Exact inversion of plane‐layered isotropic and anisotropic elastic media by the state‐space approach

Time‐domain state‐space inversion methods for non‐dispersive layered media have shown that acoustic impedance as a function of traveltime can be determined from a normally incident, plane, pressure‐wave source. The state‐space method is used here to determine the density and acoustic velocity separately as functions of depth by simultaneously inverting surface data measured at two precritical angles of incidence. The acoustic state‐space method is also applied to isotropic elastic media with normally incident P-waves and obliquely incident SH-wave sources, whereby the density, shear velocity, and compressional velocity are determined as functions of depth. The same parameters are recovered by modifying Shiva and Mendel's (1983) method for a single, obliquely incident P-wave source to accommodate a single SV-wave source, two P-wave sources, or data obtained from a previous (scalar) SH-wave inversion. Using data from multiple experiments eliminates nonuniqueness in the inversion procedure. We have extended ...