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.

Abstract: Volume imaging of geological structures and/or man-made objects having physical property using geophysical field sources and/or sensors mounted from at least one data acquisition system. The sources may include natural field sources and/or man-made sources. The sensors may measure at least one component of the geophysical field. The subsets of the geophysical survey formed by the at least one source of geophysical data are selected, and the integrated sensitivity subdomains for selected subsets of the survey are determined by determining the volumes where the integrated sensitivity of the subset is greater than a predetermined threshold. The total sensitivity is determined as the superposition of the sensitivities from all of the integrated sensitivity subdomains.

Abstract: A method for terrain correction of potential field geophysical survey data measured above an examined medium having density and/or magnetization is described, using potential field data including but not limited to gravity and/or magnetic total field and/or vector and/or tensor data. The potential field sensors may measure the gravity and/or magnetic total field and/or vector and/or tensor data at least one receiving position with respect to the examined medium. The terrain of the examined medium may be described by a spatially variable analytic function of the material properties of the examined medium. The terrain response for at least one component of the measured potential field in at least one receiver location (potential field data) may be calculated using special form of surface integral over the terrain based on 3D analog of the Cauchy-type integrals. This surface integration ensures accurate representation of the terrain response.