Full-waveform inversion for microseismic events using sparsity constraints

Abstract

Full-waveform inversion (FWI) is a powerful tool that can be used to invert for microseismic event locations and the source signature because it can exploit the complete waveform information. We have developed an algorithm to invert for a spatio-temporal source function that encapsulates microseismic events with spatially localized or distributed locations and source signatures. The algorithm does not require assumptions to be made about the number or type of sources; however, it does require that the velocity model is close to the true subsurface velocity. We reformulate the conventional FWI algorithm based on the [Formula: see text]-norm data-misfit function by adding sparsity constraints using a sparsity promoting [Formula: see text]-norm as an additional regularization term to get more focused and less noise-sensitive event locations. The Orthant-Wise Limited-memory quasi-Newton algorithm is used to solve the optimization problem. It inherits the advantageous (fast convergence) properties of the limited memory Broyden-Fletcher-Goldfarb-Shanno method and can easily overcome the nondifferentiability of [Formula: see text]-norm at null positions. We determine the performance of the algorithm on noise-free and noisy synthetic data from the SEG/EAGE overthrust model.

Recent Advances and Challenges of Waveform‐Based Seismic Location Methods at Multiple Scales

“… v is the velocity model, * denotes the convolution operator, and u ref is the data of a reference trace. Equations and are commonly used misfit functions (e.g., Kaderli et al, ; Michel & Tsvankin, , ; Shekar & Sethi, ), and equation is recently proposed by Wang and Alkhalifah, (2018) and the unknown source origin time is decoupled by convolving reference traces with the observed and modeled traces. When FWI is applied to source location problem, the source location (and maybe together with velocity model) can be inverted and imaged in one step using above misfit functions.…”

“…Hence, this methodology is extremely sensitive to selecting reference trace. Shekar and Sethi () formulated an FWI scheme for determining the spatiotemporal source function of microseismic events, and an additional regularization term in the misfit function (10) is used by exploring the sparsity inherent in the microseismic location problem. Synthetic examples based on 2‐D SEG/EAGE overthrust model have illustrated the possibility of the FWI applications (Shekar & Sethi, ).…”

“…Shekar and Sethi () formulated an FWI scheme for determining the spatiotemporal source function of microseismic events, and an additional regularization term in the misfit function (10) is used by exploring the sparsity inherent in the microseismic location problem. Synthetic examples based on 2‐D SEG/EAGE overthrust model have illustrated the possibility of the FWI applications (Shekar & Sethi, ). Most recent studies of FWI for source location and velocity are limited to 2‐D synthetic acoustic scenarios, which are still far from field application, and therefore, it is hard to judge if they will be practical because microseismic signals are dominated by S wave energy (in the vicinity of the source) and this is not captured in the acoustic models.…”

“…The basic principle of FWI is to find a model (e.g., velocities and source parameters) that can generate synthetic waveforms that match the observed waveforms best. Though FWI involves high nonlinearity and requires expensive computational effort, it is increasingly used not only for subsurface velocity estimation in exploration seismology (e.g., Virieux & Operto, ), but also for seismic source location (e.g., Kaderli et al, ; Shekar & Sethi, ). More recently, a largely data‐driven technique, known as wavefront tomography (WT), combines kinematic information estimated from wavefront attributes with time‐reverse modeling to jointly estimate source location and the velocity structure (Diekmann et al, ).…”

High-Accuracy Location of Microseismic Events in a Strong Inhomogeneous Mining Environment by Optimized Global Full Waveform Inversion

“…Therefore, some studies have simplified the source parameter model into an inversion that only considers source locations (the simplification process and description are shown in Section 2.1), which improves inversion speed and reduces the nonlinearity of convergence. Shekar and Sethi [36] formulated an FWI scheme for determining hydraulic fracturing and mining microseismic event locations, and synthetic test on the 2-D SEG/EAGE overthrust model demonstrates its feasibility. Tong et al [37] derived a waveform inversion-based location method using the time-domain wave equation and cross-correlation travel time measurement between simulated and observed waveform as the misfit.…”