It is very important to estimate the velocity model of the earth with seismic data inversion. Inverse theory concerns the problem of making inferences about physical systems from indirect noisy measurements. Information about the noise in the observations is essential to solve any inverse problem, because in the absence of this information it is impossible to say what mode is better. So in the absence of repeated measurements, it is very important to be able to estimate noise component in the data. In practice, however, one seldom has a direct estimate of noise. Here, we use Tikhonov regularization with L-curve method to construct a reference model of the system. Differences between the data predicted for this reference model and the observations represent an initial estimate of the noise. We then use the resulting noise variance estimate to determine optimally truncated singular value decomposition (OTSVD) and solve inverse problem. We use this method with synthetic examples of downhole data.
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