An Open-Source, Simple, and GPU-Accelerated Method in Python for Seismic Surface-Related Multiple Wave Elimination and Source Inversion

Surface-related multiples (SRMs) can significantly interfere with primaries if not properly addressed. The robust estimation of primaries by sparse inversion (REPSI) eliminates EPSI’s free parameters but relies on a highly complex spectral-projected gradient (SPG$\ell _{1}$) algorithm. Compared to SRM elimination (SRME) via prediction and adaptive subtraction, EPSI-type methods require many iterations and incur high computational costs due to extensive matrix multiplications and forward/inverse fast Fourier transforms on prestack shot gathers. Moreover, the common assumption of a constant wavelet across all shots may fail for field data. Based on the feedback primary-multiple model, we propose a simple and efficient estimation of multiples and sources (EMS) method to estimate primaries, SRMs, and both shot-constant and shot-variant sources without subsurface model assumptions or source priors. In this article, we first employ a simple and accelerated linearized Bregman (ALB) algorithm to solve the large-scale sparsity-promoting problem of retrieving the surface-free Green’s function. Tests demonstrate ALB converges faster than SPG$\ell _{1}$. Shot-constant and shot-variant sources are then estimated via a straightforward, exact, and efficient line-search scaling, replacing the iterative and expensive LSQR algorithm in REPSI. Finally, EMS is significantly accelerated using graphics processing units (GPUs), which effectively handle the computational demands of EPSI-type methods. Validation on synthetic and field open datasets confirms EMS’s effectiveness, robustness, and benefits. EMS outperforms REPSI in convergence speed, reconstruction quality, simplicity, and runtime, and surpasses SRME with more accurate SRM estimates. Our EMS code is released as open source.