Scattering and anelastic attenuation of seismic energy in central and south-central Alaska

Physics of the Earth and Planetary Interiors, 67 (1991) 115—122

115

Elsevier Science Publishers B.V., Amsterdam

Scattering and anelastic attenuation of seismic energy in central and south-central Alaska T.J. McSweeney 2

~‘,

N.N. Biswas

~,

K. Mayeda

2

and K.

~aj~j

2

Geophysical Institute, University ofAlaska, Fairbanks, AK 99775 (USA) Department of Geological Sciences, University of Southern California, Los Angeles, CA 90089-0740 (USA)

(Received 17 January 1990; revision accepted 23 August 1990)

ABSTRACT McSweeney, T.J., Biswas, N.N., Mayeda, K. and Aid, K., 1991. Scattering and anelastic attenuation of seismic energy in central and south-central Alaska. Phys. Earth Planet. Inter., 67: 115—122. The characteristics of seismic energy attenuation in central and south—central Alaska are described. The data analyzed are short-period seismograms of local earthquakes recorded digitally in 12 bit at 120-Hz sampling rate by permanent stations of the regional network in the study area. First, the coda amplitude decay rate was compared for two depth ranges, 0—22 km and earthquake focal depth in the 63—133 km. the ofsingle-scattering model. Theevents results show dependence of values Q~1on frequency (f)using interval 1
1. Introduction The interaction between the Pacific and North American lithospheric plates governs the principal seismotectonic features in mainland Alaska. This interaction gives rise to northerly directed horizontal compressional stresses in the uppermost (<50 km deep) part of the lithosphere beneath northeast, central and south—central Alaska and is responsible for the crustal earthquakes that occur widely in the state (Biswas et al., 1986). The *

Present address: Geophysics Program, AK-SO, University of Washington, Seattle, WA 98195 (USA).

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© 1991

—

Elsevier Science Publishers B.V.

thickness of the crust in central and south—central Alaska is of the order of 40 km (Biswas et al., 1980). Subcrustal earthquakes in mainland Alaska, on the other hand, are confined to the south— central and southwestern parts of the state. They define the Wadati—Benioff zone (WBZ) and are directly related to the subduction of the Pacific plate beneath the North American plate. The geometry of the WBZ beneath southwestern and south—central Alaska is illustrated in Fig. 1, using data compiled by Biswas and Tytgat (1988). The earthquakes used in this plot are of magnitudes 3.0 and have focal depths in the range of 40 to about 150 km.

116

T.J. MCSWEENEY ET AL.

~

165°

155°

o

i4~

700

.100

~ 65°

•

~

/ ~:

6~°

5;

~

A

0

5

—

1700

165°

.~,

.•

1600

~.‘-oI~

155°

~

~s~’~’ 150°

0

j45

i~4O

Fig. 1. Epicentral plot of earthquakes for M 3.0 recorded from 1967 to June 1988. The source of data is the Preliminary Determination of Epicenters (PDE) of the U.S. Geological Survey. The symbols refer to the following: hollow triangle, 40 120 km. The continuous solid lines show the isobaths of the upper surface of the WBZ.

In Fig. 1, the thick lines represent the isobaths of the upper surface of the WBZ. The nature of the WBZ at the bend, where its trend changes from southwest—northeast to northwest—southeast in interior Alaska, is uncertain. Accordingly, this section of the WBZ is labeled with a question mark. The zone of transition from predominantly compressional to predominantly tensional stress, as obtained by Biswas et al. (1986), is shown by a heavy broken line in Fig. 1. The results of this figure show that the North Pacific plate, before dipping steeply, underthrusts at low angle under a broad continental area. This area widens from about 200 km around 150°W to 500 km around 145°W. In addition to the above features, the two clusters of intermediate-depth hypocenters along the WBZ should be noted. Cluster A underlies the

Iliamna volcano, a typical member of the calcalkaline volcanoes associated with the Alaska— Aleutian WBZ. The second cluster (cluster B) lies in the Denali National Park area and approximately coincides with the center of the seismographic network used for this study. The tectonic implications of these two clusters are not yet resolved with certainty. However, the intense crustal and subcrustal seismicity of continental Alaska, the details of which have been given by Page et al. (1991), offer excellent scope to study the focaldepth dependence of various seismic parameters in the depth range of 0—150 km. Roecker et al. (1982) reported the results of S-wave coda quality factor (Q~)for different focal depths in the Hindu-Kush region of Afghanistan. They obtained Q~values for earthquakes located in the crust and uppermost mantle (<100 km

117

SCATFERING AND ANELASTIC ATrENUATION OF SEISMIC ENERGY

deep) that are four times lower than that for earthquakes in the deeper mantle (<400 km depth) in the frequency (f) range of 0.4—24 Hz. Tsujiura (1978) conducted a similar study for the Kanto district of Japan. He compared the S-wave coda amplitude decay rate for two depth (Z) ranges: 40—80 km and 100—160 km for frequencies varying from 0.75 to 24 Hz. He obtained Q~ for the shallow events (40
~

~

500 KM

‘~°

~40

~°

160°

150°

(a) 153°

150°

148°

146°

144°

66°

142 66°

65°

FBAA~~-~°~ ACCB

WRH2’~

LVYA

64°

GARO

o

T~ ~ 63°

~

.S•

65°

ARDA

~

~

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64°

A DDM R~D 63°

A PAX

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corded by 1-Hz vertical-component seismographs of the regional network operated by the University of Alaska, Fairbanks. The data are telemetered using a combination of VHF radio links and mlcrowave circuits to the central recording center in Fairbanks. Since mid-1988, the data are recorded digitally in 12 bit at 120-Hz sampling rate by a Masscomp-5600 computer system; we used these digital data for the present study. A data set consisting of 237 seismograms of 52 events was selected for the analysis. In sorting the events, in addition to higher signal-to-noise ratio, consideration was given to obtain a comparable number of crustal (<22 km, 30 events) and sub-

0 0

t~

600

__________

Seismograms analyzed in this study were re-

150°

680

100KM

2. Data and analysis

1600

~2°~’~°°

150°

148°

146°

144°

610 N 142°W

(b) Fig. 2. (a) Perimeter of the study area as in (b) shown by the shaded area on an outline map of Alaska. (b) Epicenter locations of crustal (hollow circle) and subcrustal (solid circle) earthquakes used in the present study with respect to the locations of the seismographic stations (open triangle).

crustal (63—133 km, 22 events) earthquakes. The locations of epicenters of the above 52 earthquakes as well as stations of the network are shown in Fig. 2b. Earthquake locations are also listed in Table 1; all but three events have location errors <5 km. Moreover, it should be noted that, with the exception of five crustal events that were

118

Ti. McSWEENEY ET AL.

TABLE 1 Location details of the earthquakes used for this study (a blank in the magnitude column indicates an event for which the value of ML is not listed in the earthquake catalog) Date

07 08 1988 0808 1988 09 08 1988 1008 1988 1408 1988 1408 1988 17 08 1988 2308 1988 2308 1988 25 08 1988 29 08 1988 31 08 1988 11 09 1988 11 09 1988 2009 1988 29 09 1988 07 10 1988 09 10 1988 03 11 1988 03 11 1988 03 111988 07 11 1988 13 111988 14 11 1988 15 11 1988 16 11 1988 27 11 1988 1001 1989 1401 1989 21 01 1989 3001 1989 01 02 1989 01 02 1989 01 02 1989 07 02 1989 0802 1989 11 02 1989 1202 1989 1702 1989 19 02 1989 2302 1989 25 02 1989 0403 1989 05 03 1989 05 03 1989 0903 1989 1903 1989 2003 1989 25 03 1989 2603 1989 2903 1989 3003 1989

Time h

m~

17 13 11 02 07 10 10 04 11 11 13 00 03 16 10 22 18 19 19 20 23 13 04 15 15 06 06 19 13 13 11 14 14 16 16 20 18 10 17 02 02 01 13 17 22 19 21 16 03 11 11 18

07 09 27 19 17 28 24 20 36 23 10 15 00 51 55 05 18 46 35 12 23 40 13 57 35 21 48 54 29 36 01 22 34 09 38 55 43 15 14 25 33 41 03 51 44 02 45 42 23 22 31 36

17.9 51.2 48.0 45.2 49.0 26.3 36.3 55.5 51.1 50.7 09.7 25.2 35.9 09.5 00.5 42.5 55.1 06.3 50.8 45.5 13.7 30.4 42.1 14.2 43.3 46.5 03.5 54.3 21.6 35.5 31.6 23.8 01.6 37.2 42.9 15.3 28.0 38.1 26.6 39.5 33.1 42.8 08.8 56.7 36.6 26.6 09.2 06.7 22.0 49.3 01.8 40.1

Latitude

Longitude

Depth

(°N)

(°W)

(km)

63.81 63.22 63.62 63.94 63.08 63.50 63.24 63.55 63.20 63.19 64.54 63.11 63.94 63.08 63.80 63.91 63.90 63.66 63.97 63.97 63.97 63.51 63.64 64.01 62.81 63.59 63.82 63.92 63.51 63.93 63.61 64.60 63.40 64.30 63.98 62.99 63.10 63.92 64.57 63.57 63.51 63.54 63.21 63.31 63.44 62.84 62.83 63.88 63.14 63.73 62.92 63.01

149.30 149.41 147.73 148.94 150.32 149.11 150.46 150.68 148.33 150.65 148.21 149.90 146.88 148.35 148.41 149.10 148.92 149.86 147.40 147.42 147.40 147.33 149.15 150.35 148.71 150.65 149.21 148.99 150.74 148.96 149.79 149.27 150.99 148.32 150.21 149.33 149.84 148.89 150.16 150.69 150.75 147.93 150.73 149.72 150.18 148.93 148.89 148.68 149.76 149.31 149.07 149.57

11.11 95.06 5.46 8.66 110.34 6.01 130.97 15.67 11.10 119.97 18.45 94.96 12.65 77.74 108.35 0.02 10.52 120.87 5.63 8.85 12.69 0.02 107.33 16.04 71.07 9.83 13.94 0.02 8.29 2.61 126.84 17.03 7.37 9.31 5.48 76.51 88.32 122.63 21.90 7.30 7.12 9.19 133.49 100.05 9.49 72.70 69.39 6.84 88.67 117.98 67.83 83.59

ML

— — — — — — — — — — — —

0.8 — — —

0.9 —

4.3 3.1 2.4 2.3 2.7 2.6 3.0 2.5 2.5

1.6 2.2 1.9 3.8 1.5 1.7 1.1 2.1 3.3 2.7 2.7 1.8 1.6 1.8 2.6 2.9 2.4 2.3 3.8 2.7 2.7 2.6 2.6 2.5 3.3

119

SCATFERING AND ANELASTIC AYrENuATLON OF SEISMIC ENERGY

located outside the perimeter of the network, all the events selected occurred inside the network. The above data set was first analyzed to find the effect of focal depth on the coda quality factor (Q~)~ defined on the basis of the single-scattering model of Aki and Chouet (1975). Accordingly, the coda section (lapse time (I)> 2 t~ where t~ is S-wave travel time) of each seismogram was filtered in the time-domain using an octave-wide Butterworth bandpass filter (Stearns, 1975) at 12 center frequencies (f) ranging from 0.6 to 16 Hz. Outside this frequency range, the data did not yield any useful results because of a poor signalto-noise ratio. The filtered data were smoothed using a moving window. The window width was linearly varied, inversely proportional to frequency, from 6-s width at 0 Hz to 2-s width at 16 Hz. The averaged amplitude was assigned to the lapse time corresponding to the center of the window and the window was shifted by one-fourth of the window width to obtain the next average value. After correcting the averaged amplitude values for instrument response and geometrical spreading, the logarithm of these values and the corresponding lapse times were fitted with a straight line using

TABLE 2 Mean coda Q~ value at each f obtained for the two focal 1)of the mean value depth ranges; also shown is 1 S.D. (±.5Q~ f Z <22 km 63 < Z <133 km (Hz) ±~Q~ Q~ ±öQ~1 0.6 0.8 1.0 1.5 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

(x103)

(x103)

(x1O~3)

(x1O~3)

7.93 6.71 6.50

0.46 0.39 0.39 0.22 0.18 0.11 0.07 0.05 0.04 0.04 0.04 0.03

7.34 6.68 4.96 3.87 3.19 2.04 1.69 1.42 1.22 1.16 1.01 1.00

0.53 0.31 0.19 0.14 0.10 0.05 0.03 0.03 0.03 0.03 0.02 0.03

4.40

3.90 2.74 2.10 1.69 1.53 1.42 1.29 1.26

the least-squares method to obtain the relation. ~ (~f)/b

Q~(f)from (1)

=

where b is the slope of the least-squares fitted line and is a function of f. The resultant Q~values are listed in Table 2. Next we obtained the total S-wave energy using the method of Wu and Aki (1988). For this purpose, we used 31 events from those listed in Table 1 with good signal-to-noise ratio. These 31 events represented the following depth (Z) ranges: 19 events for 0 < Z < 22 km, nine events for 68
If)

t~

=

n(

P(~~ I

~) 2

exp[

—

b (tr

—

t~)j

(2)

where b represents the same quantity as in eqn. (1). For a given station, the coda power spectrum at frequency f given by eqn. (2) scales linearly as the source spectrum at the same frequency. Therefore, by dividing the total S-wave energy (E(r, f)) by

120

TJ. McSWEENEY ET AL.

the value at the reference lapse time

(tr)

which is

P(t

1 I f), we can eliminate the source effect of an individual earthquake and normalize E(r, f) to a common source. Accordingly, the normalized total energy EObS(r, f) shown in Fig. 4 was obtained by the relation

f)

EObS(r,

=

~,r,

P(tr

f~ If)

(3)

3. Results and conclusions The values of Q~(f)obtained for the two focal depth (Z) ranges (Z < 22 km, and 63 < z.<

\ I

0.

I

-0.2

(1)

(2) f

(3) f

T 0

133 km) are shown in Fig. 3. For

f>

results show a clear separation between the two cases. The values for the deeper events are consistently lower than those for the shallow ones. This difference, however, becomes negligible for f < 1 Hz, a result similar to that reported by Tsujiura (1978) for the Kanto district of Japan. The frequency dependence of Q~in the form of a power law (Q~—f”) for a number of areas is available in the literature; n is seen to vary from about 0.2 to 1.1. In this range, values at the lower end are associated with tectonically stable areas, such as the northeast (Pull, 1984) and central (Singh and Herrmann, 1983) USA. Values of n in the middle of the range are typical of tectonically active areas, such as Alaska (Steensma and Biswas, 1988), the Kanto district of Japan (Tsujiura, 1978), central Asia (Rautian and Khaltunn, 1978) and Hindu-Kush for focal depths > 100 km (Roecker et a!., 1982). The results in Fig. 3 correspond to n of about 0.6, which is close to the value obtained by Steensma and Biswas (1988). Values of n of 1.0 and 1.1 have been reported for Hindu-Kush for depths <100 km (Roecker et al., 1982), and for Friuli, Italy (Rovelli, 1982), respectively. The observed total energy normalized to a cornmon source as a function of r, shown in Fig. 4 for frequencies 6, 8, 10, 12, 14 and 16 Hz, was compared with the theoretical curves of total energy computed by using the formula given by Wu (1985) 4.rrr2(E(r))4.,~.r2[E(r)+E(r)J

-

-

I

1

1~

1

00

FREQUENCY (Hz) Fig. 3. Variations of mean as a function frequency for the earthquakes with hypocenters in the depth ranges of Z < 22 km (open triangle) and 63 < Z <133 km (hollow star). The bars show the spread of 1 S.D. of the mean value. The decay curves labeled 1, 2 and 3 in the upper right-hand corner of the figure refer to the results obtained by Singh and Herrmann (1983), Steensma and Biswas (1988) and Rovelli (1982), respectively.

1 Hz, the

(4)

where Ed(r) andE~(r) are the diffused and coherent energy density, respectively. As the explicit expressions for Ed(r) and E~(r) as a function of B0 (albedo) and ~e (extinction coefficient) have been given by Wu (1985), they are not included here (see also Mayeda et al., 1991). The albedo (.8~)indicates the relative importance of scattering loss, and is defined as B0

=

~~/(~ + ~)

(5)

where is the ~ isabsorption the scattering attenuation attenuation coefficient coefficient, and 3Ja

121

SCATFERING AND ANELASTIC ATITENUATION OF SEISMIC ENERGY

0

A 0 0

6.0Hz

0

~L

8.0 Hz

.0 0

Li

.~.

0

10.0 Hz.

12.0 Hz 14.0 Hz.

-

16.0 Hz

50

100

150

200

250

(km)

Fig. 4. Variations of the averaged normalized total S-wave energy observed as a function of hypocentral distance (r), where indicates average value for a given value of r. The bars represent 1 S.D. spread of the average value shown by the triangle.

31s

+

3le~

=

They are related to the scattering

and intrinsic k~ Q~by the following relations: ‘~‘~ ‘~ ~S “J /

— —

5

16a~ ‘

11S

Q

/

and

Q~’(f)

=

k~-q

(6b)

where k is wave number. For the computation of k, we used 3.5 km s~ for the S-wave velocity. Equation (4) was evaluated by systematically varying values of B 0 and ~1eFor in the 0.1—0.99 and 0.3—0.02, respectively. eachranges pair of values of B 0 and the sum of the mean squared difference between the observed and calculated total energy was obtained.toSelecting the values of 31e corresponding the mimmum sum for B0 and each frequency, we obtained estimates for Q~1 ( f) and Q~(f)from relations (6a) and (6b). The values of B 1and Q 1 ob0, Q~ tamed for different frequencies following the1T~above procedure are listed in Table 3. The results of this table show that the study area is characterized by high seismic albedo (B 0 0.90—0.95), i.e. scattering is dominant over absorption and the scattering loss expressed by sj, IS an order of magnitude

< >

1)

varies greater than the absorption loss, represented by withThe ~1a• frequency scattering fromextinction 20 km (f= length 16 Hz) to 23 km (f= 6 Hz). These results are similar to those obtamed by Mayeda et al. (1991) for southern Cali-

(~r

forma, in spite of the difference in focal depth distribution and tectonic setting between the two regions. Table 3 also lists the average values of Q~for the two focal depth ranges given in Table 2. First, 1 are different by an we find that Q~~’ and Qj

~,

~,

~5’

=

TABLE 3

—

. . . . (multiple), Q~ (single) and of scattering Q~ Values seismic attenuations albedo (B0), extinction coefficients (~hand and intrinsic attenuation (Q~)— for various frequencies f B 2) Q~ QT1 Q~ (10-2) ~ (1~J- (x103) (X103) (X103) (Hz) 0 ~ (km~) (km1) 6 0.95 4.32 0.23 4.02 0.21 1.89 8 0.95 4.32 0.23 3.00 0.16 1.55

fla)

10

0.95 4.75

0.25

2.64

0.14

1.33

12 14 16

0.90 4.50 0.90 5.00 0.90 5.00

0.50 0.56 0.56

2.09 1.99 1.74

0.22 0.22 0.19

1.29 1.16 1.13

122

T.J. McSWEENEY ET AL.

order of magnitude. This is again similar to the result obtained for southern California. Second, the scattering Q~ is closer to Q~’ than the absorption Q~’,but there is a significant difference: Q~1is about half of Q~’.This difference may be the result of the effect of multiple scattering as, for example, predicted by Gao et al. (1983). For a highly tectonically active area, such as central and south—central Alaska, multiple scattering could lead to longer coda than that predicted by single-scattering model, thus causing underestimation of ~ 1 However, under the existing limitation in our understanding of coda, it is interesting to note that the difference between Q~’ and Q~’ decreases with increasing frequency (Q~1 0.47 Q~1at 6 Hz and Q~1 0.65 Q~’at 16 Hz). =

=

Acknowledgements The authors are very grateful to Dr. H. Satö of the Geophysical Institute, Tohoku University, Japan, and Dr. R.S. Wu of the Institute of Geophysics, Beijing, People’s Republic of China, for helpful discussions on the results presented in this paper. We also thank an anonymous reviewer and Professor S. Roecker for review and comments on the manuscript. The work of T.J. McSweeney and N.N. Biswas was supported partly by the State of Alaska funds appropriated to the Geophysical Institute, University of Alaska, Fairbanks, K. Mayeda and K. Aki were partly supported for this work by Shell Foundation and U.S. Department of Energy Grant DE-FGO3-87ER13807, respectively.

References Aki, A. 1980. Attenuation of shear waves in the lithosphere for

frequencies from 0.5 to 25 Hz. Phys. Earth Planet. Inter., 21: 50—60.

Aki, K. and Chouet, B., 1975. Origin of coda waves: source, attenuation and scattering effects, J. Geophys. Res., 80: 3322—3342. Biswas, N.N. and Tytgat, G., 1988. Intraplate seismicity in Alaska, Seismol. Res. Lett., 59: 227—233. Biswas, N.N., Gedney, L. and Agnew, J., 1980. Seismicity of western Alaska. Bull. Seismol. Soc. Am., 70: 873—883. Biswas, N.N., Aki, K., Pulpan, H. and Tytgat, G., 1986. Characteristics of regional stresses in Alaska and neighboring areas. Geophys. Res. Lett., 13: 177—180. Gao, L.S., Biswas, N.N., Lee, L.C. and Aki, K., 1983. Effects of multiple scattering on coda waves in three dimensional medium. Pure Appl. Geophys. 121: 3—15. Mayeda, K., Su, F. and Aki, K., 1991. Seismic albedo from the total seismic energy dependence on hypocentral distance in southern California. Phys. Earth Planet. Inter., 67: 104—114. Page, R.A., Biswas, N.N., Lahr, J.C. and Pulpan, H., 1991. Seismicity of continental Alaska. In: Decades of North American Geology, in press. Pulli, J.J., 1984. Attenuation of coda waves in New England. Bull. Seismol. Soc. Am., 74: 1149—1166. Rautian, T.G. and Khalturin, V.!., 1978. The use of coda for determination of the earthquake source spectrum. Bull. Seismol. Soc. Am., 68: 923—948. Roecker, S.W., Tucker, B., King, J. and Hatzfield, D., 1982. Estimates of Q in central Asia as a function of frequency and depth using coda of locally recorded earthquakes. Bull. Seismol. Soc. Am., 72: 129—149. Rovelli, A., 1982. On the frequency dependence of Q in Friuli from short period digital records. Bull. Seismol. Soc. Am., 72: 2369—2372. Singh, 5K. and Herrmann, R.B., 1983. Regionalizatjon of crustal coda Q in continental United States. J. Geophys. Res., 88: 527—538. Stearns, S.D., 1975. Digital Signal Analysis. Hayden, Rochelle Park, NJ. Steensma, G.J. and Biswas, N.N., 1988. Frequency dependent characteristics of coda wave quality factor in central and southcentral Alaska. Pageoph, 128: 295—307. Tsujiura, M., 1978. Spectral analysis of coda waves from local earthquakes. Bull. Earthquake Res. Inst., 53: 1—48. Wu, R.S., 1985. Multiple scattering and energy transfer of seismic waves. Separation of scattering effect from intrinsic attenuation I. Theoretical modeling. Geophys. J., 82: 57—80. Wu, R.S. and Aki, K., 1988. Multiple scattering and energy transfer of seismic waves—separation of scattering effect from intrinsic attenuation II, Application of the theory to Hindu-Kush region. Pageoph, 128: 48—80.