Abstract
As an essential step in seismic inversion, velocity macromodel building provides a low-wavenumber background velocity model for seismic imaging and full waveform inversion. Defined as the first-order partial derivative of traveltime with regard to spatial coordinates, slope information has been directly or indirectly applied in ray-based geophysical inversion to retrieve models containing low and intermediate wavenumbers. In this study, to use slopes of locally coherent events in background velocity model building, we extend the slope inversion from ray theory to wave equation, which we name wave-equation traveltime slope inversion (WSI). Unlike traditional ray-based slope inversion, which relies on tedious picking of continuous horizons, we compute slope conveniently and robustly through cross-correlation and finite difference methods. Furthermore, we present the formulation of wave-equation traveltime slope inversion under the framework of wave-equation traveltime inversion. Traveltime and slopes are distinct data attributes that play different roles in reconstructing low-wavenumber background velocity models. Compared with the classic traveltime inversion, the wave-equation traveltime slope inversion is more sensitive to local velocity changes. Numerical examples demonstrate that the proposed method improves the horizontal resolution in velocity model building, which especially shows excellent potential in obtaining a higher lateral resolution of reconstruction for steeply dipping structures than traditional wave-equation traveltime inversion. What's more, this study makes the joint inversion of travel time and slope based on the wave equation possible, which can theoretically bring a higher resolution stabilized inversion.
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