Small Anomalous Mass Detection from Airborne Gradiometry

This report was prepared by Puttipol Dumrongchai, a graduate student, Division of Geodesy and Geospatial Science, School of Earth Sciences at the Ohio State University under the supervision of Prof. Christopher Jekeli.This report was also submitted to the Graduate School of the Ohio State University as a dissertation in partial fulfillment of the requirements of the Ph.D. degree.A new generation of gradiometer technology is currently under development based on atom interferometry and applicable to ground and airborne mapping of geologic or anthropogenic features with signal strength as low as a few Eötvös, entirely embedded in noise and geological background. With high sensitivities of future airborne gradiometers, it may be possible to detect such anomalous sources with careful data processing. Both the detection and the estimation of parameters of the feature can be solved as an inverse problem in potential theory. However, one can also use methods developed in communications theory, provided one has some a priori, possible uncertain knowledge of the feature in question. We constructed a matched filter as well as a sophisticated estimation technique to detect and characterize particular small mass anomalies within general geologic background noise using individual gradient and six gradient combination measurements at low aircraft/helicopter altitudes of ranges of 10-30m above terrain clearance. Since both detection and estimation portions requires the inversion of large sizes of covariance matrices, we applied an orthogonal transformation to the matrices, which become diagonal and can then be easily inverted. In addition, the performance of the detection and estimation procedures is quantified by standard test statistics. With these tests, probabilities of false alarm and detection may be assigned to the detection results. We present numerical results in different noise circumstances, for instance, a simulation of airborne gradiometry over moderate terrain with the inclusion of 1E/ √Hz instrumental white noise. The proposed approaches are explored and evaluated for their effectiveness in association with location, orientation, size, and depth of a mass anomaly, and in the use of power spectral density (psd) models versus empirical psd’s obtained from the noise backgrounds. The numerical results show that a small anomaly, e.g., 2m x 2m x 10m, is detectable at shallow depths by an appropriate matched filter using, not only the empirical psd’s and the gradient component Γ33, but also the psd models and the six-gradient combination. However, the analysis shows that a strong noise level, low spatial resolution, and unknown depth limit the anomaly detectability. The parameter estimation performed through an iterative least-squares process was shown to be successful in estimating locations, orientations, and depth of the anomaly. Hypothesis testing by means of the F-test was used to quantify the performance of the estimation process

Small Anomalous Mass Detection from Airborne Gradiometry

This report was prepared by Puttipol Dumrongchai, a graduate student, Division of Geodesy and Geospatial Science, School of Earth Sciences at the Ohio State University under the supervision of Prof. Christopher Jekeli.This report was also submitted to the Graduate School of the Ohio State University as a dissertation in partial fulfillment of the requirements of the Ph.D. degree.A new generation of gradiometer technology is currently under development based on atom interferometry and applicable to ground and airborne mapping of geologic or anthropogenic features with signal strength as low as a few Eötvös, entirely embedded in noise and geological background. With high sensitivities of future airborne gradiometers, it may be possible to detect such anomalous sources with careful data processing. Both the detection and the estimation of parameters of the feature can be solved as an inverse problem in potential theory. However, one can also use methods developed in communications theory, provided one has some a priori, possible uncertain knowledge of the feature in question. We constructed a matched filter as well as a sophisticated estimation technique to detect and characterize particular small mass anomalies within general geologic background noise using individual gradient and six gradient combination measurements at low aircraft/helicopter altitudes of ranges of 10-30m above terrain clearance. Since both detection and estimation portions requires the inversion of large sizes of covariance matrices, we applied an orthogonal transformation to the matrices, which become diagonal and can then be easily inverted. In addition, the performance of the detection and estimation procedures is quantified by standard test statistics. With these tests, probabilities of false alarm and detection may be assigned to the detection results. We present numerical results in different noise circumstances, for instance, a simulation of airborne gradiometry over moderate terrain with the inclusion of 1E/ √Hz instrumental white noise. The proposed approaches are explored and evaluated for their effectiveness in association with location, orientation, size, and depth of a mass anomaly, and in the use of power spectral density (psd) models versus empirical psd’s obtained from the noise backgrounds. The numerical results show that a small anomaly, e.g., 2m x 2m x 10m, is detectable at shallow depths by an appropriate matched filter using, not only the empirical psd’s and the gradient component Γ33, but also the psd models and the six-gradient combination. However, the analysis shows that a strong noise level, low spatial resolution, and unknown depth limit the anomaly detectability. The parameter estimation performed through an iterative least-squares process was shown to be successful in estimating locations, orientations, and depth of the anomaly. Hypothesis testing by means of the F-test was used to quantify the performance of the estimation process