Nonlinear elastic waveform inversion of land seismic reflection data

Abstract

Data from 53 shot records collected in a conventional, land, seismic reflection survey are inverted to obtain subsurface maps of short‐wavelength variations in elastic parameters (impedance). The inversion method employs a robust, nonlinear, iterative, gradient algorithm which inverts waveform data; thus there is no picking of travel times or amplitudes. The algorithm is also computationnally expensive as it relies heavily upon elastic finite difference modeling. In addition, because a gradient search is employed to minimize the misfit between observed and modeled data, we attempt to solve only the weakly nonlinear problem associated with the short wavelenghts of imedance (information on the short‐wavelengths of impedance is mainly derived from amplitude variations of the data). Resolving the long wavelengths of velocity (background) is thought to be a highly nonlinear problem, at least for waveform inversion, and is not attempted herein. For the inversion of this data set, long wavelenghts have been derived from well logs located along the seismic reflection profile. Although the data set is dominated by unconverted P wave arrivals, we obtain maps of the short wavelenghts of both P impedance and S impedance. Three well logs in the survey area confirm the validity of the P impedance map; however, no S velocity well log are available from this area. There are channel sands of economic interest which have a thickness of approximately 10 m in one well and are very thin or absent in the other two wells. The 10 m occurrence of channel sands is quite visible in both impedance maps. We note that because inversion in three dimensions of a realistically sized data set is simply not possible on present‐day computers, all modeling was performed in two dimensions, and a rather crude conversion from spherical to cylindrical energy spreading was applied to the original field data before inversion. Other seismic reflection data in the survey area suggest that there is little lateral variation in the subsurface except for the channel sands; thus we feel that a two‐dimensional inversion with energy compensation is justified.