Model representation by tessellation

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

Assume that we already have estimated the velocity-depth model for the Tertiary section, and that we want estimate the layer velocity for the Cretaceous chalk layer and delineate the reflector geometry associated with the base of that layer. Hence, we may consider the subsurface velocity-depth model made up of two parts — the known part that includes the Tertiary section, and the unknown part that includes the chalk layer and the layers beneath.

Figure 10.6-4  A tessellated earth model in depth — above the surface that represents the base-Tertiary is the known part of the model; below the surface is the unknown part yet to be estimated.

By combining the layer velocities and reflector geometries associated with the known part of the model, create a 3-D velocity-depth model represented in the form of a tessellated volume (introduction to earth modeling in depth). In a tessellated model, the volume associated with each layer is divided into a set of tetrahedra, the size and shape of which depend on the geometry of layer boundaries (Figure 10.6-4). As in the present case study, the estimated velocity and vertical velocity gradient from sonic logs are assigned to each corner of the tetrahedra within the known part of the model. In the unknown part of the model, tetrahedra are populated with constant trial velocities used in the next step (coherency inversion). Tessellated velocity fields can be desirable for efficient ray tracing used in prestack traveltime inversion for velocity estimation. Shown in Figure 10.6-4 is the base-Lower Tertiary layer boundary above which the model is known, and below which is the half-space that includes the layers yet to be determined. Note that the volumes within the known and unknown parts of the model have been subdivided into a set of tetrahedra.

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