplitudes recorded at stations H3 to ASPA for the 11 ear thquakes in Table 1, and a similar velocity is est imated from the onsets of the Lg wave trains. The group velocity in central Austral ia is at the upper end of the range usually reported for stable continents (Pomeroy et al., 1982) and is somewhat higher than the only previous est imate of 3.5 km/sec for Australia, based on paths crossing both Precambrian shield and the Phanerozoic region of eastern Austral ia (Bolt, 1957).

ESTIMATES OF ng ATTENUATION

The Lg amplitude at frequency f for the ith ear thquake (i = 1, n) observed at the j t h station ( j = 1, m) can be approximated by

Aij ( f ) = Aol ( f ) I j ( f ) Rj( f )Si jDijexp( -'Yrij ) , (1)

where Aoi is a source factor, Ij is the instrument response, Rj is the site response, Dij is a geometrical spreading factor, Sij is a source radiation term, and exp(--Yrij ) is the at tenuat ion factor for source-station separation rij. The coefficient of at tenuat ion is 7 = v f~ Q U, where Q is the temporal quality factor and U the group velocity, and rij is the source-receiver distance. If the instru- ments are nominally identical and the site response is taken as unity, then

log Aij - log Dij - log S i j = log Aoi - (lOgloe),yr~j. (2)

598 J. R. B O W M A N AND B. L. N. K E N N E T T

Now, define A i* as the logarithmic amplitude corrected for geometrical spread- ing and source radiation effects, and set 7' = (logio e) 7. Under the assumptions that a single at tenuat ion coefficient adequately describes the nearly coincident paths on the Tennant Creek profile and that variations in source radiation patterns can be ignored,

Ai* = log Ao~ 7' - - r i j .

With a number of amplitude observations, we can estimate the spatial at tenua- tion coefficient 7' and the source excitation factors Aoi by a generalized least-squares technique (Press et al., 1986). The estimates are determined by m i n i m i z i n g

: , ( 4 ) j = l i=1 ~ i j

where (Tij is an estimate of the standard deviation of the logarithm of the amplitude measurements, which is scaled to the ratio (S/N) of the Lg amplitude to the noise level before the P arrival as

2 S / N > 4

aij= 2 / ( s / g / 2 - 1) 2 < S / N < 4 (5)

S / N < 2

in order to give less weight to the smallest earthquakes in the data set. The geometrical spreading factor for Lg is frequently approximated by the

simple power law

D : r n. (6)

Nuttli (1973) suggested that n = 5/6, which is the predicted amplitude decay with distance for an Airy phase trapped in the crustal waveguide in the t ime domain (Ewing et al., 1957, p. 145), and this value has been used in many subsequent studies (e.g., Nuttli, 1980; Chow et al., 1980; Dwyer et al., 1983). However, Lg is not a single Airy phase, but a superposition of Airy phases of different modes with a range of phase and group velocities. As the observed amplitude will depend on the details of interference of the constituent modes, the amplitude decrease may not follow such a simple relationship. Although results of numerical experiments by Campillo et al. (1984) and Shin and Her rmann (1987) are consistent with an average trend close to r -5/6, it is noteworthy that both of these studies focused on velocity models with sharp discontinuities at the Moho. Because of the difficulty in simultaneously estimat- ing geometric spreading and at tenuat ion owing to absorption and scattering, we initially assume r -~/6 spreading and arrive at an unexpectedly low value for Q in central Australia.

Lg WAVES IN THE NORTH AUSTRALIAN CRATON 599

We measure Lg amplitudes in six overlapping bands with center frequencies fc of 1.0, 1.4, 2.0, 2.8, 4.0, and 5.7 Hz with lower and upper corner frequencies of fc/~/2 and ~/2fc, respectively. For each frequency band, the solution to equation (4) gives an intercept for each earthquake, proportional to the size of the event, an estimate of 7 consistent with the assumed geometrical spreading, and standard deviations for each. We use three measures of the Lg amplitude: the maximum absolute amplitude, the maximum sustained amplitude, and the RMS amplitude in the group-velocity window 3.7 to 3.1 km/sec. As an example, the least-squares solution for RMS amplitudes in the 1.4 to 2.8 Hz passband (Fig. 4) provides a reasonable fit to the observed amplitude decrease with distance and shows the consistent amplitude pattern among the earthquakes. Most data fall within 0.2 logarithmic units of the best fit lines, tha t is, within the estimated measurement error. There remain systematic differences, how- ever, between the model and observed data. For example, amplitudes at station H6 at a range of 240 km are often comparable or larger than those at station H5 at 205 km range. The advantage of simultaneously fitt ing the Lg amplitudes for the suite of earthquakes is tha t it yields single values of 7 and Q as well as estimates of their errors. For example, in the band with a 2-Hz center fre- quency, using RMS amplitudes and the assumed value of n = 5/6, we find 7 = 0.0043 + 0.0008 and Q = 403(+ 102, - 85).

The at tenuat ion coefficient 7 is shown for the discrete frequency bands in Figure 5c using RMS amplitudes and n = 5/6. Within the errors estimated in the least-squares procedure (shown as bars), 7 follows a power law dependence on frequency 7 = (0.0037 +_ 0.0005) f(o.34_+ o.12), as does the quality factor Q = (230 + 36)f (°66~ 6.12) (Fig. 5d). Similar results were obtained using sustained maximum and absolute maximum as measures of the Lg amplitude.

In the next section, we discuss these at tenuat ion estimates in the context of Lg at tenuat ion in other continental regions and of other seismic observations of at tenuat ion in central Australia. We then describe the effect of crustal velocity gradients on the apparent a t tenuat ion of Lg.

I ' I I

~ . . . . . . . . . . . . . ~.'.'.&.~ 3

~ 4 3

cd

% 7 ~ 7

0 I I I

100 2oo 3oo 4o0

D i s t a n c e (km)

Fro. 4. RMS amplitudes for 2 Hz center frequency and corrected for r -5/6 geometrical spreading are shown as a function of source-receiver distance and labeled by event number as in Figure I. Lines show the least-squares fit to the data.

600 J. R. B O W M A N AND B. L. N. K E N N E T T

' I ' I = I 1500 , j , , , ,

a <~- 5.7 Hz b .008 ~ 0 4.0

0 2.8

1000 ,0 2.0 ,~ 1.4

.006 ;~ o 1 .o ©

E ~ 8 <> c, ' o E 8 o = o ~ e @ o

0 ~ 500 @ 0

,0 ~ 0 0 0

o ~ $ S 8 8 8 '~ o

.002 I I I I I I I t I I t I 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1

n n

g=0.0037 (0.0005) f**0,337 (0.117) Q= 230 ( 3 6 ) f**0.66 (0.12) :

el 04 L _o . -

- 2 . 5 2.5 i / , ~ " j

I , , I I I I I 2 . 0 I = I t I t , , .0 .4 .8 .0 .4 .8

log f requency log f requency

FIG. 5. (a) At tenuat ion coefficient -~ as a function of the power n assumed for geometrical spreading for center frequencies from 1.0 Hz (heavy black) to 5.7 Hz (light grey) wi th symbols defined in Figure 5b. RMS ampli tudes in the 3.7 to 3.1 km/sec group velocity window were used. (b) Same as (a), but for quality factor Q. (c) Est imated 7 for six frequencies with error bars determined from generalized least squares. Grey line shows best fit power law frequency dependence wi th parameters given above the frame. (d) Same as c, but for Q.

INTERPRETATION OF Lg ATTENUATION ESTIMATES

The Q estimated for this central Australian path, Q = 230f °'66, is anoma- lously low when compared to other stable continental regions. For example, estimates of Q for Lg waves in eastern Canada, which is a Precambrian shield environment similar to the North Australian Craton, are 550f °'65 (Shin and Herrmann, 1987), II00 fo.19 (Chun et al., 1987), and 900 fo.2 (Hasegawa, 1985). For the entire eastern United States, Q estimates are 800f °'32 (Gupta and McLaughlin, 1987), and for the central United States, between 415 (Gupta and McLaughlin, 1987) and 1500 fo.4 (Dwyer et al., 1983). Lower values of Q have been estimated for tectonically active areas, such as 64 in Iran (Nuttli, 1980), 80 from coda waves in California (Aki and Chouet, 1975), and 210 fo.6 (Ch~vez and Priestley, 1986) to 270f °4 (Xi and Mitchell, 1990) for the Basin and Range province. Thus, the apparent Lg attenuation in central Australia is lower than observed for most other stable continents. However, it is interesting to note that a Q value of 360 for 3 Hz Lg waves in cratonic South Africa has recently been reported by Frankel et al. (1990).

Lg WAVES IN THE NORTH AUSTRALIAN CRATON 601

These relatively low Q values estimated for the path between Tennant Creek and Alice Springs are not consistent with complementary seismic observations in this region. First, the seismograph profile lies in the Proterozoic North Australian Craton where there has been little tectonic activity in the past billion years (Plumb, 1979). Second, the group velocity 3.7 km/sec for Lg waves along the profile is high, which is characteristic of other stable continental regions exhibiting low attenuation. Third, the isoseismal areas of Australian earthquakes of M L 5 or greater are significantly larger (Fig. 4 of Greenhalgh et al., 1989) than those for tectonic areas such as southern California (Richter, 1958). Moreover, the isoseismal areas of earthquakes in the Australian craton are comparable to those in other stable continental regions (Arch Johnston, written comm., 1990). Fourth, attenuation terms in local magnitude scales derived for South Australia (White, 1968; Greenhalgh and Singh, 1986) and Western Australia (Gaull et a l . , 1989) are lower than reported for southern California (Richter, 1958; Hutton and Boore, 1987). Although no magnitude scale has been developed for the area of our profile, local magnitudes from station ASP at Alice Springs are typically biased by 0.5 magnitude units, possibly as a result of low attenuation or focusing. Fifth, seismic reflection data recorded less than 100 km west of the southern end of our profile have an unusually high frequency content. Frequencies up to 80 Hz at reflection times of 5 to 6 sec and up to 60 Hz at 6 to 10 sec are common, implying that rocks at upper crustal depths have low attenuation (Goleby et al., 1989). Sixth, intrinsic Q for the lithosphere beneath the WRA seismic array as estimated from teleseismic P waves exceeds 1000 (Korn, 1990). Finally, coda Q estimates along the same path are higher than inferred from the spatial decay of Lg amplitudes (unpublished data).

Because our Lg Q estimates are low relative to other stable continental regions, and lower than would be suggested from other types observations, it is appropriate to examine the validity of the assumptions on which the attenua- tion estimate is based. In order to extract the loss coefficient, we have made an allowance for the main propagation effects of wavefront spreading. Figure 5a illustrates the trade-off between the attenuation coefficient ~/ and the index n in the power law representation of the spreading (equation 6) at the six frequencies considered, and Figure 5b shows the tradeoff between Q and n. An appropriate choice of spreading relation is clearly critical for an accurate estimate of attenuation.

In the following section, we show how the pattern of Lg amplitude variation with distance is influenced by the character of the crust-mantle transition. A simple power law relation for the amplitude variation with distance underesti- mates the complexity of the Lg propagation process and, in those cases where focusing effects give localized high amplitudes, is a very poor representation of the behavior.

EFFECT OF CRUSTAL STRUCTURE ON Lg ATTENUATION

Estimates of the spatial attenuation coefficient for Lg waves are strongly dependent on the assumptions made in correcting for the geometric spreading component of amplitude decay. The crustal velocity structure can play an important role in determining the rate of geometric spreading (e.g., White, 1968; Banda et al., 1982; Frankel et al., 1990). Our choice of an r -5/6 geometri- cal spreading factor led to Q estimates for Lg that were low compared to most

602 J. R. BOWMAN AND B. L, N. K E N N E T T

other stable continental regions and inconsistent with other geophysical obser- vations in Australia. However, crustal models for paths east of Tennant Creek (Finlayson, 1982) indicate that the crust-mantle transition is a gradient zone rather than an abrupt discontinuity (Fig. 6c), which may have a strong influ- ence on the actual geometrical spreading in the region of our observations.

In order to investigate the influence of the nature of the crust-mantle transi- tion on the character of the Lg phase, we have constructed synthetic seismo- grams for a number of simple models of the crust-mantle transition. As a reference, we used a model (SJ0, Fig. 6a) characterized by a thin low-velocity surface layer, an increase from upper to lower crustal velocities at 25 km depth and a sharp Moho discontinuity at 38 km depth. Model SJ0 is similar to crustal models of Campillo et al. (1984) and Shin and Herrmann (1987), which have sharp Mohos at 30 km and 40 km, respectively, and for which Lg amplitude behavior has been investigated numerically. Two classes of models were con- structed by replacing the single discontinuity with a set of three stops.

In the sequence SG1 to SG3 (Fig. 6a), the discontinuity is replaced by a velocity gradient, covering the full span of the original Moho jump, extending over a progressively larger depth interval. In the second sequence of SJ1, SJ2, and SG3 (Fig. 6b), a partial jump at the base of the crust at 38 km is retained and the remainder of the velocity increase to mantle velocities is in the form of a gradient. The models SJ0 and SG3 can be regarded as the limits of both sequences. Although the 38-km Moho depth in the reference model is less than the 50-kin depth to mantle velocities interpreted by Finlayson (1982) or sug- gested in this study (Fig. 2), models SG2 and SG3 approximate the crust-mantle

a) ~,,,~ ~ / ~ b ) ~,,:, ~ / ~ 3 5 6 7 8 9 10 5 6 7 8 9 10

0 -- I' ] I I I I 0 -- I I' I I I I I

i __- i __- ........ 20 20

~ e

60 60

8O 8O

FIG. 6. Velocity models used for synthetic seismogram calculations. Heavy solid lines show reference model SJ0. (a) Moho discontinuity has been replaced by a gradient in models SG1, SG2, and SG3. (b) Moho discontinuity has been reduced in models SJ1, SJ2, and SG3. (c) Models TCML2 and TCMI-3 of Finlayson (1982), which were derived for the path between Tennant Creek and Mt. Isa, compared to our reference model SJ0 and model SG3, which has the weakest velocity gradient of the models investigated.

Lg W A V E S I N T H E N O R T H A U S T R A L I A N C R A T O N 603

C) 13,,~ ~ / ~ 6 7 8 9 0

i]' SG3 J Z TCMI-2

TCMI-3 S J0

2O

60

80

FIG. 6. (Continued).

transit ion gradients and depths proposed in Finlayson's models TCMI-2 and TCMI-3 (Fig. 6c).

Theoretical seismograms were calculated using a wavenumber integral ap- proach for each of the models (Kennett, 1983, 1988). A common set of source and integration parameters were employed to allow direct comparison between the results. The calculations were carried out for an explosive source (to avoid source radiation effects) at a depth of 15 km, with P- and S-wave Q of 1000 and 500, respectively. A frequency interval of 0.5 to 4 Hz and a phase velocity interval of 3.0 to 5.0 km/sec were used in the integration, and all P- and S-wave crustal multiples were included. The resulting seismograms for the two sequences of models are displayed in Figure 7 in a true amplitude display with a reduction velocity of 4 km/sec.

In the top panels we display the seismograms for the reference model SJ0 with the sharp Moho transition. Sn is seen as a weak arrival at 200 km with a reduced time of 5 sec which decreases to - 2 sec at 400 km. Sn is followed by a similar arrival with an extra leg reflected above the source. Such a free surface "ghost" also helps to add to the complexity of the energy propagating in the crust. The sequence of packets of multiply reflected S-wave energy within the crust build up to form the Lg wave train. The interference phenomena leading to the generation of Lg do not lead to a monotonic decay of amplitude with increasing range. Rather, the largest amplitudes occur for near critical reflec- tion.

In the sequence of gradient models (Fig. 7a), the general pat tern of the seismograms is maintained, but the locus of the maximum amplitude of Lg is shifted to greater range as the gradient tha t has replaced the Modo discontinu- ity is reduced. Because of the reduced gradient, the reflected S waves from the crust-mantle transit ion spend longer in this region and so require a greater distance to re turn to the surface. A further consequence is tha t these waves

6 0 4 J. R. B O W M A N A N D B. L. N. K E N N E T T

a)

3o. S J0 = )-

20.

10. ~ .

? -4_-- 0.

I 200. 400.

30.

20. ~ --=-

to ~,,

0.

200. 400.

~ 3o. SG2 [

20.

~ 10.

0.

200. 400.

30. S G 3

~ 2o.

~ 10.

0.

200. 400.

Distance km

FIG. 7. Vertical-component synthetic seismograms calculated with the wavenumber integral method (Kennett, 1983, 1988) for frequencies 1 to 4 Hz, with explosive source at 15 km and a constant Q of 1000 and 500 for P and S waves, respectively. Reduction velocity is 4 km/sec. (a) Gradient models. (b) Moho jump models.

Lg W A V E S IN THE N O R T H A U S T R A L I A N C R A T O N 6 0 5

b)

3O.2o. SJO ~ {"

I - ra

1O. I

0.

200. 400.

30 S J1

20.

~ 10.

0.

! 2o'o !

S J 2 ' ' 30.

~ 20.

~ 10.

0.

200. 400.

I

3o S G

20.

I 200. 400.

Distance km

FIG. 7. (Continued),

606 J. R. B O W M A N AND B. L. N. K E N N E T T

travel faster than before and so the locus of maximum amplitude in Lg shifts to higher group velocities.

The theoretical seismograms for the sequence of models with progressively smaller velocity jump at 38 km depth are displayed in Figure 7b. In model SJ1 the large velocity jump at 38 km means that critical reflections are important, even though Sn is enhanced from model SJ0 by the increased gradient below 38 km. For model SJ2 with a smaller velocity jump but increased gradient below 38 km, the Sn phase is very prominent at the shorter ranges. The interference of reflected and refracted energy gives a broad locus of increased amplitude as a function of distance. However, once the velocity jump at 38 km is largely eliminated as in model SG3, sharper amplitude maxima occur dominated by the return from the crust-mantle gradient zone.

The amplitude behavior of these theoretical seismogram calculations as a function of range is summarized in Figure 8. The maximum amplitudes are displayed together with a black dashed line corresponding to r-5/6e -Tr decay, including the effects of a t tenuat ion in the model at the 2-Hz center frequency (~ = 0.0028). As would be expected from the character of the record sections in Figure 7, the calculated amplitude pat terns are somewhat erratic and cannot be fit by any simple power law model. The model SJ0 with a sharp Moho transit ion predicts a mean amplitude decay that is closest to r-5/6e -~r, but even in this case the application of a simple geometrical spreading correction would in- evitably impose a systematic pat tern of amplitude anomalies on the corrected data being used to estimate Lg-wave at tenuation coefficients. For those models with even a partial gradient zone, the rate of Lg amplitude decay with distance is enhanced because of leakage of energy from the crustal waveguide in the phase velocity range contributing to Lg.

An additional prediction for a crust-mantle transition composed almost en- tirely of a gradient zone is that the amplitude maxima for Lg are sharply peaked as a function of distance owing to the formation of caustics from the gradients. Model SG3 predicts very strong Lg amplitude near 220 and 440 km, and it is interesting to note tha t in the normalized seismograms of Figure 2 the Lg arrivals are most clear at just these distances.

For most of the different models of the crust-mantle transition, a single analytic amplitude decay relation will represent a rather limited approximation to the actual amplitude distribution in Lg. As a result, when such a decay correction is applied to observed amplitudes, it will help to equalize amplitudes with distance, but significant variations about the analytic curve are to be expected.

The continental crust-mantle boundary is often better described by a transi- tion zone in which the velocity increases continuously with increasing depth, from velocities typical of the crust to velocities associated with the upper mantle, ra ther than as a sharp boundary (Prodehl, 1984). The crustal models of Finlayson (1982) designed to match the character of refraction data between Tennant Creek and Mt. Isa, Queensland show lower crustal velocities exceeding 7 km/sec and gradients rather than a sharp crust-mantle boundary. Model TCMI-3, in particular, has an average gradient (0.058 sec-1) between 35 and 60 km that is close to that for our model SG3 (0.064 sec -1). Two characteristics of seismograms recorded in this experiment are similar to predictions for a gradient zone between the crust and mantle. First, the Lg amplitude does not decrease monotonically with distance, but rather it exhibits focusing and

L g WAVES IN THE NORTH A U S T R A L I A N CRATON 6 0 7

a)

-3.6

-3.8 I ~ \ ~ ' ' - . - SG1 ;

4.0 i \

- [ \ -

i \ ' . -

¢6

-4.6 .,~" , ,

\ -4.8

I I I I I I I t I I I , 2.1 2.2 2.3 2.4 2.5 2.6 2.7

log x

b) L I ' I ; I i I ' I I I '

-3.6 ~ SJ0

x _._ SJ1

" , 1 \ _ _ SJ2

-4.0 x " _ _ _ SG3

\ 4.8

I i I ~ I I I I l I I 2.1 2.2 2.3 2.4 2.5 2.6 2.7

log x

FIG. 8. Maximum amplitude of synthetic seismograms shown in Figure ? for the velocity models in Figure 6 as a function of source-receiver distance. Dashed black lines show predicted behavior for an Airy phase and solid black lines show amplitudes for model SJ0. (a) Amplitudes for gradient models SG1, SG2, and SG3. (b) Amplitudes for jump models SJ1 and SJ2.

608 J . R . BOWMAN AND B. L. N. KENNETT

defocusing along the profile. Second, the Lg decay rate is larger than expected from intrinsic at tenuat ion in a stable continental region, a characteristic pro- moted by a velocity gradient, but not by an abrupt Moho discontinuity.

It is possible to use the results of the calculations for crustal gradient models to place bounds on values of Q in this region. Given observations that span at least two of the peaks in the calculated amplitude-distance relationship, and taking a plausible range of power law spreading factors for model SG3 to be r -°5 to r -1"4, we find bounds for our data set of Q = 150f °7 and Q = 6 0 0 f 0"4,

respectively. It should be emphasized, though, that the amplitude behavior is not well described by power law decay. Moreover, the average decay is a strong function of the specific crustal velocity structure and the distance range over which observations are made. Nevertheless, it is interesting to note the higher Q and the reduced frequency dependence derived using the larger geometrical spreading factor.

Our comparison of different crustal structures has shown the limitations of simple corrections for geometrical spreading in estimating at tenuat ion coeffi- cients for Lg. Even for a single path, a somewhat erratic t rend of amplitude with distance can be expected, albeit with a superimposed decay. Such decay behavior is a strong function of the character of the crust-mantle transition.

Although the commonly adopted geometrical spreading power law for r -5/6 is seen to give a reasonable representation of the behavior for a sharp Moho, it cannot be universally applied. In many areas, the assumption of an abrupt crust-mantle transition is well founded, but beneath Precambrian terrains (which are well represented in the Soviet Union) a gradational crust-mantle transition seems to be quite common.

The principal application of Lg at tenuat ion coefficients lies in applying path corrections to estimate the magnitude of a source (and in the case of an explosion to thereby estimate the yield). The use of inappropriate amplitude corrections could lead to misleading estimates of source parameters.

ACKNOWLEDGMENTS

We thank J. Hulse for installing the portable seismographs, P. Cummins for programs to read field tapes, S. Ingate and K. Muirhead for supplying data from the Alice Springs array, and J. Lahr for a copy of HYPOELLIPSE. This work was supported in part by the Advanced Research Projects Agency of the U.S. Department of Defence under Grant AFOSR-89-0330.

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RESEARCh SCHOOL OF EARTH SCIENCES AUSTRALIAN NATIONAL UNIVERSITY GPO Box 4 CANBERRA, ACT 2601 AUSTRALIA

Manuscript received 29 July 1990