Wave equation-based traveltime inversion is a method that uses traveltime information to obtain the low-wavenumber components of subsurface velocity models. This helps create a reliable initial model for full waveform inversion (FWI). However, this method usually requires identifying the first arrival waves or specific seismic events to calculate the traveltime differences between the observed and synthetic data. When working with multiple seismic events, such as those from elastic wavefields or simultaneous sources-based seismic data, it becomes difficult to obtain the low-wavenumber components of velocity models by traveltime inversion. In this letter, we propose a simultaneous source-based elastic wave local-scale traveltime inversion (SS-ELTI) method. This method utilizes both P-wave and S-wave data, along with local-scale traveltimes from various seismic events generated by simultaneous sources. This approach enables the simultaneous inversion of the low-wavenumber components of both P-wave and S-wave velocity parameters. Numerical tests demonstrate that the proposed SS-ELTI method can effectively reduce the computational costs and mitigate the cycle-skipping problem of elastic full waveform inversion (EFWI).

The envelope inversion (EI) is an effective method to recover low-wavenumber components, which helps to produce a good initial model for full-waveform inversion (FWI). However, when the initial model is not capable of generating reflections, it brings enormous challenges for EI to invert deep low-wavenumber components, especially for short offset data. In contrast, reflection waveform inversion (RWI) uses demigration data to fit the observed reflection, which focuses on the transmission information with short offset seismic data. However, the cycle skipping and high nonlinearity of the RWI misfit still exist when the low-frequency information is absent. In this letter, we develop a joint traditional and reflection envelope inversion (JREI) that utilizes both reflection and transmission waves with envelope low-frequencies to recover low-wavenumber components in the shallow and deep regions simultaneously. We then use the FWI with high-frequency seismic data to obtain the high-wavenumber components. Applications to the modified Marmousi and Overthrust models demonstrate that the JREI can invert a better starting velocity model for the FWI to achieve a high-resolution inversion result.

Least-squares reverse time migration (LSRTM) aims to produce a high-quality migration image of complex geological structures. However, the weaker deep seismic reflections are often masked by the overlying strata in migration images. Therefore, it is difficult for the LSRTM to image the deeper structures. This letter proposes a phase-amplitude LSRTM (PA-LSRTM) in the time-frequency domain to improve the migration image of deep seismic reflections and subsalt structures. The PA-LSRTM is formulated as an inverse problem that minimizes the time-frequency phase-amplitude difference between the predicted and observed data. The seismic data was initially transformed into the time-frequency domain to establish a PA-LSRTM misfit. An amplitude factor was then introduced in the time-frequency misfit to weaken the weights of amplitude components. In this case, it emphasized the similarity of phase components. Furthermore, the sparsity promotion method was combined with a simultaneous source technique to increase the computational efficiency and reduce the crosstalk noise. The PA-LSRTM with sparsity promotion (SPA-LSRTM) misfit can finally be solved using a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The numerical and marine field data tests demonstrate that the SPA-LSRTM can effectively produce a high-resolution image of deep structures.

Full waveform inversion (FWI) is, as an optimization problem, strongly nonconvex and is influenced intensely by the cycle skipping issue, especially for multiparameter inversions like the elastic case. When there are strong scattering heterogeneities in the target media, there will be more challenges for the inversion problem. The direct envelope inversion strategy uses the envelope Fréchet derivative to tackle the cycle skipping problem for strong scattering inversion and has been effectively used for the acoustic case. We extend the direct envelope inversion method to the elastic situation in this letter. We derive the elastic envelope Fréchet derivative and show how the strong scattering multiparameter elastic inversion is accomplished under the direct envelope inversion framework. Numerical tests with the SEG/EAGE salt velocity model proved the effectiveness of this method for the strong scattering elastic medium.

Least-squares reverse time migration (LSRTM) attempts to produce a high-quality image for complicated subsurface structures. However, large amplitude discrepancies between the synthetic and observed seismic data are problematic for high-resolution imaging. Alternatively, correlative LSRTM (CLSRTM) misfit has been proposed to improve the imaging quality of complicated structures. However, the CLSRTM ignores the local characteristics of the 2-D seismic data. Thus, we developed a 2-D local correlative misfit for LSRTM (2-D-LCLSRTM) to improve the imaging resolution. In this case, a 2-D sliding window was used to obtain local-scale seismic data. A 2-D correlation method was then used to measure the similarity between the local-scale synthetic and observed data. Consequently, the 2-D-LCLSRTM misfit could reduce amplitude constraints and emphasize phase similarity, which has a potential for improving deep structure as it can boost weak seismic signals. To suppress the migration artifacts, we incorporated the sparsity promotion method with the 2-D-LCLSRTM misfit and used the fast iterative shrinkage-thresholding algorithm (FISTA) to solve it iteratively. In the numerical examples, a Marmousi model, a Salt model, and a marine field seismic dataset were used to test the effectiveness of the 2-D-LCLSRTM method. Compared with the commonly used RTM and sparsity promotion-based CLSRTM methods, the 2-D-LCLSRTM with sparsity promotion can better image deep reflectors and obtain high-resolution imaging results.

Surface monitoring of microseismic monitoring events is generally challenging because microseismic data have a low signal-to-noise ratio (SNR). Traditional event-detection methods struggle to detect weak microseismic events. A variance fractal dimension (VFD) method for automatic microseismic event detection via multitrace energy envelope stacking (MTEES) is introduced. In the first stage, we propose a processing microseismic data method based on the MTEES method. It increases the energy of weak microseismic data to avoid missed and false microseismic detection. Furthermore, it can greatly improve computational efficiency to satisfy real-time processing requirements. In the second stage, the VFD algorithm is applied to the data processed in the first stage to improve the feasibility and validity of microseismic event detection. A simulation test with perforation data shows the reliability of the new method in the automatic detection of microseismic events. In addition, we demonstrate that analogous results can be obtained when perforation data are not available by introducing a novel approach based on synthetic correction time. The new approach is particularly useful when perforation data are not recorded, representing a significant advantage over previous approaches. We describe the application of the novel method to a real microseismic data example from monitoring hydraulic fracture treatments in Shanxi Province, China, with and without perforation data. The new method yields improvement in microseismic event detection for microseismic monitoring. Therefore, we find a wide range of applications requiring analysis of microseismic data.

Uncertainty quantification related to nonlinear inverse scattering problems often involves the posterior covariance matrix that cannot be effectively estimated but still need to be considered as an important part of the nonlinear inverse scattering problem. The objective of this work is to show how to take advantage of a Bayesian framework to estimate the uncertainty of velocity reconstruction in the nonlinear inverse scattering imaging. The key ingredients are twofold. On the one hand, we rely on a Kalman Filter method, equipped with an optimization scheme, to solve the inverse problem. We use the distorted Born iterative method to formulate the sensitivity kernel. It directly uses an explicit representation of the data sensitivity function in terms of Green functions, rather than the indirect optimization approach based on the adjoint state method, in which the Green’s functions are based on integral equations. On the other hand, we use the direct envelope methods to provide the initial guess (large-scale smooth model) to overcome the nonlinearity in the inverse scattering problems. We first investigate the uncertainty of velocity imaging in high contrast media. Then we show by means of Lippmann-Schwinger-type equations that the uncertainty of multiparameter inverse scattering problems can be addressed. Numerical results dealing with the uncertainty of nonlinear inverse scattering problems in the case of both isotropic and anisotropic media highlight the important role played by uncertainty quantification.

Time-frequency analysis can reveal local variations and allow for separation of phase and amplitude information of nonstationary seismic waveforms. Seismic signals are used since long as a robust tool for inversion of underground structures, as has been the practice in geophysical exploration. However, the mixing of phase and amplitude in seismic data increases the nonlinearity of seismic inversion. The authors first use Gabor transform to separate the phase and amplitude information of envelope data, and then introduce an adaptive factor into the misfit function to redistribute the weight of phase and amplitude information for direct envelope inversion (DEI) in the time-frequency domain. By adopting this procedure, greater flexibility can be achieved in operating the local phase of envelope and waveform spectra to enhance stability of multiscale phase inversion. For DEI, the direct envelope Fréchet derivative is used, and thus, no weak scattering assumption is imposed on the joint multiscale DEI of phase and amplitude (PADEI). Compared with the DEI method, the PADEI can better recover the deeper parts of salt-bottom and subsalt structures by boosting the signal energy and weakening the nonlinearity of the waveform inversion.