Constrained optimisation of the parameters for a simple isostatic Moho model

In a regional-scale integrated 3D crustal mapping project for the offshore Capel-Faust region, approximately 800 km east of the Australian east coast, gravity data were being used by the Geoscience Australia Remote Eastern Frontiers team to evaluate the viability of an interpretation of the upper crustal sequence that had been derived from a network of 2D seismic lines. A preliminary gravity forward modelling calculation for this sequence using mass density values derived from limited well log and seismic velocity information indicated a long wavelength misfit between this response and the observed data. Rather than draw upon a mathematical function to account for this component of the model response (e.g., low order polynomial), a solution that would lack geological significance, I chose to first investigate whether the gravity response stemming from the density contrast across the crust-mantle boundary (i.e., the Moho) could account for this misfit. The available direct observations to build the Moho surface in the 3D geological map were extremely sparse, however. The 2D seismic data failed to provide any information on the Moho. The only constraints on the depth to this interface within the project area were from 2 seismic refraction soundings. These soundings were in the middle of a set of 11 soundings forming a profile across the Lord Howe Rise. The use of relatively high resolution bathymetry data coupled with an Airy-Heiskanen isostatic model assumption was investigated as a means of defining the form of the Moho surface. The suitability of this isostatic assumption and associated simple model were investigated through optimisation of the model parameters. The Moho depths interpreted from the seismic refraction profile were used as the observations in this exercise. The output parameters were the average depth to the Moho (Tavg), upper crust density (RHOzero), and density contrast across the lower crust and upper mantle (RHOone). The model inputs were a grid of elevation / bathymetry values (H), Moho depth observation values from the seismic refraction soundings (Tm), the water density value (RHOw), and prior estimates and bounds for the output parameters. A number of different deterministic and stochastic inversion methods were used to derive solutions for the optimisation, enabling an evaluation of the uncertainty and sensitivity of the posterior estimates to be carried out. The output parameters that provided the scaling and vertical positioning of an isostatic model Moho surface that best fitted the seismic refraction Moho depths were found to be in general accord with parameters chosen by others when working in similar geological environments. A reasonable match between the Moho surfaces defined from seismic refraction and isostatic methods suggested that the use of an isostatic model assumption was valid in this instance. Further, the gravity response of the 3D geological map was found to match the observed gravity data after making relatively minor adjustments to the geometry of the Moho surface and the upper crustal basin thicknesses. It was thus concluded that the integrated regional 3D geological understanding of the upper crustal and Moho surfaces, and the related mass density contrasts across these units, was consistent with the observed gravity data.