Inversion procedures for earth modeling
Series | Investigations in Geophysics |
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Author | Öz Yilmaz |
DOI | http://dx.doi.org/10.1190/1.9781560801580 |
ISBN | ISBN 978-1-56080-094-1 |
Store | SEG Online Store |
Practical methods for estimating layer velocities and delineating reflector geometries can be appropriately combined to form inversion procedures to construct earth models in depth from seismic data. Listed in Table 9-1 are four such combinations.
These combinations are ordered from top to bottom with an increasing level of accuracy. Also, for a given combination, the methods for layer velocity estimation and reflector geometry delineation are compatible. This means that, for instance, if you think you can afford the accuracy of stacking velocity inversion to estimate the layer velocities, it should suffice to perform image-ray depth conversion to define the reflector geometries. Nevertheless, in practice, you may wish to choose other combinations of the methods from the left- and right-hand columns. For instance, the combination of Dix conversion with image-ray depth conversion is another inversion procedure that is used widely. Also, you may be compelled to apply an inversion procedure that involves multiple combinations. For instance, in areas where salt tectonics has caused formation of diapiric structures, the earth model may be estimated in three parts — the overburden above the salt diapir, the salt diapir itself, and the substratum. You may then use coherency inversion combined with poststack depth migration to estimate the overburden model, and image-gather analysis combined with prestack depth migration to define the base-salt geometry and estimate the substratum model.
Figure 8.0-11 The response of a point diffractor buried in a medium with strong lateral velocity variation (top frame) is a skewed hyperbola with its apex shifted to the left of the true position. Time migration no longer is a valid process; instead, depth migration is needed.
Figure 8.0-12 The response of a point diffractor buried in a medium with mild to moderate lateral velocity variation (top frame) is a slightly skewed hyperbola with its apex shifted to the left of the true position. Time migration still can be an acceptable way to image the diffractor.
Figure 8.0-13 The response of a point diffractor buried in a medium with severe lateral velocity variation (top frame) is a distorted traveltime curve that implies false structural features. Time migration no longer is acceptable; instead depth migration is imperative.
The following are the general guidelines for implementing the procedures listed in Table 9-1. For convenience, we shall refer to these procedures with keywords — vertical stretch, map migration, poststack depth migration, and prestack depth migration. The primary consideration in the choice for an inversion procedure is the degree of lateral velocity variations and the complexity of reflector geometries. A mild-to-moderate lateral velocity variation is associated with a zero-offset diffraction response that is represented by a skewed, but almost hyperbolic traveltime trajectory (Figure 8.0-12). A strong lateral velocity variation is associated with a zero-offset diffraction response that is represented by a distorted, nonhyperbolic traveltime trajectory (Figure 8.0-11). A severe lateral velocity variation is associated with a zero-offset diffraction response that is represented by a complex, multivalued traveltime trajectory (Figure 8.0-13).
- Vertical Stretch: A combination of Dix conversion of stacking velocities to estimate layer velocities and vertical-ray time-to-depth conversion of time horizons picked from a time-migrated volume of data to delineate reflector geometries: This is a procedure appropriate for cases with negligible ray bending at layer boundaries, gentle dips, and lateral velocity variations judged to be within the bounds of time migration.
- Map Migration: A combination of stacking velocity inversion to estimate layer velocities and image-ray time-to-depth conversion of time horizons picked from a time-migrated volume of data to delineate reflector geometries: This is a procedure appropriate for cases with moderate ray bending at layer boundaries, moderate vertical velocity gradients, and moderate lateral velocity variations.
- Poststack Depth Migration: A combination of coherency inversion to estimate layer velocities and poststack depth migration to delineate reflector geometries: This is 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.
- Prestack Depth Migration: A combination of image-gather analysis to estimate and update layer velocities, and stacking of image gathers to delineate reflector geometries: This is a procedure appropriate for cases with significant ray bending at layer boundaries, and severe lateral velocity variations associated with salt and overthrust tectonics.
Layer Velocities | Reflector Geometries |
Dix conversion of rms velocities | vertical-ray time-to-depth conversion (vertical stretch) |
stacking velocity inversion | image-ray time-to-depth conversion (map migration) |
coherency inversion | poststack depth migration |
image-gather analysis | prestack depth migration |
The inversion methods listed in Table 9-1 are used to estimate an initial earth model in depth. Seismic inversion also is used to update the estimated model (model updating). A common application of inversion to estimate the errors in the initial model parameters — layer velocities and reflector depths, is reflection traveltime tomography. Tomographic inversion involves perturbing the model parameters by a small amount so as to match the modeled reflection traveltimes with the observed traveltimes. Refraction traveltime tomography (Section C.9) and reflection traveltime tomography (Section J.6) both are based on the assumption that the perturbation required to update the model parameters is very small compared to the spatial variations in the model parameters themselves. In practice, tomography is best used strictly to touch-up a carefully estimated earth model based on some plausable geologic constraints; it should never be used by itself to estimate the model.
See also
- Introduction to earth modeling in depth
- Inversion methods for data modeling
- Velocity-depth ambiguity
- Model representation and visualization