2012 Honorary LecturerSponsored by Shell

Central & South America

Eduardo Filpo

PETROBRAS E&P/Exploration Rio de Janeiro, Brazil

Image ray time-to-depth conversion and model ray applications


Eduardo Filpo

Although the use of prestack depth migration (PSDM) images has become a standard procedure recently, the imaging in time, associated with time-to-depth conversion, is still largely used for two reasons: lower cost in computational terms and it does not need an extremely accurate velocity field. Time-to-depth conversion using Dix inversion and vertical-stretching algorithms have restricted applicability because they are based on the assumption of one-dimensional seismic models.

In this lecture, I explore the concept of image rays to present techniques that assume three-dimensional, smoothed seismic models, which are much more geological. The key is to apply an image-wavefront construction algorithm that uses the velocity field in time. This algorithm is used not only to trace rays and wavefronts, but also to convert the time velocity field to depth.

The set of image rays and its corresponding wavefronts establish a curvilinear coordinate system that can be applied to solve problems associated with conversion from time-to-depth and vice versa. In this perspective, the time-to-depth conversion of seismic attributes can be performed as a simple coordinate transformation in which a vertical grid line of the Cartesian system (seismic trace) is mapped into an image ray and a horizontal line (time slice) into an image wavefront.

In the inverse problem (i.e., the depth-to-time conversion), vertical grid lines in depth are mapped into curves in the time domain. These curves are determined by a differential equation that is very similar to the eikonal equation. Because of this similarity, I suggest denominating them model rays. Model ray tracing can be applied to solve several problems related to depth-to-time conversion, such as building synthetic seismograms, time conversion of PSDM images, well calibration, and construction of hybrid migration algorithms.