Craig A. Schultz

Effect of three-dimensional topography on seismic motion

We present a semianalytical, seminumerical method to calculate the diffraction of elastic waves by an irregular topography of arbitrary shape. The method is a straightforward extension to three dimensions of the approach originally developed to study the diffraction of SH waves [Bouchon, 1985] and P-SV waves [Gaffet and Bouchon, 1989] by two-dimensional topographies. It relies on a boundary integral equation scheme formulated in the frequency domain where the Green functions are evaluated by the discrete wavenumber method. The principle of the method is simple. The diffracted wave field is represented as the integral over the topographic surface of an unknown source density function times the medium Green functions. The Green functions are expressed as integrals over the horizontal wavenumbers. The introduction of a spatial periodicity of thc topography combined with the discretization of the surface at equal intervals results in a discretization of the wavenumber integrals and in a periodicity in the horizontal wavenumber space. As a result, the Green functions are expressed as finite sums of analytical terms. The writing of the boundary conditions of free stress at the surface yields a linear system of equations where the unknowns are the source density functions representing the diffracted wave field. Finally, this system is solved iteratively using the conjugate gradient approach. We use this method to investigate the effect of a hill on the ground motion produced during an earthquake. The hill considered is 120 m high and has an elliptical base and ratios of height-to-half-width of 0.2 and 0.4 along its major and minor axes. The results obtained show that amplification occurs at and near the top of the hill over a broad range of frequencies. For incident shear waves polarized along the short dimension of the hill the amplification at the top reaches 100% around 10 Hz and stays above 50% for frequencies between 1.5 Hz and 20 Hz. For incident shear waves polarized along the direction of elongation of the topography, the maximum amplification occurs between 2 Hz and 5 Hz with values ranging from 50% to 75%. The results also show that the geometry of the topography exerts a very strong directivity on the wave field diffracted away from the hill and that at some distance from the hill this diffracted wave field consists mostly of Rayleigh waves.

The western margin of the Rio Grande Rift in northern New Mexico: An aborted boundary?

The northwestern margin of the Espanola basin, part of the Rio Grande rift in northern New Mexico, is characterized by a zone >17 km wide of oblique-slip faults that offset upper Paleozoic and Mesozoic strata of the eastern Colorado Plateau from Eocene and younger sedimentary rocks of the rift. Along this margin, a reasonably complete section of pre- and synrift Tertiary sediments is exposed. Combined interpretations of seismic reflection, seismic refraction, gravity, and geologic data acquired along a profile perpendicular to this boundary define the geometry of faulting, possible rotation of sedimentary units, and stratigraphy of rift fill. Vertical separation on the westernmost major fault, assumed to be the bounding fault between the rift and the Colorado Plateau, is Although Tertiary units are progressively faulted downward toward the axis of the rift, depth to inferred Precambrian crystalline rocks becomes shallower and the stratigraphic thickness of the intervening Paleozoic and Mesozoic units decreases toward the axis. We interpret pinching out of these units toward the east as erosional thinning on the western flanks of the Laramide-age Sangre de Cristo/Brazos geanticline, which underlay much of the present rift basin. Imprecise age constraints suggest that faulting of the rift margin began 10-7 Ma, but was not active after 7 Ma. Extension was apparently transferred to the Embudo fault zone, which remained active until at least 2.5 Ma and possibly into Quaternary time. The Embudo transfer zone effectively decoupled the Abiquiu embayment from the main Espanola basin. Thus the boundary at Abiquiu preserves an early stage in the formation of the rift boundary. The shift in activity may have resulted from a change in regional stress field, or from increasing magnitude of strain, or both. The change in locus of extension reflects a narrowing of rift basins through time and an integration of main bounding structures between adjacent basins. Although we are uncertain whether the Abiquiu region, which uniquely preserves an early stage of deformation, is representative of other areas of continental extension, our results indicate that the initial formation of rift basins may occur as high-angle, planar normal faults distributed over a broad zone. No evidence from seismic data or from rotation of beds exists to indicate that faults become listric with depth, which is compatible with the small amount of extension (3.5%) inferred at this boundary.

Experimental study of enhanced backscattering from a highly irregular, acoustic–elastic interface

In this study, experimental and numerical statistical models are developed for the scattering of an acoustic P wave which is incident on a highly irregular, random acoustic–elastic interface to determine the general nature of reflected energy. It is then elucidated whether or not enhanced backscattering, already identified numerically for acoustic (SH) and fully elastic media (P‐SV), occurs. Experimentally, a glass etching process using photoresist templates with Gaussian statistics allowed for the generation of characterized interface irregularities. Experiments were performed on a glass surface with an ‘‘rms’’ slope of 30 deg, for the case of an incident wavelength with a size on the same order as the interface irregularities. The numerical models predict an enhancement of energy diffracted back toward the source, and results obtained in our ultrasonic laboratory strongly support the presence of this retroreflective energy. In terms of general scattering, it is found that, at smaller incident angles (re...