We have developed an efficient elastic full-waveform inversion (FWI) based on the P-wave excitation amplitude (maximum energy arrival) approximation in the source wavefields. Because, based on the P-wave excitation approximation (ExA), the gradient direction is approximated by the crosscorrelation of source and receiver wavefields at only excitation time, it estimates the gradient direction faster than its conventional counterpart. In addition to this computational speedup, the P-wave ExA automatically ignores SP and SS correlations in the approximated gradient direction. In elastic FWI for ocean bottom cable (OBC) data, the descent direction for the S-wave velocity is often degraded by undesired long-wavelength features from the SS correlation. For this reason, the P-wave excitation approach increases the convergence rate of multiparameter FWI compared with the conventional approach. The modified 2D Marmousi model with OBC acquisition is used to verify the differences between the conventional method and ExA. Finally, the feasibility of the proposed method is demonstrated on a real OBC data from the North Sea.

To increase the feasibility of full waveform inversion on real data, we suggest a new objective function, which is defined as the global correlation of the envelopes of modelled and observed data. The envelope-based global correlation norm has the advantage of the envelope inversion that generates artificial low-frequency information, which provides the possibility to recover long-wavelength structure in an early stage. In addition, the envelope-based global correlation norm maintains the advantage of the global correlation norm, which reduces the sensitivity of the misfit to amplitude errors so that the performance of inversion on real data can be enhanced when the exact source wavelet is not available and more complex physics are ignored. Through the synthetic example for 2-D SEG/EAGE overthrust model with inaccurate source wavelet, we compare the performance of four different approaches, which are the least-squares waveform inversion, least-squares envelope inversion, global correlation norm and envelope-based global correlation norm. Finally, we apply the envelope-based global correlation norm on the 3-D Ocean Bottom Cable (OBC) data from the North Sea. The envelope-based global correlation norm captures the strong reflections from the high-velocity caprock and generates artificial low-frequency reflection energy that helps us recover long-wavelength structure of the model domain in the early stages. From this long-wavelength model, the conventional global correlation norm is sequentially applied to invert for higher-resolution features of the model.

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

Seismic anisotropy is an important physical phenomenon that significantly affects wave propagation in complex sedimentary basins. When geological structures exhibit steep dips or severe folding, the symmetry axis of the transversely isotropic (TI) representation of the region can be rotated, leading to tilted transversely isotropic (TTI) media. We seek to find the optimal full-waveform inversion (FWI) strategy to estimate both the seismic velocities and the anisotropic parameters, including the tilt angle, in the presence of elastic TTI media. We first formulate the forward and inverse problems for elastic TTI media and analyse the radiation patterns of the model parameters. Based on the analyses of the radiation patterns, we propose two similar multistage FWI strategies that add inversion parameters over three stages, beginning with the isotropic parameters (horizontal P- and vertical S-wave velocity) and moving to the anisotropic parameters; the tilt angle is directly inverted in the last stage. Since diving waves, which are useful for providing long-wavelength updates, are mainly controlled by horizontal motion in anisotropic media, it is reasonable to choose the horizontal P-wave velocity rather than the vertical P-wave velocity. Then, the anisotropic parameters are inverted mainly using the reflected waves based on the isotropic background model built in the first stage. The main difference between the two multistage FWI strategies is whether the anisotropic parameter η is inverted. Comparing the two multistage FWI strategies with the simultaneous inversion strategy for a downsized version of the synthetic BP TTI model, we confirm that the multistage FWI strategies yield better inversion results than the simultaneous inversion strategy. When we compare the two multistage FWI strategies with each other for surface seismic data, ignoring η during the FWI process (focused multistage FWI) yields better inversion results for the tilt angle than those obtained with the inversion of η because η has less influence on the FWI than the other parameters and is not recovered well, which plays a role in degrading the tilt angle. Numerical examples support our conclusions that the focused multistage FWI strategy (neglecting η) is the optimal FWI strategy for TTI media and achieves computational efficiency for surface seismic data.

The orthorhombic (ORT) anisotropic description of earth layers can allow the capture of much of the earth’s anisotropic complexity. The inversion for high-resolution azimuthal variation of anisotropy is important for reservoir characterization, among other applications. A high-resolution description of the azimuth of fractures can help us to predict flow preferences. To verify the feasibility of multiparameter full-waveform inversion (FWI) for marine data assuming azimuthally rotated elastic ORT media, we have analyzed the radiation patterns and gradient directions of ORT parameters to the reflection data. First, we express the gradient direction of the ORT parameters considering the azimuthal rotation of the symmetric planes. Then, to support our observations in the gradient direction, the radiation patterns of the partial derivative wavefields from each parameter perturbation are also derived under the rotated elastic ORT assumption. To find an optimal parameterization, we compare three different parameterizations: monoclinic, velocity-based, and hierarchical parameterizations. Then, we suggest an optimal multistage update strategy by analyzing the behavior of the rotation angle as a FWI target. To analyze the trade-off among parameters in different parameterizations, we calculate the gradient direction from a hockey-puck model, in which each parameter is perturbed at the different location on a horizontal layer. The trade-off analysis supports that the hierarchical parameterization provides us with more opportunities to build up subsurface models with less trade-off between parameters and less influence of the azimuthal rotation of ORT anisotropy. The feasibility of the proposed FWI strategy is examined using synthetic marine streamer data from a simple 3D reservoir model with a fractured layer.