Interferometric imaging in random media
The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components corresponding to large scale and small scale variations. In practice, the large scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small scale component cannot. Therefore, wavefield reconstruction does not completely describe the recorded data and migrated images are perturbed by artifacts.
There are two possible ways to address this problem: improve wavefield reconstruction by estimating more accurate velocity models and image using conventional techniques (e.g. wavefield cross-correlation), or reconstruct wavefields with conventional methods using the known smooth velocity model, and improve the imaging condition to alleviate the artifacts caused by the imprecise reconstruction.
The unknown component of the velocity model is described as a random function with local spatial correlations. Imaging data perturbed by such random variations is characterized by statistical instability, i.e. various wavefield components image at wrong locations that depend on the actual realization of the random model. Statistical stability can be achieved by local wavefield averaging either in spatial windows defined in the vicinity of the data acquisition locations, or in local windows defined in the vicinity of image points.
The pictures show 3 scenarios of media with random variations of increasing magnitude. The pictures on the left correspond to no random variations in the medium, the pictures in the middle correspond to 30% random variation relative to the background, and the pictures on the right correspond to 60% random variation relative to the background. Waves are generated by 3 active sources in the subsurface. Receivers are located on the surface. Interferometric imaging is more stable than conventional imaging, even in cases of large random velocity variation.
Velocity models and source positions.
Acoustic wavefield movies.
Data recorded on the surface.
Images obtained by conventional imaging (left) and interferometric imaging (right).
ReferencesSava, P.C., Poliannikov, O., 2008, Interferometric imaging condition for wave-equation migration, Geophysics, v. 73, pp. S47-S61. (PDF) (reprint)