Comparison of near-surface properties derived from non-linear inversion of refraction amplitudes versus the refraction convolution section

Abstract

The amplitude of a critically-refracted arrival is proportional to the strength of the shot and inversely dependent on the offset at which the refraction energy is measured. The constant of proportionality is the head-wave coefficient. This term is itself a function of the physical properties of the layers through which the wave propagates. With knowledge of the sub-weathering layer velocity, it is theoretically possible to derive the surface-layer velocity from the head-wave coefficient. This can be of use when the surface-layer velocity is unknown, e.g., surveys in which a surface source is used. Improved understanding of the surface-layer velocity has practical value in statics solutions and geotechnical engineering. In order to derive near-surface properties from the head-wave coefficient, the effects of the shot and offset must be removed. One published method of doing this is to calculate the amplitude product of forward and reverse shot records which have been convolved together (RCS method). The resulting amplitude product is proportional to the square of the head-wave coefficient. An alternative approach is to formulate the problem as a surface-consistent, non-linear inversion scheme. The Levenberg-Marquardt algorithm is used to invert observed amplitude into constituent shot, receiver and offset terms. The receiver term is assumed to be representative of the head-wave coefficient. This paper applies this inversion technique to a Vibroseis dataset acquired by Geoscience Australia near Wirrinya in NSW in 1999 which has been previously analysed using the RCS method. Regularisation of the inverse problem is also discussed in the context of the speed of the problem converging to a stable solution and potential effects on the solution itself.