A fast least-squares migration with ultra-wide-band phase-space beam summation method

Least-squares migration (LSM) problems are often formulated as iterative schemes. At each iteration, traditional LSM methods require solving the wave equation several times to compute the gradient and single scattering (Born) predicted data, which makes LSM computationally expensive. We use a beam approach to overcome this problem, based on the ultra-wide-band phase space beam summation (UWB-PS-BS) method. We use the beams to expand and propagate the measured data. The beams calculation is performed via a small number of Green’s functions (GFs). These GFs are calculated once and then stored in the computer’s disk memory. Thus, wave equation calculations are avoided within each iteration. We use a beam transformation of shot gathers which can be considered as the data obtained by a pair of source and receiver beams. This data has a physical interpretation. The beam amplitudes extract the medium reflectivity generated from a localized region in subspace at a specific angle (local Snell’s law). This data calculation is performed before the iterative scheme. Thus, we may a-priori threshold beams with low amplitude beams, as they contain less essential information. Using the beam propagators spectral locality, we may further reduce the number of beams used to construct the image. In this work, we establish a new local beam-based data domain LSM in the frequency domain (FD). We use the properties described above to reduce the computational complexity of the LSM problem. We demonstrate the advantages of the proposed LSM algorithm via numerical examples.