Frequency Domain Adjoint-state Least-squares Migration

Least-Squares Migration based on the inversion formulation will provide the amplitude-preserved imaging if inversed-Hessian kernel are applied. The inversed-Hessian kernel reflects the forward and backward propagation of the operator. Under the assuming of infinite receiver coverage and smooth velocity model, LSM using one-way operator can provide believable imaging. However, in other cases, for the areas the operator can not covered, LSM can not compensate. To avoid the zero-illuminated cases, we apply the full-wave operator to propagate the wave in frequency domain. Frequency-domain Reverse Time Migration use efficient full wave extrapolator in the frequency domain. We combine the LSM frame and the FRTM method and implement a Least-Squares Frequency domain Reverse Time Migration. To enhance the computational efficiency, we introduce the Adjoint State method based on the local Born approximation. The algorithms are tested using the BP 2004 Benchmark model and results show improved image quality and amplitudes.