Simulating migrated and inverted seismic data by filtering a geologic model

Abstract

The simulation of migrated and inverted data is hampered by the high computational cost of generating 3D synthetic data, followed by processes of migration and inversion. For example, simulating the migrated seismic signature of subtle stratigraphic traps demands the expensive exercise of 3D forward modeling, followed by 3D migration of the synthetic seismograms. This computational cost can be overcome using a strategy for simulating migrated and inverted data by filtering a geologic model with 3D spatial-resolution and angle filters, respectively. A key property of the approach is this: The geologic model that describes a target zone is decoupled from the macrovelocity model used to compute the filters. The process enables a target-oriented approach, by which a geologically detailed earth model describing a reservoir is adjusted without having to recalculate the filters. Because a spatial-resolution filter combines the results of the modeling and migration operators, the simulated images can be compared directly to a real migration image. We decompose the spatial-resolution filter into two parts and show that applying one of those parts produces output directly comparable to 1D inverted real data. Two-dimensional synthetic examples that include seismic uncertainties demonstrate the usefulness of the approach. Results from a real data example show that horizontal smearing, which is not simulated by the 1D convolution model result, is essential to understand the seismic expression of the deformation related to sulfate dissolution and karst collapse.

Controlled-source interferometric redatuming by crosscorrelation and multidimensional deconvolution in elastic media

“…The interferometric PSF has a lot in common with the resolution function or PSF as we find it in seismic migration (Schuster and Hu, 2000;Thorbecke and Wapenaar, 2007;Toxopeus et al, 2008;van Veldhuizen et al, 2008). Interferometry by multidimensional deconvolution as such can be compared with migration deconvolution (Hu et al, 2001;Yu et al, 2006;Zhang and Ulrych, 2010).…”

Point‐spread functions for interferometric imaging

“…Lecomte () and Toxopeus et al . () showed that seismic images can be simulated by filtering a geological model with the migration point‐spread function. In a similar way, interferometric images can be simulated by filtering a geological model with the interferometric migration point‐spread function.…”

“…We could replace the grid of point scatterers by any other object to analyse how such an object would be imaged by physical sources or virtual sources. Lecomte (2008) and Toxopeus et al (2008) showed that seismic images can be simulated by filtering a geological model with the migration point-spread function. In a similar way, interferometric images can be simulated by filtering a geological model with the interferometric migration point-spread function.…”

Imaging velocity and attenuation scatterers with wave equation migration

“…For a delta-function source at position x s with wavelet w(ω), S = w(ω)δ(x − x s ), the solution at some receiver location x r can be expressed by equation (3.2.1) of Bleistein et al (2000), which in our notation becomes (Devaney, 1984;Gjøystdal et al, 2002) or resolution function (von Seggern, 1991;Wapenaar, 1997;Chen and Schuster, 1999;Berkhout et al, 2001;Toxopeus et al, 2004Toxopeus et al, , 2008. Lailly (1983) and Tarantola (1984) showed that the gradient or sensitivity of the least-squares error functional is a migration image.…”