Papers and reports

Unexploded ordnance

Billings, S. D., 2004.  Discrimination and classification of buried unexploded ordnance using magnetometry: IEEE Transactions of Geoscience and Remote Sensing, 42, 1241 - 1251.  PDF 391 kB
In this paper we develop a method for discrimination of unexploded ordnance using magnetometry and apply the methodology to two sites in Montana.

Billings, S. D., Pasion, L. R., Oldenburg, D. W. and Foley, J., 2003,  The influence of magnetic viscosity on electromagnetic sensors: EUDEM-SCOT2 2003, International Conference on Requirements and Technologies for the Detection, Removal and Neutralization of Landmines and UXO, Brussels, September 15-18, 2003 PDF 220 kB
We develop a model of the effect of magnetic viscosity on both the time and frequency domain signal recorded by an electromagnetic sensor.  We concentrate in particular on the effect different pulse lengths and transmitter waveforms have on the time-domain response.

Billings, S. D. and Herrmann, F., 2003,  Automatic detection of position and depth of potential UXO using a continuous wavelet transform:, in Proceedings of SPIE Vol 5089, Detection and Remediation Technologies for Mines and Minelike Targets VII, edited by Russell S. Harmon, John H. Holloway, J.T. Broach, pp 1012-1022. PDF 607 kB
In this paper we develop an Automatic Wavelet Detection (AWD) algorithm, for automatically detecting and characterising dipole anomalies in a magnetic dataset.  

Billings, S. D., Pasion, L. R. & Oldenburg, D., 2003,  Discrimination and classification of UXO using magnetometry: Inversion and error analysis using robust statistics: SAGEEP Conference, San Antonio, April 6-10, 2003 PDF 225 kB
Discusses the selection and use of robust statistical norms for recovering the best fitting dipole parameters for a magnetic anomaly.  The likelihood function that measures the fit between modelled and observed data is chosen to be self consistent: that is the residuals follow the same statistical distribution as the likelihood.  Discrimination and classification ability are enhance by using the robust statistical norm.

Billings, S. D., Stanley, J. M. and Youmans, C., 2002, Magnetic discrimination that will satisfy regulators: UXO Forum 2002, Orlando, September 3-6 2002. PDF 180 kB
Argues that it is possible to structure magnetic discrimination of UXO in such a way that it would be acceptable to the regulatory community.

Billings, S. D., Pasion, L. R. & Oldenburg, D., 2002, Inversion of magnetics for UXO discrimination and identification:  UXO Forum 2002, Orlando, September 3-6 2002. PDF 170 kB
Investigates the potential of eliminating dipole ambiguity in UXO identification by inverting for the higher order magnetic moments of a compact metallic object.

Billings, S. D., Pasion, L. R. & Oldenburg, D., 2002, Discrimination and Identification of UXO by Geophysical Inversion. Phase II: Inversion of Total-Field Magnetic: Technical Report, US Army Corps of Engineers, ERDC\GSL TR-02-16. PDF 2.6 MB
A 49 page report on inversion methodologies for discrimination and identification of UXO's using total field magnetometry.

Billings, S. D., Pasion, L. R. & Oldenburg, D., 2002, UXO discrimination and identification using magnetometry, SAGEEP Conference, Las Vegas, Feb 10-14, 2002 PDF 90 kB
Discusses the use of magnetometer surveys for the discrimination and identification of buried unexploded ordnance.

Gamma-ray spectrometry

Billings, S. D., Minty, B. R. S., Newsam, G. N., 2003, Spatial resolution and deconvolution of airborne gamma-ray spectrometry, Geophysics, 68, 1257-1266.  PDF 1.2 MB
Describes a method for deconvolution of noisy radiometric data and investigates the effect increasing detector height has on spatial resolution.

Billings, S. D. & Hovgaard, J, 1999, Modeling detector response in airborne gamma-ray spectrometry, Geophysics, 64, 1378-1392. PDF 390 kB
This paper presents a geometrical model of gamma-ray detection which accounts for the change in solid angle and thickness of a rectangular detector as the source position changes.

Interpolation and Fourier methods

Billings, S. D. and Newsam, G. N., 2002, Fourier filtering of continuous global surfaces, 14th International Conference on Digital Signal Processing, Santorini, Greece, July 2002. PDF 130 kB
A conference paper that describes a method for Fourier domain filtering of geophysical data using continuous global surfaces.  An example is presented of the calculation of the second vertical derivative of a regional gravity compilation.

Billings, S. D., Beatson, R. K and Newsam, G. N., 2002, Interpolation of geophysical data by continuous global surfaces: Geophysics, 67, 1810-1822. PDF 1.3 MB
A paper that describes a wide class of interpolation methods including thin-plate and tension splines, kriging, sinc functions, equivalent source and radial basis functions that can be encompassed in a common mathematical framework involving continuous global surfaces (CGS).  Recent developments in computational methods are described and an example of gridding a difficult gravity data set is presented.

Billings, S. D., Newsam, G. N. and Beatson, R. K., 2002, Smooth fitting of geophysical data using continuous global surfaces: Geophysics, 67, 1823-1834. PDF 1.9 MB
This paper follows on from the interpolation paper and considers methods for obtaining smooth fits to noisy data.  Examples are given of surface fitting for noisy radiometric data.

Billings, S. D., Newsam, G. N. and Beatson, R. K., 2002, Continuous Global Surfaces and Fourier transformation of geophysical data: Unpublished manuscript. PDF 2.6 MB
Describes methods for Fourier transformation of CGS surfaces.

Beatson, R. K., Light, W. A., and Billings, S. D., 2001, Domain decomposition methods for solution of the radial basis function interpolation equations: SIAM J on Sci. Comput., 22, 1717 - 1740.   PDF 245 kB
A mathematical description of the domain decomposition method which is a key component of the computational scheme for CGS gridding and smooth fitting.

Billings, S. D. & Fitzgerald, D., 1998, An Integrated Framework for Interpolating Airborne Geophysical Data with Special Reference to Radiometrics, PDF 562 kB
A brief non-mathematical description of the CGS interpolation method.

Aeromagnetics

Billings, S.D. & Richards, D, 1999, Quality control of gridded aeromagnetic data, Internal report, Rio Tinto Exploration, Australia Region PDF 5.4 MB
A lengthy report that looks at the influence interpolation methods have on the quality of gridded aeromagnetic data.  A FFT based method for diagnosing problems in gridded images is developed and applied to a number of data sets.

Billings, S. D. & Richards, D., 2001, Quality control of gridded aeromagnetic data, Exploration Geophysics, 31, 611-616. PDF 4.5 MB
Basically a short summary of the quality control report.

Seismology

Billings, S. D., Sambridge, M. S. & Kennett, B. L. N., 1994.  Errors in hypocentre location: picking, model and magnitude dependence.  Bull. seism. Soc. Am. 84, 1978–1990.  (no figures).  PDF 154 KB
Presents a Monte Carlo based method for determining errors in Earthquake hypocenter locations.

Billings, S. D., 1994.  Simulated annealing and earthquake location.  Geophys. J. Int. 118, 680–692.

Billings, S. D., Kennett, B. L. N. & Sambridge, M. S., 1994.  Hypocentre location: genetic algorithms incorporating problem specific information.  Geophys. J. Int. 118, 693–706. 

PhD thesis

Geophysical aspects of soil mapping using airborne gamma-ray spectrometry PDF 8.0 Mb
A lengthy dissertation that investigates the geophysical aspects of surveying with gamma-ray spectrometry.  A geometrical model of gamma-ray detection is developed, as well as a method for determining uncertainty and spatial resolution of gamma-ray surveys.  Interpolation and smoothing fitting techniques based on continuous global surfaces are investigated and methods for Fourier transformation and filtering of these surfaces are developed.  The papers above probably give more readable accounts of these developments.