# Development of an Inversion Method for Low Velocity Medium

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2013.45.1.8## Keywords:

Eikonal-solver method, Fermat principle, knot-point parameterization, low velocity structure, pseudo-bending method## Abstract

The main problem with the inversion of a low velocity medium is the application of an appropriate ray tracing method after choosing a suitable model parameterization. Block parameterization is not suitable, because it is not capable of representing the velocity model well. A large amount of blocks with a small grid size are needed to express the model well, but in that case, a ray coverage problem will be encountered. A knot-point parameterization model is better suited than a block model, because it can express the velocity model well, while the number of variables is much smaller. Ray calculation using the pseudo-bending method is not appropriate for the velocity model because of an instability problem at high velocity gradients. The crucial problem of this method involves the initial ray-path that is optimized in order to obtain the "true" ray, but does not satisfy the Fermat principle. These problems can be solved by applying the eikonal-solver method, because this can handle high-velocity gradients and does not need an initial ray path. Using a suitable model parameterization and appropriate ray tracing method, the inversion can obtain good results that fit the desired output. Applying a block model and the pseudo-bending method will not produce the desired output.## References

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