An important application of 3D ray modelling is in sensitivity analyses, i.e., to calculate how sensitive a certain result (e.g. traveltime) is to the variation of a given model parameter (e.g. velocity). A good example is seismic reflection tomography used to estimates parameters of the velocity model based on observations of reflected events in prestack seismic data. The misfit function (also called objective function or cost function) for reflection tomography was originally formulated in the time domain of the seismic data, but for quite a few years now, it has been popular to use a misfit function in the depth domain In the latter type of approaches it is essential to calculate perturbations in reflection depths resulting when selected model parameters are perturbed. NORSAR have developed a special application of the wavefront construction (WFC) in order to perform ray perturbation calculations efficiently. A small example is illustrated in the figure.
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The figure shows a vertical cross section with a superimposed coarse grid (blue) of P-wave velocity values (velocities are given in each grid node). A selected grid node is indicated (within the red rectangle). For a given depth-migrated shot gather, horizons have been identified. Based on WFC results, two-way rays were reconstructed, and ray perturbation calculations were performed with respect to the selected grid node. The velocity function was evaluated by linear interpolation, which yields an area of influence indicated by the yellow rectangle in the figure. The shown perturbed depths (green) correspond to changing the P-wave velocity in the selected node by +/- 100 m/s, +/- 200 m/s, …, +/- 500 m/s. |
This very efficient WFC based ray perturbation technique is an important tool for generating the coefficients of the large sets of tomographic equations to be solved for updating the seismic velocity parameters. NORSAR is conducting considerable research in this field, and a number of key issues are listed below.
- anisotropic, velocity functions (Vp, Vs, Thomsen parameters, etc.)
- different types of ray paths integrated (reflected, VSP, check-shot, etc.)
- geological constraints (well data, petromarkers, etc.)
- primary and converted waves
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