Teleseismic long-period P waves recorded at the World-Wide Standard Seismograph Network station LON (Longmire, Washington) are shown to exhibit strong anomalous particle motion not attributable to instrument miscalibration or malfunction. In particular, a large and azimuthally smoothly varying tangential component is observed after vector rotation of horizontal P waves into the ray direction and after application of a deconvolution technique which equalizes effective source time functions and removes the instrument response. These tangential waves attain amplitudes comparable to the radial component and demonstrate wave form antisymmetry about a NNE azimuth. A model which contains a single high-contrast interface dipping toward the NNE at a depth of 15–20 km can explain most of the characteristics of the long-period P wave data, provided dips are greater than about 10° and only the interference of P and Ps generated at the interface is considered. The model breaks down for later arrivals which are presumably multiples or scattered waves. Examination of long-period S waves from several deep teleseisms shows a prominent Sp arrival 18 s before S. The timing of this phase conversion suggests an interface at about 145-km depth, and its sense of polarity suggests that the velocity contrast is from higher to lower velocities as depth decreases. This interface may correspond to the bottom of the upper mantle low-velocity zone in the area.

Structure under Mount Rainier, Washington, inferred from teleseismic body waves

We have developed a method that inverts seismic body waves to determine the mechanism and rupture pattern of earthquakes. The rupture pattern is represented as a sequence of subevents distributed on the fault plane. This method is an extension of our earlier method in which the subevent mechanisms were fixed. In the new method, the subevent mechanisms are determined from the data and are allowed to vary during the sequence. When subevent mechanisms are allowed to vary, however, the inversion often becomes unstable because of the complex trade-offs between the mechanism, the timing, and the location of the subevents. Many different subevent sequences can explain the same data equally well, and it is important to determine the range of allowable solutions. Some constraints must be imposed on the solution to stabilize the inversion. We have developed a procedure to explore the range of allowable solutions and appropriate constraints. In this procedure, a network of grid points is constructed on the τ - I plane, where τ and I are, respectively, the onset time and the distance from the epicenter of a subevent; the best-fit subevent is determined at all grid points. Then the correlation is computed between the synthetic waveform for each subevent and the observed waveform. The correlation as a function of τ and I and the best-fit mechanisms computed at each τ - I grid point depict the character of allowable solutions and facilitate a decision on the appropriate constraints to be imposed on the solution. The method is illustrated using the data for the 1976 Guatemala earthquake.

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Inversion of complex body waves

Measurements of ground motion generated by nuclear explosions in Nevada were made for 37 locations near San Francisco Bay, California. The results were compared with the San Francisco 1906 earthquake intensities and the strong-motion recordings of the San Francisco earthquake of March 22, 1957. The recordings show marked amplitude variations which are related consistently to the geologic setting of the recording site. For sites underlain by a layer of younger bay mud or artificial fill, maximum horizontal ground velocities generally increased with thickness of the layer and were as much as ten times greater than those recorded on nearby bedrock. The maximum vertical velocities for these sites were between 1 and 3.5 times greater. Spectral amplification curves clearly define a “dominant ground period” of about 1 second for sites underlain by younger bay mud. For sites underlain by older, more consolidated sediments, no clearly defined “dominant ground period” was found. Maximum ground velocities for the older bay sediment sites were about twice those recorded on bedrock. Consistent correlations of the results from the nuclear recordings with the 1906 earthquake intensities and the spectral amplification curves for the 1957 earthquake suggest that areas of high amplification determined from small ground motions may also be areas of high intensity in future earthquakes.

Effects of local geology on ground motion near San Francisco Bay

Seismic shear-wave velocity as a function of depth for generic rock sites has been estimated from borehole data and studies of crustal velocities, and these velocities have been used to compute frequency-dependent amplifications for zero attenuation for use in simulations of strong ground motion. We define a genetic rock site as one whose velocity at shallow depths equals the average of those from the rock sites sampled by the borehole data. Most of the boreholes are in populated areas; for that reason, the rock sites sampled are of particular engineering significance. We consider two genetic rock sites: rock, corresponding to the bulk of the borehole data, and very hard rock, such as is found in glaciated regions in large areas of eastern North America or in portions of western North America. The amplifications on rock sites can be in excess of 3.5 at high frequencies, in contrast to the amplifications of less than 1.2 on very hard rock sites. The consideration of unattenuated amplification alone is computationally convenient, but what matters for ground-motion estimation is the combined effect of amplification and attenuation. For reasonable values of the attenuation parameter K 0, the combined effect of attenuation and amplification for rock sites peaks between about 2 and 5 Hz with a maximum level of less than 1.8. The combined effect is about a factor of 1.5 at 1 Hz and is less than unity for frequencies in the range of 10 to 20 Hz (depending on t%). Using these amplifications, we find provisional values of about Ao- = 70 bars and K 0 = 0.035 sec for rock sites in western North America by fitting our empirically determined response spectra for an M 6.5 event to simulated values. The borehole data yield shear velocities 033o) of 618 and 306 rrdsec for "rock" and "soil" sites, respectively, when averaged over the upper 30 m. From this, we recommend that V30 equals 620 and 310 m/sec for applications requiring the average velocity for rock and soil sites in western North America. By combining the amplifications for rock sites and the site factors obtained from our analysis of strong-motion data, we derive amplifications for sites with 17'3o = 520 m/sec (NEHRP class C, corresponding to a mix of rock and soil sites) and V3o = 310 and 255 m/sec (average soil and NEHRP class D sites, respectively). For the average soil site, the combined effect of amplification and attenuation exceeds a factor of 2.0 for frequencies between 0.4 and about 4 Hz, with a peak site effect of 2.4; the peak of the NEHRP class D site effect is 2.7.

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Site amplifications for generic rock sites

Synthetic seismograms produced by the finite difference method are used to study the scattering of elastic and acoustic waves in two-dimensional media with random spatial variations in seismic velocity. The results of this study provide important insights about the propagation of short-period ( 5), the self-similar medium is characterized by a scattering Q that is constant with frequency, whereas theory predicts that the apparent Q in an exponential medium is proportional to frequency. These alternative models of crustal heterogeneity can thus be tested by improved measurements of the frequency dependence of crustal Q at frequencies greater than about 1 Hz, assuming that scattering is responsible for most of the attenuation at these frequencies. Measurements of the time decay of the synthetic coda waves clearly show that the single scattering model of coda decay is not appropriate in the presence of moderate amounts of scattering attenuation (scattering Q ≤ 200). In these cases, Q values derived from the coda decay rate using the single scattering theory do not correspond to the transmission Q of the medium. The cross correlation of synthetic waveforms observed for an array of receivers along the free surface is observed to be dependent on the correlation distance of the medium. The self-similar random medium proposed here for the crust produces waveform variations at high frequencies (15–30 Hz) similar to those reported for actual small-scale seismic arrays with apertures of hundreds of meters.

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Finite difference simulations of seismic scattering: Implications for the propagation of short‐period seismic waves in the crust and models of crustal heterogeneity

An equation has been derived for the amplitude of the free surface displacement due to plane SH waves incident at any angle at the base of a layered crust Numerical computations have been carried through for the case of a single-layered model of the continental crust At any given angle of incidence the surface amplitude goes through a series of minima and maxima at periods which, in the single layered case, are harmonically related At nearly grazing angles of incidence the surface amplitude is relatively small except at periods in the neighborhood of the cutoff periods of the second- and higher-order Love-wave modes

The results throw some doubt on the ‘whispering gallery’ effect as an explanation of the mode of propagation of long-period (20 to 30 sec) S waves at Sn velocity

Applied to the case of an alluvial layer over a hard-rock basement, the theory appears to give an adequate explanation of the abnormally large amplitudes that occur on unconsolidated formations in the epicentral region of earthquakes

Crustal Reflection of Plane SH Waves

Expressions in terms of layer matrices have been derived for the motion of the free surface when plane harmonic P or SV waves are incident at any given angle at the base of a horizontally layered crust. A computer program has been written to calculate normalized surface displacements as functions of horizontal phase velocity (or angle of incidence) and wave period. Numerical values have been obtained for the same single-layered model of the continental crust for which the corresponding calculations for SH waves have been presented previously. The surface motion pattern is similar to that of the SH case, but it is somewhat more complex owing to PS and SP conversions at the layer boundaries. Variations in amplitude and phase of the surface displacements are particularly large and erratic in the case of SV waves that are incident at angles such that α1 αn, the crustal transfer functions for incident SH and SV waves are sufficiently similar for conventional methods to be used in determining the angle of polarization with moderate accuracy.

Crustal reflection of plane P and SV waves

According to the theory of Latter, Martinelli, and Teller the amplitude of the distant seismic signal from a completely contained underground explosion is determined by the permanent displacement produced in the neighborhood of the source. A static-equilibrium theory of this displacement is developed. A Coulomb-Mohr type of yield condition is used to determine the stresses in the near zone where the stresses are beyond the elastic limit. If the internal friction parameter that occurs in the Coulomb-Mohr yield condition is treated as a phenomenological constant, to be determined by the seismic data, it is possible to obtain reasonably good agreement with the relative amplitudes of the seismic signals observed in the Project Cowboy series of chemical explosions in cavities of various sizes in salt. The indicated value of the friction parameter is, however, appreciably less than the values usually observed in compression tests on unconsolidated materials. The theory is also consistent with the observed size of the cavity produced in tuff by the underground nuclear explosion Rainier, but an even smaller value of the friction parameter must be assumed in this case.

A static theory of the seismic coupling of a contained underground explosion

An equation has been derived for the amplitude of the free surface displacement due to plane SH waves incident at any angle at the base of a layered crust. Numerical computations have been carried through for the case of a single-layered model of the continental crust. At any given angle of incidence the surface amplitude goes through a series of minima and maxima at periods which, in the single layered case, are harmonically related. At nearly grazing angles of incidence the surface amplitude is relatively small except at periods in the neighborhood of the cutoff periods of the second- and higher-order Love-wave modes.

The results throw some doubt on the ‘whispering gallery’ effect as an explanation of the mode of propagation of long-period (20 to 30 sec) S waves at Sn velocity.

Applied to the case of an alluvial layer over a hard-rock basement, the theory appears to give an adequate explanation of the abnormally large amplitudes that occur on unconsolidated formations in the epicentral region of earthquakes.

Norman A. Haskell

Papers

Crustal Reflection of Plane SH Waves

Crustal reflection of plane P and SV waves

A static theory of the seismic coupling of a contained underground explosion

Crustal Reflection of Plane SH Waves