Spatial gradient analysis for linear seismic arrays
I incorporate the spatial gradient of the wave field recorded from one-dimensional arrays into a processing method that yields the horizontal-wave slowness and the change of geometrical spreading with distance. In general, the model for seismic-wave propagation is enough to be appropriate for body and surface waves propagating from nearby seismic sources but can be simplified into a plane-wave model. Although computation of the spatial gradient requires that array elements be closer than 10% of the horizontal wavelength, seismic-array apertures, in the usual sense, may extend over many horizontal wavelengths and illuminate changes within the wave field. Array images of horizontal slowness and the relative geometrical-spreading changes of seismic waves are derived using filter theory and used to interpret observed array wave fields. Errors in computing finite-difference spatial gradients from array nodes are explicitly considered to avoid spatial aliasing in the estimates. I apply the method to interpret waves in strong ground motion and small-scale refraction data sets. Use of the wave spatial gradient accentuates spatial differences in the wave field that can be theoretically exploited in fine-scale tomographic studies of structure and is complementary to frequency/wavenumber or beamforming array-processing techniques.
Bulletin of the Seismological Society of America
Langston, C. (2007). Spatial gradient analysis for linear seismic arrays. Bulletin of the Seismological Society of America, 97 (1 B), 265-280. https://doi.org/10.1785/0120060100