arXiv subjects

Mahdi Sonbolestan

Publications and source records attributed to Mahdi Sonbolestan.

3 recordsLinked to original sources

arXiv2026

Dual Reverse Time Migration: Efficient Least-squares Imaging with Multiple Scattering in Dual Space

Least-squares reverse time migration (LSRTM) estimates a broadband reflectivity image by iteratively minimizing the data misfit. Despite its superior imaging performance over conventional reverse time migration (RTM), LSRTM is fundamentally limited by the first-order Born approximation and incurs a high computational cost due to the iterative solution of a source-dependent model-space Hessian. We propose dual RTM, a seismic imaging framework that reformulates the inverse problem in the dual space, where the optimization variable is the scattering information of all orders, rather than being limited to the first-order scattering of the Born approximation. Unlike LSRTM, which directly estimates the reflectivity model, dual RTM reconstructs the missing scattering data (dual variable) through a fixed-point iteration governed by the full wave equation, enabling the recovery of higher-order scattering and multiple reflections without repeated background velocity updates. Furthermore, dual RTM replaces the source-dependent model-space Hessian with a source-independent data-space Hessian. A hybrid time--frequency formulation enables this Hessian to be assembled and inverted once in the Fourier domain as an offline preprocessing step, reducing the online computational cost of each dual iteration to that of a single RTM application. Numerical experiments on challenging synthetic benchmarks demonstrate that dual RTM suppresses acquisition footprints, improves amplitude fidelity, and enhances deep imaging where primary reflections alone provide insufficient illumination. These results establish dual RTM as an efficient bridge between conventional RTM/LSRTM and nonlinear waveform inversion for high-resolution large-scale seismic imaging.

physics.geo-ph↗

arXiv2025

Direct inversion of data-space Hessian for efficient time-domain extended-source waveform inversion using the multiplier method

The augmented Lagrangian (AL) method has been successfully applied for solving the full waveform inversion (FWI) problem. In AL-based FWI, the Lagrange multipliers serve as source extensions, offering several advantages to the inversion, such as improved robustness to cycle skipping, faster convergence, and simplified penalty parameter tuning. Time-domain applications of this method have been enabled by reformulating the optimization problem in the data space, significantly reducing memory requirements by projecting source-side multipliers into the data space. These data-side multipliers act as data extensions, effectively expanding the data space. A key challenge in these methods lies in computing the data-side multipliers, which involves solving a linear system to deblur the data residuals using the data-space Hessian matrix before it serves as the adjoint source. This Hessian matrix is prohibitively large to construct and invert explicitly. Iterative Krylov methods can be applied to solve this system as inner iterations, but they require two PDE solves per inner iteration per source, leading to significant computational costs. In this work, we present a key improvement to extended waveform inversion based on multiplier methods. We propose a novel approach that significantly reduces the computational cost of Hessian inversion. The method computes receiver-side Green functions in the time domain and directly constructs frequency-domain Hessian matrices for all required frequencies. These Hessian matrices, with dimensions equal to the number of receivers, can be computed, inverted, and stored in memory. Once constructed, they can be used simultaneously for all sources, further enhancing efficiency. Numerical experiments demonstrate the substantial computational gains achieved by the proposed method, highlighting its effectiveness for extended-source FWI in the time domain.

physics.geo-ph↗

arXiv2022

Large-scale highly-accurate extended full waveform inversion using convergent Born series

Full-waveform inversion (FWI) is a seismic imaging method that provides quantitative inference about subsurface properties with a wavelength-scale resolution. Its frequency-domain formulation is computationally efficient when processing only a few discrete frequencies. However, classical FWI, which is formulated on the reduced-parameter space, requires starting the inversion with a sufficiently-accurate initial model and low frequency to prevent being stuck in local minima due to cycle skipping. FWI with extended search space has been proposed to mitigate this issue. It contains two main steps: first, data-assimilated (DA) wavefields are computed by allowing for wave-equation errors to match the data at receivers closely. Then, subsurface parameters are estimated from these wavefields by minimizing the wave-equation errors. The DA wavefields are the least-squares solution of an overdetermined system gathering the wave and observation equations. The numerical bandwidth of the resulting normal-equation system is two times that of the wave-equation system, which can be a limiting factor for 3D large-scale applications. Therefore, computing highly accurate DA wavefields at a reasonable computational cost is an issue in extended FWI. This issue is addressed here by rewriting the normal system such that its solution can be computed by solving the time-harmonic wave equation several times in sequence. Moreover, the computational burden of multi-right-hand side (RHS) simulations is mitigated with a sketching method. Finally, we solve the time-harmonic wave equation with the convergent Born series method, which conciliates accuracy and computational efficiency. Application of the new extended FWI algorithm on the salt benchmark shows that it reconstructs at a reasonable cost subsurface models that are similar to those obtained with the classical extended FWI.

math.OC↗