
doi: 10.1007/bfb0011773
Apart from variables estimated from data, fixed parameters (e.g. seismic velocity distribution) necessary for theoretical modeling of wave propagation are also involved in the seismic location problems. It is a general feature of all inverse tasks that in spite of “variables” to be estimated from a given data set, the parameters needed for theoretical modeling with values known from somewhere else are present in the problem. The (possibly) erroneous values of these fixed parameters introduce additional errors to the solution of the inverse problem. They sometimes manifest themselves as a shift of the maximum likelihood solution and sometimes lead to a decrease in the accuracy of inversion. If the parameters deviate little from their “true” values the maximum likelihood solution shift is masked by the spread of the a posteriori probability distribution. In this case the standard methods of error estimation based on the a posteriori distribution give reasonable results. On the other hand, for large deviations, the systematic errors become dominating and lead to a completely wrong maximum likelihood solution. Then, error estimation which does not take into account the presence of systematic bias is not reliable.
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