A line spacing compression method and an improved minimum curvature operator for grid interpolation of airborne magnetic surveys

Michael D. O’Connell; Matthew Owers

doi:10.1071/EG08016

RESEARCH ARTICLE

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A line spacing compression method and an improved minimum curvature operator for grid interpolation of airborne magnetic surveys

Michael D. O’Connell ¹ ³ Matthew Owers ²

+ Author Affiliations

- Author Affiliations

¹ 1679 Laurelwood Place, Ottawa, Ontario K1C 6Y4, Canada.

² Fugro Airborne Surveys, 65 Brockway Road, Floreat, Perth, WA 6014, Australia.

³ Corresponding author. Email: moconnell_phys@hotmail.com

Exploration Geophysics 39(3) 148-154 https://doi.org/10.1071/EG08016
Submitted: 5 May 2007 Published: 22 September 2008

Abstract

We have modified the minimum curvature gridding method to cope with various flight line gaps, by employing a line spacing compression technique. The line spacing compression method was applied to magnetic data from a survey in northern Canada and was able to smoothly interpolate across the unevenly spaced lines without creating false anomalies. We have also derived a new, longer minimum curvature operator to handle flight lines of various lengths. The longer operator was applied to South Australia Salinity Project data and it removed the artificial boundaries at changes in flight line spacing and smoothly interpolated anomalies even over wider flight line gaps.

Key words: anisotropy, gridding, magnetics, minimum curvature, variable line spacing.

Acknowledgments

We thank Richard Smith, Pierre Keating and an anonymous reviewer for their comments and suggestions and to Fugro Airborne Surveys for allowing publication. The aeromagnetic data in Figures 5–7 were acquired for the South Australian Salinity Mapping and Management Support Project funded by the National Action Plan for Salinity and Water Quality. The National Action Plan for Salinity and Water Quality is a joint initiative between the State and Commonwealth Governments. Fugro Airborne Surveys acknowledges their permission to use these data.

References

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| Crossref | GoogleScholarGoogle Scholar | Marcotte D. L. , Hardwick C. D. , Lemieux J. , O’Connell M. D. , and Reford M. , 1990, Aeromagnetic gradiometry methods: A study using real data: 60^th Annual International Meeting, SEG, Expanded Abstracts, 584–586.

O’Connell M. D. , and Smith R. S. , 2005, Recent improvements to bi-directional gridding using Akima spline with minimum curvature and tension [Web document]. Available at: http://www.fugroairborne.com/resources/technical_notes/time_domain_em/pdfs/Akima_tension_III.pdf (accessed 9 August 2008)

O’Connell, M. D., Smith, R. S., and Vallée, M. A., 2005, Gridding aeromagnetic data using longitudinal and transverse horizontal gradients with the minimum curvature operator: Leading Edge 24, 142–145.
| Crossref | GoogleScholarGoogle Scholar | Sheriff R. E. , 1991, Encyclopedic Dictionary of Exploration Geophysics: Vol. 1, Geophysical References Series, Society of Exploration Geophysicists.

Smith, R. S., and O’Connell, M. D., 2005, Interpolation and gridding of aliased geophysical data using constrained anisotropic diffusion to enhance trends: Geophysics 70, V121–V127.
| Crossref | GoogleScholarGoogle Scholar | Webring M. , 1981, MINC: A gridding program based on minimum curvature: U.S. Geological Survey Open File Report, 81–1224.

Appendix

A SOLUTION OF FINITE-DIFFERENCE EQUATIONS FOR PROFILES

For interpolated points near an observation along a profile, w_n , Briggs’ (1974) equations 15 to 21 can be modified to have two b_j values, and ξ is defined as the distance from the profile location, i, to the observation point at y_n :

and for the point near the observation,

where u_k is the closest value on the profile. Note that all distances are in units of grid intervals.

Smith and Wessel (1990) describe a formulation to include tension (T) in the 2D minimum curvature algorithm (Briggs, 1974) that will give continuous second derivatives and relax the minimum curvature constraint. Smith and Wessel’s (1990) equations, A-4 and A-7, are modified to the 1D case.

O’Connell and Smith (2005) show that

and for the point near the observation, Eqn (A-3) becomes

where the subscript k = ±1 and u_i ₊ _k is the interpolated point on the profile that is nearest to w_n . The tension, T, can take on values in the range of [0,1].