Geodetic Science Reports (School of Earth Sciences)http://hdl.handle.net/1811/244852016-05-03T12:44:19Z2016-05-03T12:44:19ZThe Statistical Performance of the Matched Filter for Anomaly Detection Using Gravity GradientsJekeli, ChristopherAbt, Tin Lianhttp://hdl.handle.net/1811/652232015-02-18T07:01:07Z2010-05-01T00:00:00ZThe Statistical Performance of the Matched Filter for Anomaly Detection Using Gravity Gradients
Jekeli, Christopher; Abt, Tin Lian
This document first reviews the theory of detecting a subsurface linear anomaly using the
matched filter applied to observations of the gravitational gradient in the presence of a nominal
gravitational background field and along tracks crossing the anomaly orthogonally or at an
arbitrary angle. The maximum filter output indicates the likely location along the track and, with
appropriate statistical assumptions on the background field and measurement 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 calculated probabilities of either a miss or a
false alarm, respectively. 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 certain signals in typically correlated gravity
fields using observations of elements of the gravity gradient tensor. We also evaluated the
reliability of the hypothesis testing and of the associated calculated probabilities of misses and
false alarms. We found that the hypothesis test that yields the probability of a miss is more
robust than the one for the probability of a false alarm. Moreover, the probability of a miss is
somewhat less than the probability of a false alarm under otherwise equal circumstances. 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.
Finally, we found that the statistical methods apply only to single tracks (one-dimensional
matched filter) and that the matched filter itself performs poorly for multiple parallel tracks (two-dimensional
formulation) crossing a linear anomaly obliquely. Therefore, these methods are
most useful, with respect to both the detection and the probability calculation, for single tracks of
data crossing a linear anomaly (at arbitrary angle).
2010-05-01T00:00:00ZJekeli, ChristopherAbt, Tin LianGlobal Ice Mass Balance and its Contribution to Early Twenty-first Century Sea Level RiseDuan, Jianbinhttp://hdl.handle.net/1811/652222015-02-18T07:01:16Z2014-03-01T00:00:00ZGlobal Ice Mass Balance and its Contribution to Early Twenty-first Century Sea Level Rise
Duan, Jianbin
Originally published as a dissertation (Ph. D.) -- Ohio State University, 2013.
2014-03-01T00:00:00ZDuan, JianbinCovariance expressions for second and lower order derivatives of the anomalous potentialTscherning, C. C.http://hdl.handle.net/1811/367862015-02-18T07:01:18Z1976-01-01T00:00:00ZCovariance expressions for second and lower order derivatives of the anomalous potential
Tscherning, C. C.
Auto- and cross-covariance expressions for the anomalous potential of the Earth and its first and second order derivatives are derived based on three different degree-variance models.
A Fortran IV subroutine is listed and documented that may be used for the computation of auto- and cross-covariance between any of the following quantities: (1) the anomalous potential (T), (2) the negative gravity disturbance/r, (3) the gravity anomaly Δg, (5) the second order radial derivative of T, (6), (7) the latitude and longitude components of the deflection of the vertical, (8), (9) the derivatives of northern and eastern direction of Δg, (10), (11) the derivatives of the gravity disturbance in northern and eastern direction, (12) – (14) the second order derivatives of T in northern, in mixed northern and eastern and in eastern direction.
Values of different kinds of covariance of second order derivatives for varying spherical distance and height are tabulated.
The University Archives has determined that this item is of continuing value to OSU's history.
1976-01-01T00:00:00ZTscherning, C. C.