Seismic modeling by demigration

Abstract

Kirchhoff‐type, isochron‐stack demigration is the natural asymptotic inverse to classical Kirchhoff or diffraction‐stack migration. Both stacking operations can be performed in true amplitude by an appropriate selection of weight functions. Isochron‐stack demigration is closely related to seismic modeling with the Kirchhoff integral. The principal objective of this paper is to show how demigration can be used to compute synthetic seismograms. The idea is to attach to each reflector in the model an appropriately stretched (i.e., frequency‐shifted) spatial wavelet. Its amplitude is proportional to the reflection coefficient, transforming the original reflector model into an artificially constructed true‐amplitude, depth‐migrated section. The seismic modeling is then realized by a true‐amplitude demigration operation applied to this artificially constructed migrated section. A simple but typical synthetic data example indicates that modeling by demigration yields results superior to conventional zero‐order ray theory or classical Kirchhoff modeling.

The stationary phase analysis of the Kirchhoff-type demigrated field

“…(7) The amplitude distortion effect is discovered. This effect is not mentioned in all of the published works (e.g., Tygel et al, 1996;Jaramillo and Bleistein, 1999;Santos et al, 2000;Sun, 2002aSun, , 2002b.…”

“…Whether the two conditions are reasonable is the subject of future investigation. Furthermore, besides imaging, the Kirchhoff-type demigration operator is also used as a modeling operator (Santos et al, 2000) for computing synthetic seismograms. As indicated in the work cited here, modeling performed by demigration needs to construct the depth-migrated image with E m ≡ 1 artificially.…”

Wave equation-based imaging of mode converted waves in ultrasonic NDI, with suppressed leakage from nonmode converted waves

“…Numerical simulations may be accurate, but time consuming. Therefore, we used a more efficient analytical approach to determine the L-L arrivals from the reflectivity model, called de-migration [32]- [34]. In our experience, this approach is at least 10 times faster than the above-mentioned methods.…”

Coupling Modeling and Migration for Seismic Imaging

“…Note that this combined operator, defined in the data domain, can also be interpreted as the Hessian of an alternative objective function (Ferguson, 2006). Although expensive, this process provides a good data interpolation (and even extrapolation) technique because it accounts more correctly for the propagation effects in the reflector overburden (Santos et al, 2000). With the use of the same model m for the modeling and migration parts, the kinematic aspect of the wave propagation is preserved (Bleistein, 1987).…”

“…We can distinguish between methods that rely on a direct inversion of the combination of migration and demigration (Ferguson, 2006;Stolt, 2002) and methods that consecutively apply the migration and modeling operators to reconstruct the data at the new locations. The latter methods can be separated into algorithms based on partial prestack migration (Chemingui & Biondi, 2002;Ronen, 1987) and those based on full prestack migration, either with a Kirchhoff operator (Duquet et al, 2000;Nemeth et al, 1999;Santos et al, 2000) or with a wavefield-continuation operator (Kaplan et al, 2010;Kühl & Sacchi, 2003;Trad, 2003).…”