An adaptive unstructured mesh based solution to topography least-squares reverse-time imaging

Least-squares reverse-time migration (LSRTM) attempts to invert for the broadband-wavenumber reflectivity image by minimizing the residual between observed and predicted seismograms via linearized inversion. However, rugged topography poses a challenge in front of LSRTM. To tackle this issue, we present an unstructured mesh-based solution to topography LSRTM. As to the forward/adjoint modeling operators in LSRTM, we take a so-called unstructured mesh-based “grid method”. Before solving the two-way wave equation with the grid method, we prepare for it a velocity-adaptive unstructured mesh using a Delaunay Triangulation plus Centroidal Voronoi Tessellation (DT-CVT) algorithm. The rugged topography acts as constraint boundaries during mesh generation. Then, by using the adjoint method, we put the observed seismograms to the receivers on the topography for backward propagation to produce the gradient through the cross-correlation imaging condition. We seek the inverted image using the conjugate gradient method during linearized inversion to linearly reduce the data misfit function. Through the 2D SEG Foothill synthetic dataset, we see that our method can handle the LSRTM from rugged topography.