Magnetic multipoles: forward modelling the gradient tensor, and hybrid global/linearised inversion

Abstract

With magnetic gradiometry emerging as a new tool for geophysical exploration, the mathematical modelling of gradient fields is necessary for interpretation of field measurements. Magnetic multipoles may be useful for the modelling of complex geological sources, and so formulae for their field responses are presented here in Cartesian form. The formulae required for the forward modelling of the magnetic gradient tensor can be expressed as a set of linear equations. This fact is exploited to create a hybrid global and local inversion technique whereby simulated multipoles must satisfy the gradient tensor measurements for more than a single measurement. The inversion process yields subsurface images showing the variation of multipole moment components, as each component is calculated to satisfy measured components of the magnetic gradient tensor. The images exhibit high probability (or small variance) if a multipole is found. The inversion routine is quick, and can be applied automatically to data as it is being collected, or applied to an already complete data set.