ALBERT

Description: SUMMARY Seismic data recorded using a marine acquisition geometry contain both upgoing reflections from subsurface structures and downgoing ghost waves reflected back from the free surface. In addition to the ambiguity of propagation directions in the data, using the two-way wave equation for wavefield extrapolation of seismic imaging generates backscattered/turned waves when there are strong velocity contrasts/gradients in the model, which further increases the wavefield complexity. For reverse-time migration (RTM) of free-surface multiples, apart from unwanted crosstalk between inconsistent orders of reflections, image artefacts can also be formed along with the true reflector images from the overlapping of up/downgoing waves in the data and in the extrapolated wavefield. We present a wave-equation-based, hybrid (data- and model-domain) wave separation workflow, with vector seismic data containing pressure- and vertical-component particle velocity from dual-sensor seismic acquisition, for removing image artefacts produced by the mixture of up/downgoing waves. For imaging with free-surface multiples, the wavefield extrapolated from downgoing ghost events (reflected from the free surface) in the recorded data act as an effective source wavefield for one-order-higher free-surface multiples. Therefore, only the downgoing waves in the data should be used as the source wavefield for RTM with multiples; the recorded upgoing waves in the seismograms will be used for extrapolation of the time-reversed receiver wavefield. We use finite-difference (FD) injection for up/down separation in the data domain, to extrapolate the down- and upgoing waves of the common-source gathers for source and receiver wavefield propagation, respectively. The model-domain separation decomposes the extrapolated wavefield into upgoing (backscattered) and downgoing (transmitted) components at each subsurface grid location, to remove false images produced by cross-correlating backscattered waves along unphysical paths. We combine FD injection with the model-domain wavefield separation, for separating the wavefield into up- and downgoing components for the recorded data and for the extrapolated wavefields. Numerical examples using a simple model, and the Sigsbee 2B model, demonstrate that the hybrid up/down separation approach can effectively produce seismic images of free-surface multiples with better resolution and fewer artefacts.

Description: Conventional full waveform inversion (FWI) updates a velocity model by minimizing the data residuals between predicted and observed data, at the receiver positions. We propose a new full waveform inversion to update the velocity model by minimizing virtual source artifacts, at the receiver positions, in the source domain (SFWI). Virtual source artifacts are created by replacing the propagating source wavefield by the forward-time observed data at the receiver positions, as a data-residual constraint. Therefore, no matter whether the velocity model is correct or not, the data residuals, at the receiver positions, are always forced to be zero. If the velocity model is correct, this data-residual constraint has no effect on the wavefield, since the predicted data is the same as the observed data. However, if the estimated velocity model is incorrect, the mismatch between the replaced forward-time observed data and the incorrect predicted upgoing waves (e.g., reflected waves) at the receiver positions, will produce downgoing artifact waves. Thus, the data-residual constraint behaves as a virtual source to create artifact wavefields. By minimizing the virtual source artifacts (equivalent to producing the artifact wavefield), the velocity model can be iteratively updated toward the true velocity model. Similar to conventional FWI, SFWI can be implemented in either the frequency or the time domain, which is unlike previous source-domain solutions, which have to be implemented only in the frequency domain, to solve the normal equations. SFWI does more over-fitting of noisy observed data than conventional FWI does, because noise is amplified by the differential operators when calculating the virtual source artifacts. Tests on synthetic data show that the SFWI inverts for the velocity model more accurately than conventional FWI for noise-free or low-noise data.

Description: A 2D algorithm for angle-domain common-image gather (CIG) calculation is extended and modified to produce 3D elastic angle and azimuth CIGs. The elastic seismic data are propagated with the elastic particle displacement wave equation, and then the PP-reflected and PS-converted waves are separated by divergence and curl calculations during application of the excitation-time imaging condition. The incident angles and azimuths are calculated using source propagation directions and the reflector normals. The source propagation direction vector is computed as the spatial gradient of the incident 3C P-wavefield. The vector normal to the reflector is calculated using the Hilbert transform. Ordering the migrated images with respect to incident angles for a fixed azimuth bin, or with respect to azimuths for a fixed incident angle bin, creates angle- or azimuth-domain CIGs, respectively. Sorting the azimuth gathers by the incident angle bins causes a shift to a greater depth for too-high migration velocity and to a smaller depth for too-low migration velocity. For the sorted incident angle gathers, the velocity-dependent depth moveout is within the angle gathers and across the azimuth gathers. This method is compared with three other 3D CIG algorithms with respect to the number of calculations and their disk storage and RAM requirements; it is three to six orders of magnitude faster and requires two to three orders of magnitude less disk space. The method is successfully tested with data for a modified part of the SEG/EAGE overthrust model.

Description: The physical basis, parameterization, and assumptions involved in root-mean-square (RMS) velocity estimation have not significantly changed since they were first developed. However, all three of these aspects are good targets for novel application of the recent emergence of Machine Learning (ML). So it is useful at this time to provide a tutorial overview of two state-of-the-art ML implementations; we design and evaluate classification and regression neural networks for extraction of apparent RMS velocity trajectories from semblance data. Both networks share a similar end-to-end trainable structure, except for the final layer. In the classification network, the velocity picking is performed by finding the largest amplitude trajectory through all velocity bins. The regression network, on the other hand, applies a differentiable Soft-argmax function that converts the feature maps directly to apparent RMS velocity values as functions of traveltime. Relative confidence maps can also be estimated from both neural networks. A large number of synthetic models with horizontal layers are created, and common-midpoint gathers are simulated from those models as training samples. Transfer learning is applied to fine tune the networks with a small number of samples for testing with synthetic and field data from more complicated (2D) models. Tests using synthetic data show that both the regression and classification networks can give reasonable velocity predictions from semblances, but the regression network gives higher accuracy.