Locating anomalies by gravity gradiometry using the matched filter with a probabilistic assessment

Abstract

The matched filter can be used to identify the location of a specific signal embedded in background correlated noise. The maximum filter output indicates the likely location and, with appropriate statistical assumptions on the noise, it also serves as a test statistic in the probabilistic evaluation of the filter’s performance. Different setups of the Neyman-Pearson statistical hypothesis test yield predictions of either the probability of a miss or that of a false alarm. The needed statistics of the maximum filter output are properly obtained using the distribution of order statistics. Through Monte Carlo simulations, we analyzed the ability of the matched filter to identify a sub-surface anomaly in typically correlated gravity fields using observations of elements of the gravity gradient tensor. We also evaluated the reliability of the hypothesis testing and the associated predicted probabilities of misses and false alarms. Our simulations and statistical analyses confirm that the power of the tests increases as the signal strength increases and as more gradient tensor components per observation point are included. We also found that the hypothesis test that is designed to predict the probability of a miss is more robust and powerful than the one for predicting a false alarm. Moreover, the probability of a miss is somewhat smaller than the probability of a false alarm under otherwise equal circumstances.