Method of simultaneous imaging of different physical properties using joint inversion of multiple datasets

Abstract

A method for the simultaneous imaging of different physical properties of an examined medium from the simultaneous joint inversion of multiple datasets of physical field measurements is described. The method introduces Gramian spaces of model parameters and/or their transforms, and Gramian constraints computed as the determinants of the corresponding Gram matrices of the model parameters and/or their transforms. Gramian constraints are introduced as additional regularization terms, and their minimization enforces the correlation between different model parameters and/or their transforms. The method does not require a priori knowledge about specific analytical or empirical or statistical correlations between the different model parameters and/or their attributes, nor does the method require a priori knowledge about specific geometric correlations between different model parameters and/or their attributes. The method is a generalized in that it can be applied to the simultaneous joint inversion of any number and combination of physical field measurements.