A reflection-based efficient wavefield inversion

Full-waveform inversion (FWI) is popularly used to obtain a high-resolution subsurface velocity model. However, it requires either a good initial velocity model or low-frequency data to mitigate the cycle-skipping issue. Reflection-waveform inversion (RWI) uses a migration/demigration process to retrieve a background model that can be used as a good initial velocity in FWI. The drawback of the conventional RWI is that it requires the use of a least-squares migration, which is often computationally expensive, and is still prone to cycle skipping at far offsets. To improve the computational efficiency and overcome the cycle skipping in the original RWI, we incorporate it into a recently introduced method called efficient wavefield inversion (EWI) by inverting for the Born scattered wavefield instead of the wavefield itself. In this case, we use perturbation-related secondary sources in the modified source function. Unlike conventional RWI, the perturbations are calculated naturally as part of the calculation of the scattered wavefield in an efficient way. As the sources in the reflection-based EWI (REWI) are located in the subsurface, we are able to update the background model along the reflection wave path. In the background velocity inversion, we calculate the background perturbation by a deconvolution process at each frequency. After obtaining the REWI inverted velocity model, a sequential FWI or EWI is needed to obtain a high-resolution model. We demonstrate the validity of the proposed approach using synthetic data generated from a section of the Sigsbee2A model. To further demonstrate the effectiveness of the proposed approach, we test it on an ocean bottom cable (OBC) dataset from the North Sea. We find that the proposed methodology leads to improved velocity models as evidenced by flatter angle gathers.

Anisotropic 3D elastic full-wavefield inversion to directly estimate elastic properties and its role in interpretation

Elastic properties from seismic data are important to determine subsurface hydrocarbon presence and have become increasingly important for detailed reservoir characterization that aids to derisk specific hydrocarbon prospects. Traditional techniques to extract elastic properties from seismic data typically use linear inversion of imaged products (migrated angle stacks). In this research, we attempt to get closer to Tarantola's visionary goal for full-wavefield inversion (FWI) by directly obtaining 3D elastic properties from seismic shot-gather data with limited well information. First, we present a realistic 2D synthetic example to show the need for elastic physics in a strongly elastic medium. Then, a 3D field example from deepwater West Africa is used to validate our workflow, which can be practically used in today's computing architecture. To enable reservoir characterization, we produce elastic products in a cascaded manner and run 3D elastic FWI up to 50 Hz. We demonstrate that reliable and high-resolution P-wave velocity can be retrieved in a strongly elastic setting (i.e., with a class 2 or 2P amplitude variation with offset response) in addition to higher-quality estimation of P-impedance and VP/VS ratio. These parameters can be directly used in interpretation, lithology, and fluid prediction.

A sequential inversion with outer iterations for the velocity and the intrinsic attenuation using an efficient wavefield inversion

Full-waveform inversion (FWI) has become a popular method to retrieve high-resolution subsurface model parameters. It is a highly nonlinear optimization problem based on minimizing the misfit between the observed and predicted data. For intrinsically attenuating media, wave propagation experiences significant loss of energy. Thus, for better data fitting, it is sometimes crucial to consider attenuation in FWI. Viscoacoustic FWI aims at achieving a joint inversion of the velocity and attenuation models. However, multiparameter FWI imposes additional challenges including expanding the null space and facing parameter trade-off issues. Theoretically, an ideal way to mitigate the trade-off issue in multiparameter FWI is to apply the inverse Hessian operator to the parameter gradients. However, it is often not practical to calculate the full Hessian and its matrix inverse because this will be extremely expensive. To improve the computational efficiency and mitigate the trade-off issue, we have used an efficient wavefield inversion (EWI) method to invert for the velocity and the intrinsic attenuation. This approach is implemented in the frequency domain, and the velocity, in this case, is complex-valued in the viscoacoustic EWI. We evaluate a sequential update strategy for the velocity and the intrinsic attenuation, and we repeat the separate optimizations, which we refer to as outer iterations, until the convergence is achieved. Because viscoacoustic EWI is able to recover an accurate velocity model, the velocity update leakage to the [Formula: see text] model is largely reduced. We determine the effectiveness of this approach using synthetic data generated for the viscoacoustic Marmousi and Overthrust models. To further demonstrate the validity of our approach, we generate data in the time domain using a viscoelastic wave equation solver and obtain reasonable inversion results in the frequency domain using the viscoacoustic approximation.

Source-independent efficient wavefield inversion

SUMMARY Full-waveform inversion (FWI) is an effective tool to retrieve a high-resolution subsurface velocity model. The source wavelet accuracy plays an important role in reaching that goal. So we often need to estimate the source function before or within the inversion process. Source estimation requires additional computational cost, and an inaccurate source estimation can hamper the convergence of FWI. We develop a source-independent waveform inversion utilizing a recently introduced wavefield reconstruction based method, which we refer to as efficient wavefield inversion (EWI). In EWI, we essentially reconstruct the wavefield by fitting it to the observed data as well as a wave equation based on iterative Born scattering. However, a wrong source wavelet will induce errors in the reconstructed wavefield, which may lead to a divergence of this optimization problem. We use a convolution-based source-independent misfit function to replace the conventional data fitting term in EWI to formulate a source-independent EWI (SIEWI) objective function. By convolving the observed data with a reference trace from the predicted data and convolving the predicted data with a reference trace from the observed data, the influence of the source wavelet on the optimization is mitigated. In SIEWI, this new formulation is able to mitigate the cycle-skipping issue and the source wavelet uncertainty simultaneously. We demonstrate those features on the Overthrust model and a modified Marmousi model. Application on a 2-D real data set also shows the effectiveness of the proposed method.