Applied Seismic Inversion for Estimating Earth Models in Depth

Processing and inversion, both are intended to estimate earth models from seismic data. Nevertheless, they differ in one fundamental respect - the output domain. Processing yields an earth model in time, whereas inversion yields an earth model in depth.

A way to judge accuracy of an earth model derived from processing and inversion is by way of time and depth migration, respectively. In fact, we apply these two migration methods to post- and prestack data to derive an earth model itself. Representation of an earth model in time usually is in the form of a velocity field for time migration. Representation of an earth model in depth usually is in the form of a detailed velocity-depth model for depth migration, which comprises two sets of parameters – layer velocities and reflector geometries.

In processing seismic data, we usually make a straight-ray assumption and do not have to honour significant ray bending at layer boundaries. As a result, we obtain earth models with velocities which vary smoothly in the vertical and lateral directions. In contrast, detailed definition of earth models derived from inversion of seismic data with a more stringent requirement in accuracy means that we do have to honour ray bending at layer boundaries, account for vertical velocity gradients and strong lateral velocity variations. Hence, to a large extent, processing can be automated, while inversion requires an interpretive pause at each layer boundary.

A fundamental problem with inversion is velocity-depth ambiguity, which requires independent estimate of layer velocities and reflector geometries. Due to velocity-depth ambiguity, an output from inversion is an estimated velocity-depth model with a measure of uncertainty in layer velocities and reflector geometries. It now is widely accepted that results of inversion are geologically plausible only if there is a sound interpretation effort put into the data analysis. In this context, inversion can be viewed as interpretive processing in contrast with conventional processing.

In practice, there exist several ray- and wave-theoretical methods of estimating layer velocities and delineating reflector geometries. Estimation of velocity-depth models for structural and stratigraphic targets from different exploration basins generally require different procedures which are made up of a suitable combination of inversion methods. What the explorationist wants is not the individual methods, rather a proper combination of appropriate methods - a procedure for inversion, to solve a specific exploration problem. Below are four examples of inversion procedures:

1. A combination of Dix conversion of stacking velocities to estimate layer velocities and vertical-ray depth conversion of time horizons picked from time-migrated volume of data to delineate reflector geometries. A procedure appropriate for cases with negligible ray bending at layer boundaries, and lateral velocity variations judged to be within the bounds of time migration.
2. A combination of stacking velocity inversion to estimate layer velocities and image-ray depth conversion of time horizons picked from time-migrated volume of data to delineate reflector geometries. A procedure appropriate for cases with some ray bending at layer boundaries and significant vertical velocity gradients, and moderate lateral velocity variations.
3. A combination of coherency inversion to estimate layer velocities and poststack depth migration to delineate reflector geometries. A procedure appropriate for cases with significant ray bending at layer boundaries and significant vertical velocity gradients, and strong lateral velocity variations with sharp changes in reflector curvatures.
4. A combination of image-gather analysis to estimate and update layer velocities, and stacking of image gathers from pres tack depth migration to delineate reflector geometries. A procedure appropriate for cases with significant ray bending at layer boundaries and significant vertical velocity gradients, and severe lateral velocity variations associated with salt and overthrust tectonics.

Estimation of earth models in depth may require application of multiple combinations of inversion procedures. For example, in the Southern Gas Basin of the North Sea, which has been subjected to salt tectonics, combination 3 can be used to estimate the earth model within the overburden and combination 4 must be used to estimate the earth model within the subsalt region. In the eastern half of the Gulf of Mexico, where there exist large masses of salt embedded into a thick sand-shale sequence, combination I may be used to estimate the earth model associated with the simple background velocity field for the sand-shale sequence, and combination 4 can be used to refine the model in the subsalt region. I shall present examples of earth models in depth estimated from inversion of seismic data from various exploration basins in the world.