A robust migration velocity analysis through an asymptotic inverse via generalised Radon transform

Abstract

Migration velocity analysis (MVA) has been widely used for large scale model construction. To make full use of the wavefield information and obtain stable inversion results, wave-equation-based methods, such as differential semblance optimisation (DSO) or travel-time tomography, become popular in recent years. Compared with traditional ray-based methods, wave-equation-based methods are intrinsically more robust, which can accurately describe subsurface wave phenomenon and thus solve multipathing problem occurred in ray-based methods especially in dramatically lateral variation areas. Although robust for wave-equation-based methods, the inversion results can be severely affected by spurious oscillations, such as migration smile, due to uneven illumination and limited geometry observations. To eliminate those artefacts and improve imaging and inversion results, we introduce a new asymptotic inversion method in subsurface offset domain based on two-way wave equation. The new method, derived from the generalised Radon transform, introduces a new weighting function which can be treated as an approximate inverse under the assumption of high-frequency approximation. By applying the new weighting function to the practical applications, the imaging artefacts can be significantly attenuated. Furthermore, we extend the new method to DSO with a new form of velocity inversion expressions. We also give three numerical examples to illustrate the effectiveness of the method. It appears smooth and is free of artefacts both in gradients and imaging results, which leads to stable imaging and reliable model update.