Spatial Gradients, Wave Gradiometry, and Large N Arrays

Abstract:

Accuracy of spatial gradients derived from wave field data recorded on a “geodetic” seismic array depends on the spatial distribution of array elements, signal-to-ambient-noise ratio, site amplitude statics, and instrument calibration. Application of the wave gradients in wave gradiometry additionally requires an accurate estimate of the wave field at the test location that is, in turn, subject to the same sources of noise, compounding inaccuracy in estimates of wave apparent velocity, amplitude changes, and direction. The spatial distribution of array elements can be controlled for a particular array design to yield potentially accurate spatial gradients. However, dense, large N arrays naturally alleviate problems with site statics, instrument calibration, and incoherent noise when the inverse problem is posed such that wave gradients and the wave field at the test location become the unknowns; both the wave gradients and test wave field become averages of the data over the array, reducing the effect of noise. A Taylor’s series expansion of the wave field around any test point within the array becomes possible, even at those places that do not contain an array element. The resulting wave gradiometry parameters improve proportional to the number of array elements used. This method is used to examine the wave field using data from a 180 m x 300 m dense array associated with a 3D controlled source seismic experiment in southeastern Ohio demonstrating the complexity of the wavefield due to scattering in near-surface structure. The method is also used to analyze teleseismic P waves from the Long Beach, California, NodalSeismic array.