Joint inversion of gravity and magnetic data using indicator functions

Gravity and magnetic joint inversion using petrophysical information can recover more accurate geophysical models, but the petrophysical constraints often require complex objective functions. We introduce a simple and efficient mathematical device called indicator functions to couple multiple physical properties determined from petrophysical information. The indicator function is flexible enough to represent arbitrary ranges and relationships of multiple physical property parameters by a set or a union of several subsets. Our objective function combines the indicator function with the L1-norm regularization for more accurate and stable results. Such objective function involving non-differentiable terms is then conveniently solved by an extended version of the alternating direction method of multipliers (ADMM). ADMM treats each term in the objective function as an independent subproblem that can be solved easily and quickly in parallel, and has the advantage of solving some non-differentiable terms. To demonstrate the performance of the indicator function and ADMM, we apply our method to the gravity and magnetic data synthesized from the realistic model of DO-27 kimberlite pipe at Tli Kwi Cho in northern Canada. The results show that our new inversion method has improved accuracy and efficiency while being simple.