Volumetric wavefield recording and wave equation inversion for near-surface material properties

"Volumetric recording" of the seismic wavefield implies that the local receiver group or array approximately enclose a volume of the earth. We show how volumetric recording can be used to measure several spatial derivatives of the wavefield. By making use of the full elastic wave equation, the free surface condition on elastic wavefields, and derivative centering techniques analagous to Lax-Wendroff corrections used in synthetic finite-difference modeling, these derivative estimates can be inverted for P- and S-velocities in the near surface directly beneath the receiver group. The quantities estimated are the effective velocities of the P- and S-components experienced by the wavefield at any point in time. Hence, the velocity estimates may vary with both wave type and wavelength. The estimates may be useful to aid statics estimation and are exactly the effective velocities required for separation of the wavefield into P- and S- and up- and down-going components.