Modified surface boundary conditions for elastic waveform inversion of low-frequency wide-angle active land seismic data

Abstract

In presence of large wavelength-scale shear-velocity variations in the Earth, acoustic waveform inversion may not be sufficient even when inverting long-offset data to retrieve the long-to-intermediate wavelengths of the compressional velocity. An acoustic modelling does not always correctly represent the compressional/primary waves when tuning effects and energy conversion between compressional and shear waves occur. Elastic waveform inversion with land data is challenging not only because of its computational cost but also due to the presence of the very energetic ground roll. To avoid inverting the ground roll and focus the inversion on the body waves recorded at long offsets, we propose to modify the surface boundary conditions in the elastic modelling. Zeroing the normal derivatives of the shear stress components parallel to the surface instead of the shear stress components themselves as with the free-surface boundary conditions leads to an elastic modelling that does not generate ground roll. These modified elastic surface conditions allow us to invert the seismic data that have been pre-processed to remove the ground roll as we do in acoustic waveform inversion. In this way, the inversion can focus on the retrieval of the long-to-intermediate wavelengths of the compressional velocity and we can apply the standard frequency continuation approach without having to process out the ground roll in the (elastic) synthetic data. An analysis of the modified surface conditions based on a plane wave decomposition shows that the reflection coefficients at the surface do not depend on incident angles and earth parameters. With a not too high shear-to-compressional (S-to-P) velocity ratio at the surface, the PP-reflection coefficients are close to the ones with the free-surface conditions, but with a high ratio they differ significantly. The approximation is then valid when the (S-to-P) velocity ratio is not too high at the surface in the actual Earth. Based on some synthetic examples, we discuss the limitations of the approach and the possible computational gain by playing with the shear velocity background value. This elastic modelling with the modified surface boundary conditions aims at inverting low-frequency wide-aperture active land seismic data that correspond to measurements of the vertical component of the particle displacement or velocity due to a vertical force source. It may be seen as an intermediate step between the acoustic waveform inversion and the elastic waveform inversion with the free-surface conditions.