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Deblending technology aims at separating simultaneous source seismic data between adjacent shots by allowing multiple sources to be shot simultaneously. Conventional deblending methods based on sparse inversion assume that the primary source is coherent, and the secondary source is randomized. The L2‐norm minimization constraint can effectively minimize the Gaussian random noise while deblending in the transform domain. Nonetheless, the L2‐norm misfit function is highly sensitive to outliers, negatively influencing the deblending performance. An effective optimization strategy is developed with deblending in pre‐stack seismic data to eliminate outliers and enhance deblending accuracy. For this reason, we introduce the deblending algorithm in the morphological component analysis framework, modify the L2‐norm misfit function to outlier‐robust L1‐norm and provide the corresponding derivation in detail via the alternating direction method of multipliers. Applications to synthetic and field data sets prove the improved robustness and efficiency of our deblending method. [ABSTRACT FROM AUTHOR]

A robust misfit function is essential for mitigating cycle-skipping in full-waveform inversion (FWI), leading to stable updates of the velocity model in this highly nonlinear optimization process. State-of-the-art misfit functions, including matching filter or optimal transport misfits, are all hand-crafted and developed from first principles. With the growth of artificial intelligence in geoscience, we propose learning a robust misfit function for FWI, entitled ML-misfit, based on machine learning. Inspired by the recently introduced optimal transport of the matching filter objective function, we design a specific neural network architecture for the misfit function in a form that allows for global comparison of the predicted and measured data. The proposed neural network architecture also guarantees that the resulting misfit is a pseudo-metric for efficient training. In the framework of meta-learning, we train the network by running FWI to invert for randomly generated velocity models and update the parameters of the neural network by minimizing the meta-loss, which is defined as the accumulated difference between the true and inverted velocity models. The learning and improvement of such an ML-misfit are automatic, and the resulting ML-misfit is data-adaptive. We first illustrate the basic principles behind the ML-misfit for learning a convex misfit function using a travel-time shifted signal example. Furthermore, we train the neural network on 2D horizontally layered models and apply the trained neural network to the Marmousi model; the resulting ML-misfit provides robust updating of the model and mitigates the cycle-skipping issue successfully.

Reflection full-waveform inversion (RFWI) updates the low- and highwavenumber components, and yields more accurate initial models compared with conventional full-waveform inversion (FWI). However, there is strong nonlinearity in conventional RFWI because of the lack of low-frequency data and the complexity of the amplitude. The separation of phase and amplitude information makes RFWI more linear. Traditional phase-calculation methods face severe phase wrapping. To solve this problem, we propose a modified phase-calculation method that uses the phase-envelope data to obtain the pseudo phase information. Then, we establish a pseudophase-information-based objective function for RFWI, with the corresponding source and gradient terms. Numerical tests verify that the proposed calculation method using the phase-envelope data guarantees the stability and accuracy of the phase information and the convergence of the objective function. The application on a portion of the Sigsbee2A model and comparison with inversion results of the improved RFWI and conventional FWI methods verify that the pseudophase-based RFWI produces a highly accurate and efficient velocity model. Moreover, the proposed method is robust to noise and high frequency. [ABSTRACT FROM AUTHOR]

Fundamental mode dispersions, particularly higher ones obtained from weak and hard interlayers, are usually used for inversion to obtain the S-wave velocity profile. Higher mode dispersions are more informative for surface-wave inversion, thus benefiting both inversion stability and model resolution. In the multimodal inversion of the Rayleigh wave dispersion curves, the conventional root-mean-square based misfit function (RMF) is often deviated when the dispersion modes are misidentified. Alternatively, the inversion based on the determinant misfit function (DMF) may avoid misidentifications, but will still be limited to its inherent local minima. In order to reduce this complexity, the paper presents a generalized misfit function (GMF) for estimating the S-wave velocity profile. The generalized function allows for the inversion of both fundamental and higher modes dispersion, without mode-numbering. Before the inversion, the dispersion points are divided into the recognizable fundamental mode dispersion points and others. The RMF is then calculated using data from distinct fundamental mode dispersion, while the DMF was calculated using data from other points. Lastly, the RMF and the DMF were combined to form the GMF by normalizing. The results are based on both theoretical and real data sets and confirm the advantages of GMF in mode identification and inversion accuracy compared to both RMF and DMF. • We propose a generalized misfit function (GMF) in a multimodal inversion of dispersion curves. • A point classification technique can be used to identify the discriminable fundamental mode. • Mode identification of the multimode dispersions was avoided in the GMF inversion. [ABSTRACT FROM AUTHOR]

Four simple mathematical models of pharmacokinetic, competition between immune and tumor cells, infectious disease and tuberculosis epidemic are considered. An optimization approach for identification those models based on gradient type methods is introduced. Inverse problems are formulated in the form of an operator equation and then reduced to the minimization of the corresponding misfit functionals. The adjoint problems are used for the calculation of gradients. A mathematical model of competition between immune and tumor cells is considered numerically. The results of a numerical experiment are demonstrated. [ABSTRACT FROM AUTHOR]

ABSTRACT Waveform inversion met severe challenge in retrieving long-wavelength background structure. We have proposed to use envelope inversion to recover the large-scale component of the model. Using the large-scale background recovered by envelope inversion as new starting model, we can get much better result than the conventional full waveform inversion. By comparing the configurations of the misfit functional between the envelope inversion and the conventional waveform inversion, we show that envelope inversion can greatly reduce the local minimum problem. The combination of envelope inversion and waveform inversion can deliver more faithful and accurate final result with almost no extra computation cost compared to the conventional full waveform inversion. We also tested the noise resistance ability of envelope inversion to Gaussian noise and seismic interference noise. The results showed that envelope inversion is insensitive to Gaussian noise and, to a certain extent, insensitive to seismic interference noise. This indicates the robustness of this method and its potential use for noisy data. [ABSTRACT FROM AUTHOR]