L0-norm gravity inversion with new depth weighting function and bound constraints

Delineating geologic features through the inversion of gravity data is an important goal in a range of geophysical investigations. However, it is a well-known fact that gravity data inversion has no inherent depth resolution. In order to overcome this limitation, different depth weighting approaches have been developed. With the purpose of finding an effective and a more convenient way to precisely estimate the depth of the anomalous body, we have tested the most popularly used depth weighting function. Our test showed that it does not properly counteract the decay of the gravity kernel and is strongly dependent on the exponent term. To resolve this, we have proposed a new depth weighting function that can easily be automated and counteracts the depth dependent natural decay of the gravity kernel more appropriately. Through this, the challenges in trial and error selection of the exponent of the old depth weighting function are avoided. The new depth weighing function was then implemented to improve a gravity inversion method, which produces compact and sharp images of the subsurface density distributions. The inversion method is obtained from the minimization of an objective function, which consists of data misfit and L0-norm stabilizing functions, by iteratively reweighted least-squares algorithm. To evaluate the practicality and resolution capability of the method, it was tested using a number of synthetic data sets from geometrically complex models and real data. The inversion results proved the effectiveness of our method in producing geologically acceptable multiple localized bodies with improved depth resolution. This in turn illustrates the applicability of the newly proposed function in the inversion of gravity data.