Abstract

Different methods for estimating parameters in a layered geologic model are discussed. Traveltime parameters, estimated from seismic data, are used to estimate the layer parameters defining the velocity function in each layer and the interfaces between the layers.Seismic measurement data are assumed to consist of a sum of nonoverlapping reflected pulses and additive white Gaussian noise. An estimate of the covariance of the traveltime parameters is then given by the inverse of Fischer's information matrix. It is shown how the information matrix can be computed theoretically or directly from data. Expressions for the covariance matrix of the layer parameters are given. The results can be used to compute confidence regions for the estimated parameters.Optimal seismic measurement systems are discussed, resulting in a criterion for designing an optimal seismic pulse: The energy of the derivative of the received signal (the source pulse convolved with the impulse response of the earth and the impulse response of the instruments) should be maximized.Parameter estimation in a horizontally layered model is considered as an example, and the covariance matrix of the layer velocity and layer thickness is given explicitly.

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