Integrating two or more geophysical datasets is now a common practice as it is of paramount importance to take advantage of all available datasets while constraining sub-surface geology. There are numbers of constraining terms that can be added to the objective function for coupling different properties. Among those, there is the cross-gradient constraint which can be used without any assumption for different methods and different area of studies. However, this constraint only considers the direction of changes in physical properties within the model. The magnitudes of these changes, however, can lead the inversion to a more precise boundary recognition. In this study, we introduce and test a weighted constraint which considers the magnitude as a weighting matrix of the vector product of gradients. The results on a synthetic dataset show a noticeable improvement in model recovery which reveals that the methodology has the potential to be applied to real case scenarios in mineral environments where prior information is available.


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