A stable downward continuation method for processing gravity data using the equivalent sources with compactness and smoothing constraints

The downward continuation of the potential field is often a necessary step in data processing and interpretation, in which equivalent source is an available method. Unfortunately, due to the physical property distribution of the equivalent source obtained from the observed data inversion, this is an unstable operation. Particularly in the case of noisy data, the generation of false signals can severely obscure the useful information in the original data. To deal with the instability fundamentally, we have developed a constrained equivalent-source method to improve the physical property distribution in the equivalent layer for stable downward continuation of the gravity anomaly. In this method, the compactness constraint is applied to reduce divergent signals, and multiple smoothing is used to further eliminate the signals causing instability. Experiments on synthetic gravity anomalies show that the proposed method yields cleaner images of the physical properties and more accurate amplitudes of the downward-continuing gravity field. Application to measured data also shows that the proposed method can significantly attenuate the divergent signals and enhance the amplitude of the effective signals.