Good morning everyone,
I should parameterize in a 3D grid my shear-wave velocity model deduced from receiver function analysis. Considering that the best velocity model which represents a discontinuity in the receiver functions is represented by a step function, how can I solve in 3D the problem of singularity (Dirac delta in mathematical terms) keeping constant (no flexibility) the discontinuity value? Someone knows or can suggest me some papers about this key point, please?
Thank you very much for your big help,
Leonardo
Sorry, but for what purpose are you making a 3-D grid? If it is for display or comparison with other observations, a discontinuity would seem to not be a problem. If it is to then do wave propagation, it depends on the software or algorithm you are intending to use. Most applications are content with a strong gradient rather than a true discontinuity (and receiver functions are sensitive to gradients above some threshold, so the presence of a converted arrival only reflects the presence of a strong gradient, not necessarily a discontinuity).
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