Reconstruction of the parameters of plane‐layered elastic media by generalized ray theory

This paper seeks to reconstruct the parameters of elastic layered media such as P‐wave velocity, S‐wave velocity, density and thickness from the multioffset seismic reflection data. Since the data are highly non‐linear to the low‐wavenumber components, the non‐linear waveform inversion method, with the aid of generalized ray theory, is proposed to solve this problem in space–time domain. As opposed to the layer‐stripping method, the present method attempts to invert all layer parameters simultaneously, thus reducing the cumulative errors resulting from the upper layers. The parameters are inverted by minimizing the weighted square error between the observed data and the calculated data of the layered model, the optimization of which is based on the quasi‐Newton method. In synthetic tests, we find that the inverted results are good when the variation of parameters between layers is not too large. The modified method for large variation of parameters is first to fix those of deeper layers and neglect the signals reflected from them, then recover some other parameters simultaneously until those of upper layers attain a stable value, and finally, invert all parameters simultaneously. The results so obtained show a significant improvement. This method was tested to be stable in the presence of noise in seismograms.