Two-dimensional velocity models from wide-angle seismic data by wavefield inversion

Abstract

Modern wide-angle surveys are often multi-fold and multi-channel, with densely sampled source and receiver spacings. Such closely spaced data are potentially amenable to multi-channel techniques involving wavefield propagation methods, such as those commonly used in reflection data processing. However, the wide-angle configuration requires techniques capable of handling very general wave types, including those not commonly used in reflection seismology. This is a situation analogous to that faced in cross-borehole seismics, where similar wave types are also recorded. In a real cross-borehole example, we compare pre-stack migration, traveltime tomography and wavefield inversion. We find that wavefield inversion produces images that are quantitative in velocity (as are the tomograms) but are of significantly higher resolution; the wavefield inversion results have a resolution comparable to that of the (qualitative) pre-stack migration images. We seek to extend this novel development to the larger-scale problem of crustal imaging. An essential element of the approach we adopt is its formulation entirely within the temporal frequency domain. This has three principal advantages: (1) we can choose to ‘decimate’ the data, by selecting only a limited number of frequency components to invert, thus making inversion of data from large numbers of source positions feasible; (2) we can mitigate the notorious non-linearity of the seismic inverse problem by progressing from low-frequency components in the data to high-frequency components; and (3) we can include in the model any arbitrary frequency dependence of inelastic attenuation factors, Q(ω), and indeed solve for the spatial distribution of Q. An initial synthetic test with an anomaly located within the middle crust yields a velocity image with the correct structural features of the anomaly and the correct magnitude of velocity anomaly. This is related to the fact that the reconstruction is obtained from forward-scattered waves. Under these conditions, the method thus behaves much like tomography. A second test with a deeper, more extensive anomaly yields an image with the correct velocity polarity and the correct location, but with a deficiency in low and high wavenumbers. In this case, this is because the reconstruction is obtained from backscattered waves; under these conditions the method behaves not like tomography, but like migration. A more extensive test, based on a large wide-angle survey in south-eastern California and western Arizona, demonstrates a real potential for high-resolution imaging of crustal structures. Although our results are limited by the acoustic approximation and by the relatively low frequencies that we can model today, the images are sufficiently encouraging to warrant future research. The problem of local minima in the objective function is the most significant practical problem with our method, but we propose that appropriate ‘layer’ stripping methods can handle this problem.