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1 Center for Earthquake Research
and Information
University of Memphis
3876 Central Ave., Suite 1
Memphis, Tennessee 38152-3050
The spatial displacement gradient of a seismic wave is related to
displacement and velocity through two spatial coefficients for any one
dimension. One coefficient gives the relative change of wave geometrical
spreading with distance and the other gives the horizontal slowness and its
change with distance. The essential feature of spatial gradient analysis is a
time-domain relation between three seismograms that yields information on the
amplitude and phase behavior of a seismic wave. Filter theory is used to find
these coefficients for data from 2D areal arrays of seismometers, termed
gradiometers. A finite-difference star is used to compute the displacement
gradient for irregularly shaped gradiometers, and a relation for the
frequency-dependent error in the displacement gradient is obtained and applied
to ensure accurate estimates. This kind of array analysis is useful for
gradiometers at any distance from a source and yields a variety of time-domain
and frequency-domain views of wave-amplitude changes and horizontal phase
velocity estimates across the gradiometer. For example, time-dependent
horizontal slowness and wave-azimuth plots are natural results of the analysis.
These time-domain maps may be used in conjunction with
time–distance and
horizontal
slowness–distance
models to locate seismic sources or may be used directly to study earth
structure. These methods are demonstrated by using data from a small-aperture
(
40 m) seismic
gradiometer.
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