The vertical component P-wave receiver function is an important source of data in studies of the crust/mantle transfer function for determining Earth structure under isolated receivers or under receiver arrays. This waveform illuminates a missing aspect of the wave propagation in receiver function studies that employ only the horizontal components of motion, and yields complementary constraints on near-receiver heterogeneity and P-wave propagation. The vertical component P-wave receiver function is formed using an array estimate for the effective teleseismic source function that is then deconvolved from all the vertical and horizontal components of ground motion at each station in the array. One-dimensional, three-dimensional, and stochastic wave-propagation models are used to test the robustness of the technique. Breakdown of single-station receiver function deconvolution occurs because of high levels of noncorrelated noise between the ground-motion components. Receiver functions for stations of the southern California TERRAscope array are investigated using the array technique. Vertical receiver functions for stations in the Los Angeles Basin and Long Valley Caldera show high-amplitude secondary arrivals that cannot be explained by simple 1D structures but probably reflect wave propagation in 3D basin structures. Three-component receiver functions from the station at Mammoth Lakes, California, show pathological behavior where the horizontal components of ground motion exceed the amplitude of the vertical components, suggesting extreme topographic and 3D velocity heterogeneity. Use of all three components of the receiver function in modern passive array experiments is encouraged to reduce the problems of nonuniqueness in determining Earth models.

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