Wave Equation Reflectivity Inversion

PGS Wave Equation Reflectivity lnversion (WEl) has been specifically developed to correct for wavefield distortions caused by acquisition and propagation effects. WEI is a wave-equation based reflectivity inversion method that improves the amplitude fidelity and resolution of depth migrated images.

WEI provides images with broader spectra and higher resolution than images from simple migration.

Seismic waves undergo various propagation effects as they travel through the subsurface resulting in alterations in both the amplitude and the frequency content of the recorded seismic signal.

Complex subsurface geology, such as rugose salt bodies similar to the ones in the Gulf of Mexico, results in poor illumination of the underlying geology because of focusing and de-focusing of the seismic wavefield. Moreover, the illumination of the subsurface can be distorted by incomplete or inadequate acquisition geometries that results in uneven coverage of imaging targets. Therefore, the reflectivity of subsurface formations cannot be reliably used to estimate their corresponding rock properties unless the distortions are removed from the migrated image.

WEI illumination strengthIllumination strength underneath a salt body (left). Blue colors represent low and red colors high illumination strength. Grid of scatter points representing the Point Spread Functions (PSF) for the same salt velocity model (right). The more the PSF are focused into a small well localized area, the higher the resolution of the image at that location.

WEI consists of three steps:

  • Depth migration of seismic data
  • Explicit computation of so called Point Spread Functions (PSF) by modeling and migration of discrete scatter points positioned throughout the earth model
  • A deconvolution of the PSF from the migrated image to recover the correct earth reflectivity.

Using WEI not only corrects for illumination effects but it also balances the wave number content of the depth migrated image; henceforth improving the representation of sharp contrast features such as fault boundaries.

Regular migration versus WEIComparison of regular migration and WEI enhanced imaging. WEI balances the wave number content of the final depth migrated image and improves the recovery of sharp contrast features such as fault boundaries.


Example of WEI implementation on Gulf of Mexico data

 

Example of WEI implementation on Gulf of Mexico dataSeismic section from the Gulf of Mexico showing the subsalt reflectivity. Note the effects of the illumination variation due to the focusing and defocusing effects of the base salt.
Migrated image shows uneven illumination due to propagation through a salt body.Migrated image shows uneven illumination due to propagation through a salt body.

WEI image shows more balanced illumination, improved resolution and sharper reflections. WEI image shows more balanced illumination, improved resolution and sharper reflections.