Avoiding pitfalls of least-squares inversion by using the energy-flux error criterion

Seismic inversion by modelling and data fitting depends on the criterion chosen to measure the misfit between observed and modelled data. The popular least-squares error criterion has an important drawback: it is sensitive both to the shape of the recording surface and to velocity variations along this surface. Tests on synthetic seismic reflection data show that least-squares inversion may work surprisingly poorly in situations where (i) the range of angles between reflected rays and the acquisition surface is large, (ii) the velocity varies significantly along this surface, or (iii) a compensation for the effects of dissipation is applied to the gradients. In these situations, the gradients may contain important artefacts and have incorrect amplitudes. The outgoing flux of energy of the residual wavefield across the acquisition surface provides an alternative measure of the data misfit which is independent of the recording surface, provided this surface is closed, and which is only sensitive to the aperture in the practical situation of an open surface or line of receivers. Energy-flux inversion presents a strong resemblance to reverse-time migration, but with the additional possibility of iteratively improving the images. In all the tests, energy-flux inversion provided better images than least-squares inversion.