Abstract
Abstract We expand the theoretical development of seismic‐wave gradiometry to 3D using the polarized wavefield. First, we develop a map that relates the Cartesian spatial derivatives to the spatial derivatives in spherical coordinates. We then develop a set of partial differential equations that relate the spherical derivatives of the observed wavefield to the body‐wave radiation patterns. Because the spherical derivatives of the wavefield depend on the direction of wave propagation, we also develop relationships to find the propagation direction using simple ratios of the Cartesian‐based wave derivatives. Finally, we test the robustness of estimating the wave‐propagation direction, and its sensitivity to noise.
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