Seismic Moment from Long-period Surface waves

Part I: Source Analysis of Large Earthquakes in Mexico

Chapter 3 The Rupture of the Michoacan Gap: 1981-1986

5. Seismic Moment from Long-period Surface waves

The April 80, 1986 Aftershock

Long-period P-waves of the aftershock of April 30, 1986 from 15 WWSSN sta- tions are shown in Figure 3.6. The synthetic seismograms are calculated for a point source 21 km deep and source time duration of 10 s. First motion data constrain only one of the nodal planes as is common for most large Mexican subduction events. The second fault plane was resolved from waveform modeling. The fault parameters deter-

mined are 8=280°, 6=12°, 'A=70°. The seismic moment is given next to the station code; values within parentheses are obtained from diffracted P-arrivals that are not included to determine the average seismic moment that is 2.0X 10²⁶ dyne em. This value is consistent with that obtained from long-period centroid moment tensor inver- sion 3.1 ^X 10²⁶ dyne em (Dziewonski and Woodhouse, 1983).

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auxiliary plane fixed at the orientation determined from the P-wave first motion solu- tion (c5a=81°, 8a=127°). A data set of 42 Rayleigh-wave phases with a good azimuthal coverage gave a solution with Aa=91.9° and Mo=l.70X 10²⁸dyne-cm with an assumed source depth of 16 km. The fault plane parameters are then 8=9.2°, 8=295°, and >-.=78°. This is very close to the body-wave focal mechanism, with a difference of only 7° in fault strike and 6° in slip angle. Figure 3.7 shows the fit between the

Table 3.2: Stations used in the Surface-wave Inversion

Station Distance Azimuth Sept. 19, 1985 Sept. 21, 1985

(deg) (deg)

ALE Alert, Canada 66.1 5.3 R3,R4 R2,R3

RSON+ Red Lake, Canada 333 10.2 R2,R3,G2,G3

ESK Eskdalemuir, Scotland 80.3 34.9 R2,R3 R2,R3

RSNY+ Adirondack, New York 35.1 35.6 R2,R3

scp· State College, Pennsylvania 30.8 38.1 R2,R3

HAL Halifax, Canada 41.7 42.3 R2,R3 R2,R3

SJG San Juan, Pto. Rico 34.5 84.4 R2,R3 R2,R3

SUR Sutherland, RSA 127.4 117.1 R3,R4 R2,R3

BDF Brasilia, Brasil 63.4 118.5 R2,R3 R2,R3

NNA Nana, Peru 393 138.0 R2,R3 R2,R3

RAR Rarotonga, Cook Is. 68 5 237.6 R3,R4 R2,R3

TWO Adelaide, Australia 123.7 239.7 R3,R4 R2,R3

HON" Honolulu, Hawaii 49 8 280.3 R2,R3,G2,G3

KIP Kipapa, Hawaii 52.1 283.2 R2,R3 R2,R3

GUA Guam, Mariana Is. 106.4 290.5 R2,R3 R2,R3

ERM Erimo, Japan 94.8 317.0 R2,R3 R2,R3

BJT Bejin, China 111.7 328.9 R3,R4 R2,R3

coL· College, Alaska 55.5 3384 R2,R3,G2,G3

ANMo· Alburquerque, New Mextco 17.0 348 8 R2,R3 RSNT+ Yellowknife, Canada 45.0 352.1 R2,R3,G2,G3 RSSD+ Black Hills, S.Dakota 25.8 357.4 R2,R3,G2,G3

• GDSN (Global Digital Seismic Network)

IDA (International Deployment of Accelerographs) + RSTN (Regional Seismic Test Network)

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Figure 3.7: Observed phase (triangles) and amplitude (circles) spectral values as a function of azimuth of Rayleigh wave data used in the surface wave inversion from GDSN, IDA and RSTN stations, compared with the theoretical pattern for the be t

fitting solution for the September 19, 1985 Michoacan earthquake. Spectral \'alues are for a period T

=

256 s.

observed Rayleigh-wave radiation pattern and that calculated for this solution. When 10 Love-wave phases were included, the solution was virtually identical. Due to the large size of the earthquake, the fault finiteness and finite rise time of the source dislocation function may introduce a source phase delay. Following Kanamori and Given (1981), this effect can be included, assuming the rate of moment release to be constant with time, by introducing a source process time r. We find that the errors in the inversion are minimized with a source process time r=100s for a period of 256 s. A simultaneous inversion of long-period surface waves at different periods (150 - 300 s) gives r=80s for the Michoacan earthquake (Zhang and Kanamori, 1987).

For the aftershock, we used 26 Rayleigh-wave phases from the IDA network, again holding the auxiliary plane fixed as determined from the main shock first- motion data. The inversion gives a fault orientation of 8=9.5°, 8=289°, A=73°, essentially the same as the mainshock, with a seismic moment of 4.7 x 10²⁷ dyne em, 28 % that of the mainshock, and a source process time r=60s. Figure 3.8 shows the observed and calculated Rayleigh-wave radiation pattern for the aftershock.

Because the auxiliary plane is tightly constrained to have a steep dip from the first-motion data, the fault plane given by the inversion will have a shallow dip for any mechanism that is predominantly thrust. By relaxing this constraint, the inver- sion for the long-period source might return a fault plane orientation with a slightly different dip angle that will sensibly modify the moment estimate. For shallow thrust events, the seismic moment determined from the surface-wave inversion, Me,, depends on the dip angle 8 as Me,= Monm/ sin 28, where M₀ntn is the minimum seismic moment (Kanamori and Given, 1982). Thus, for a dip of 15° instead of 9° the moment is smaller by about a factor of 1.6. For a mechanism with a maximum fault plane dip

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Figure 3.8: Observed phase (triangles) and amplitude (circles) spectral values as a function of azimuth of Rayleigh wave data from IDA stations used in the surface wave inversion, compared with the theoretical pattern for the best fitting solution for the large September 21 aftershock. Spectral values are for a period T = 256 s.

of 15° and a mm1mum of 9°, for the mainshock the moment ranges from 1.05 to 1.70X 10²⁸dyne-cm or Mw=7.9-8.1, respectively. Locations of aftershocks from local networks define a dip of approximately 12° to 14° (Stolte et al., 1986; UNAM Seismol- ogy Group, 1986), indicating that the lower end of the range is more appropriate. For

the aftershock, the moment range is 2.9 to 4.7X10²⁷dyne-cm, or Mw=7.6-7.7.

Results of other studies of the long-period source of the 1985 Michoacan earth- quake are summarized in Table 3.3 and compare favorably with those presented here.

Details of the solutions vary due to differences in the data sets, techniques, con- straints on the solutions or Earth models used. In particular, different approaches can be taken to provide control on the poorly determined components of the moment ten- sor. All the studies found an overall thrust geometry (rake angles deviating from 2° to 17° from pure thrust) on a fault plane striking parallel to the Middle-America trench (N289°E - N302°E). Shallow dip angles ( <20°) were determined or inferred in all the studies; for example, Priestley and Masters {1986) fixed the dip at 15°, while Riedesel et al. {1986) left the dip unconstrained and resolved it to be 19±15°. In view of the dependence of the seismic moment value on fault-plane dip angle, we correct the values in Table 3.3 to correspond to a dip angle of 15° for comparison. Values of seismic moment are then very consistent, varying from 1.03-1.32x10^28, with an aver- age value of 1.17x10²⁸ dyne em or Mw=8.0.

Riedesel et al. (1986) determine the characteristic time Tc for the September earthquakes from the scalar-moment algorithm of Silver and Jordan (1983) and obtain rc=49±7s for the main event and 30±11s for the aftershock. This compares favorably with the source process times r resolved above because r=1.73rc (Silver and Jordan, 1983).

6 <P Mo Moat 6=15°

x 10²⁸dyne-cm X 10²⁸dyne-cm

This Study go _{295° 7f!!' 1.70 1 05}

Ekstrom and Dziewonsk1 ( 1986) 18° 302° 107° 1.10 1 29

Priestley and Masters ( 1986) 15° (fixed) 298° Sf!!' 1.03 1.03

Riedesel et al. (1986) 19±15° 289° 76° 1.07 1.32