Classical Waveform Inversion Research Articles

Multiparameter shallow-seismic waveform inversion based on the Jensen–Shannon divergence

SUMMARY Seismic full-waveform inversion (FWI) or waveform inversion (WI) has gained extensive attention as a cutting-edge imaging method, which is expected to reveal the high-resolution images of complex geological structures. In this paper, we regard each 1-D signal in the inversion system as a 1-D probability distribution, then use the Jensen–Shannon divergence from information theory to measure the discrepancy between the predicted and observed signals, and finally implement a novel 2-D multiparameter shallow-seismic WI (MSWI). Essentially, the novel approach achieves an implicit weighting along the time-axis for each 1-D adjoint source defined by the classical WI (CWI), thus enhancing the extra illumination for a deeper medium compared with the CWI. By evaluating the inversion results of the two-layer model and fault model, the reconstruction accuracy for S-wave velocity and density of the new method is increased by about 30 and 20 per cent compared with that of the CWI under the same conditions, respectively. The reconstruction performance for P-wave velocity of these two methods is almost equal. In addition, the new 2-D MSWI is also resilient to white Gaussian noise in the data. Numerically, the inversion system has almost the strongest sensitivities to the S-wave velocity and density, performing the poorest sensitivity to the P-wave velocity. Finally, we test the novel method with a detection case for a power tunnel.

Source-encoded waveform inversion in the Northern Hemisphere

SUMMARY We use source-encoded waveform inversion to image Earth’s Northern Hemisphere. The encoding method is based on measurements of Laplace coefficients of stationary wavefields. By assigning to each event a unique frequency, we compute Fréchet derivatives for all events simultaneously based on one ‘super’ forward and one ‘super’ adjoint simulation for a small fraction of the computational cost of classical waveform inversion with the same data set. No cross-talk noise is introduced in the process, and the method does not require all events to be recorded by all stations. Starting from global model GLAD_M25, we performed 100 conjugate gradient iterations using a data set consisting of 786 earthquakes recorded by 9846 stations. Synthetic inversion tests show that we achieve good convergence based on this data set, and we see a consistent misfit reduction during the inversion. The new model, named SE100, has much higher spatial resolution than GLAD_M25, revealing details of the Yellowstone and Iceland hotspots, subduction beneath the Western United States and the upper mantle structure beneath the Arctic Ocean.

Coseismic stress parameter of three California Earthquakes derived from the stochastic finite fault technique

Stochastic finite fault modeling is used to derive the coseismic stress parameter distribution on the fault surface of three well-recorded California earthquakes: M7.0, 1989, Loma Prieta; M7.3, 1992, Landers; and M6.7, 1994, Northridge. Classical waveform inversion techniques are inherently more powerful than stochastic modeling as a means of deriving detailed source parameters. However, the application of stochastic methods to the source modeling problem is useful to: (1) explore and calibrate the limitations and boundaries of stochastic modeling, (2) understand its relationship to more deterministically based techniques, and (3) provide a view of the source radiation not available from deterministic modeling. The stress parameter distribution for the M7.0 1989 Loma Prieta earthquake fault shows a concentration of stress in the lower part of the northwest side of the fault and another concentration in the upper southeast side of the fault, with an average stress parameter of 80 bars over the fault surface. The stress parameter distribution for the M7.3 1992 Landers earthquake fault shows a gradual increase of stress starting from the southeast side of the fault, close to the hypocenter, towards the center. The maximum stress occurs in the lower central part of the modeled fault surface. The average stress parameter is 70 bars for the Landers earthquake. The stress parameter distribution of the M6.7 1994 Northridge earthquake shows a concentration at the lower southeast end of the fault surface, extending toward the center of the fault surface and stretching to the northwest end. The average stress parameter is 80 bars for Northridge earthquake. The stress parameter distributions derived in this study by stochastic finite-fault modeling of high-frequency motions show considerable similarity to many of the slip distributions provided by different research groups for the same earthquakes, suggesting that the derivation of stress parameter distribution on a fault surface by the method applied in this study is reliable and closely tied to slip on the fault.

Waveform inversion using a logarithmic wavefield

Although waveform inversion has been studied extensively since its beginning [Formula: see text] ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our wave form inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noise-free synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below [Formula: see text] are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.