Density Modelling by Monte Carlo Inversion--I Methodology

Abstract

Summary Monte Carlo inversion of geophysical data provides a method of specifying the Earth's density distribution within the uncertainties present in the data. It is possible to estimate the reliability of non-uniqueness bounds defined by a family of randomly generated models by means of a statistical procedure proposed by Anderssen & Seneta. We have devised a technique by which physically realistic models are generated without violating the condition of randomness, to counter the criticism that the method is inherently biased towards complex models. We have also examined a further criticism that the use of variational parameters to calculate theoretical eigenperiods favours the acceptance of -near (as opposed to -far) solutions. The objection is valid in principle, but may be circumvented by the adoption of suitably conservative acceptability criteria for the eigenperiod residuals. Our Monte Carlo technique was used to invert the seismic data from which the model HB2 is derived. The suite of models thus obtained provide a measure of the non-uniqueness inherent in the HB2 data, whilst confirming that the parametric constraints imposed on the density gradient by Bullen & Haddon are entirely compatible with their data. We conclude that major discrepancies between the density models of Bullen & Haddon and those of Press cannot be attributed to methodological differences in the derivation of these models.