On one hand, seismic inversion (oil-and-gas E&P) is the procedure for reconstructing earth properties from seismic data (Aki et al.,1977; Aki and Richards, 1980; Bishop et al., 1985; Tarantola, 1987). We are transforming seismic relative impedance contrast into a quantitative rock-property description of a reservoir, at a sedimentary basin-scale.

It may be two main scenarios: prestack or poststack. The prestack elastic impedance combines the benefits framework in which we calibrate and invert non-zero-offset data, with P-wave, S-wave and density logs from key-wells. The purpose is to show the desired fluid anomalies (oil and gas). So, we need the far offset traces / wide-angle trace. Solution is not unique: In a typical 3D seismic survey, the sources and receivers are located only over a portion of the area of interest, not at whole area. And, the solution should depend continuously on the data, otherwise the solution could be unstable, and is important to calibrate with logs. We use commercial E&P seismic inversion softwares, the most common such as H&R, Interwell, Petrel...

On the other hand, wide-angle seismic have the potential to provide detailed knowledge about structures in the Crust and Upper Mantle, studying the relationship between P-wave velocity and density (gravity inversion). There is empirical velocity and density experimental functions over main regions of the world, based on both: lab tests and well-log data, of course, with a range of uncertainties of the relation between velocity and density, in contrast with the E&P Gardner’s relationship, for example.