Interlocked optimization and fast gradient algorithm for a seismic inverse problem

We give a nonlinear inverse method for seismic data recorded in a well from sources at several offsets from the borehole in a 2D acoustic framework. Given the velocity field, approximate values of the impedance are recovered. This is a 2D extension of the 1D inversion of vertical seismic profiles [18]. The inverse problem generates a large scale undetermined ill-conditioned problem. Appropriate regularization terms render the problem well-determined. An interlocked optimization algorithm yields an efficient preconditioning. A gradient algorithm based on the adjoint state method and domain decomposition gives a fast parallel numerical method. For a realistic test case, convergence is attained in an acceptable time with 128 processors.

► A 2D extension of the 1D nonlinear inversion of well-seismic data is given.
► Appropriate regularization yields a well-determined large scale inverse problem.
► An interlocked optimization loop acts as an efficient preconditioner.
► The adjoint state method is used to compute the misfit function gradient.
► Domain decomposition method yields an efficient parallel implementation.