Comparison of different methods for the estimation of depth, location and source-type of magnetic and gravity fields


1 PhD Student Of Geophysics-Electromagnetism, Institute of Geophysics, University of Tehran,

2 Institute of Geophysics- University of Tehran

3 University of Naples Federico II, Department of Earth Sciences, Environment and Resources


The main goal of interpretation of potential fields (gravity and magnetic) data is determination of the buried source parameters including the depth, horizontal position, the structural index and the physical properties, which is magnetic susceptibility in the magnetic cases and density for gravity fields. For a large number of data it is so expensive modelling the data by using the inversion algorithms. So, in the last decades a variety of algorithms have been developed for source parameters estimate (Nabighian et al, 2005a, b). The depth is often the most important parameter to being determined. Early depth to source methods were mainly graphically. The automatic methods began to appear owing to computers and digital data available in 2D and 3D cases, most of them being field derivative based methods. Many of these approaches have restricted use because of limiting assumptions in their theory.
Since there is no method being the best, it is wise to use a variety of methods. In this paper, firstly, some of the widely used methods are described, such as Euler deconvolution (Thompson, 1982), analytic signal (Nabighian, 1972, 1974), source parameter imaging (SPI) (Thurston and Smith, 1997), Improved source parameters imaging (iSPI) (Smith et al, 1998), enhanced local wavenumber (ELW) (Salem et al, 2005) and ANEUL (Salem and Ravat, 2003). These are applied to a synthetic data produced by a fairly complex model simulating a magnetic basement, in order to estimate the position and structural index of its structures.
The SPI method requires second-order derivatives of the field and uses the local wavenumber concept. The SPI is a fast and automatic method, assuming as source-model either a 2D sloping contact or a 2D dipping thin sheet model; it provides estimates of depth, dip, edge location and physical property contrast. iSPI uses the same concept as in SPI and is applied to 2D data. ELW is a combination of local wavenumber in Euler equation to determine source location and structural index. In this method a window is selected around the local-wave number peaks, and the source position is estimated by solving an over determined problem in each window. Once the source location is estimated, the structural index is obtained by using the main equations of the method. ANEUL is a fully automatic method, whose main equation is obtained by using analytic signal up to order 2 in Euler-homogeneity equation.
Since all the above mentioned methods make use of the field derivatives of different orders, high-quality datasets are needed, otherwise the final results may be affected by even severe errors.
Multiscale methods (Fedi and Pilkington, 2012), are a different class of interpretative methods, based on the behavior of the potential fields at different altitudes. They allow determination of depth, horizontal location and source-type. Taking advantage of a combined use of upward continuation and field differentiation, these methods are very stable and not sensitive to noise as the other methods are.
In this paper, among the several multiscale methods we use DEXP transformation (Fedi, 2007), automatic DEXP (Abbas et al, 2014) and Geometric method (Fedi et al, 2009, 2012). By DEXP transformation the field is calculated at some altitudes and it is scaled by using a power-law of the altitude. The depth can be obtained by finding the extreme points of the DEXP field. Automatic DEXP is based on computing the local wavenumber (of any order) at several latitudes and then scaling with a proper function to estimate the structural index and the source position. This new version of the DEXP transform is fully automatic and does not need any priori information. By the geometric approach, the maxima of the field at various scales are located along lines that are called ridges. Extrapolating the true ridges below the measurement surface, is enough to find the source position at the ridge intersection.
In spite of using noise-free data set in the synthetic case, it is shown that the classical methods do not provide results as accurate as those by multiscale methods. Comparison among more methods and evaluation of their consistency will be really important and practical, in real cases, to evaluate the final results and to make decision about individuating the best ones.
We conclude the paper by applying all the methods to a magnetic profile over a 2D structure, in order to estimate its parameters. None of these methods is restricted to the magnetic fields, and they can be also applied to gravity fields or its derivatives as well.


Main Subjects

بنی‏عامریان، ج. و اسکویی، ب.، 1388، مقایسه نتایج به‏دست آمده از اِعمال روش ANEUL روی داده‏های مغناطیسی، داده‏های منتقل شده به قطب و داده‏های شبه‌‌گرانی، م. فیزیک زمین و فضا، 3، 41-57.
Abbas, M., A., Fedi, M. and Florio, G., 2014, Improving the local wavenumber method by automatic DEXP transformation, Journal of Applied Geophysics, 111, 250-255.
Abbas, M., A. and Fedi, M., 2015, Application of the DEXP method to the streaming potential data, 21st European Meeting of Environmental and Engineering Geophysics, Turin, Italy.
Bracwell, R. N., 2000, The Fourier transform and it application, Mc Graw Hill Press, Third Edition.
Fedi, M. and Florio, G., 2006, SCALFUN: 3D analysis of potential field scaling function to determine independently or simultaneously Structural Index and depth to source, SEG Expanded Abstract, 25, 963-967.
Fedi, M., 2007, DEXP: a fast method to determine the depth and the structural index of potential fields sources, Geophysics, 72(1), I1-I11.
Fedi, M., Florio, G. and Quarta, T., 2009, Multiridge analysis of potential fields, geometric method and reduced euler deconvolution, Geophysics, 74(4), L53-L65, doi: 10.1190/1.3142722.
Fedi, M. and Pilkington, M., 2012, Understanding imaging methods for potential field data, Geophysics 77(1), G13-G24, doi: 10.1190/ geo2011-0078.1.
Fedi, M., Florio, G. and Cascone, L., 2012, Multiscale analysis of potential fields by a ridge consistency criterion: the reconstruction of the Bishop basement, Geophysical Journal international, 188, 103-114.
Florio, G., Fedi, M. and Rapolla, A., 2009, Interpretation of regional aeromagnetic data by multiscale methods: the case of Southern Apennines (Italy), Geophysical Prospecting, 57, 479-489.
Grant, F. S. and Martin, L., 1966, Interpretation of aeromagneticanomalies by the use of characteristic curves, Geophysics, 31, 135-148.
Hinze, W. J., vonFrese, R. B. and Saad, A. H., 2013, Gravity and magnetic exploration principles, Practices and Application. Cambridge University Press.
Hsu, S. K., Coppens, D. and Shyu, C. T. 1998, Depth to magneticsource using the generalized analytic signal, Geophysics, 63, 1947-1957.
Hsu, S. K., 2002, Imaging magnetic sources using Euler’s equation, Geophysical Prospecting. 56, 15-25.
Keating, P., 2009, Improved use of the local wavenumber in potential-field interpretation, Geophysics, 74(6), L75-L85.
Koulomzine, T., Lamontagne, Y. and Nadeau, A., 1970, New methodsfor the direct interpretation of magnetic anomalies caused byinclined dikes of infinite length, Geophysics, 35, 812-830.
Li, X., 2006, Understanding 3D analytic signal amplitude, Geophysics, 71, L13-L16.
Mushayandebvu, M. F., van Driel, P., Reid, A. B. and Fairhead, J. D., 2001, Magnetic source parameters of two-dimensionalstructures using extended Euler deconvolution, Geophysics, 66, 814-823.
Mushayandebvu, M. F., Lesur, V., Reid, A. B. and Fairhead, J. D., 2004, Grid Euler deconvolution with constraints for 2D structures, Geophysics, 69, 489-496.
Nabighian, M. N., 1972, The analytic signal of two-dimensional magnetic bodies with polygonal cross-section: its properties and use for automated anomaly interpretation, Geophysics, 37, 507-517.
Nabighian, M. N, 1974, Additional comments on the analytic signal with two-dimensional magnetic bodies with polygonal cross-section, Geophysics, 39, 85-92.
Nabighian, M. N. and Hansen, R. O., 2001, Unification of Eulerand Werner deconvolution in three dimensions via the generalizedHilbert transform, Geophysics, 66, 1805-1810.
Nabighian, M. N., Ander, M. E., Grauch, V. J. S., Hansen, R. O., LaFehr, T. R., Li, Y., Pearson, W. C., Peirce, J. W., Phillips, J. D., and Ruder, M. E., 2005a, Historical development of the gravity method in exploration, Geophysics, 70, 63ND-89ND.
Nabighian, M. N., Ander, M. E., Grauch, V. J. S.Hansen, R.O., LaFehr, T.R., Li, Y., Peirce, J.W., Phillips, J.D., Ruder, M. E., 2005b, Historical development of the magnetic method in exploration, Geophysics, 70, 33ND-61ND.
Phillips, J. D., Hansen, R. O. and Blakely, R., 2007, The use ofcurvature in potential-field interpretation. Exploration Geophysics., 38, 111-119.
Ravat, D., 1996, Magnetic properties of unrusted steel drumsfrom laboratory and field-magnetic measurements, Geophysics, 61, 1325-1335.
Reford, M. S., 1980, History of geophysical exploration-magnetic method, Geophysics, 45, 1640-1658.
Reid, A. B., Allsop, J. M., Granser, H., Millett, A. J. and Somerton, I. W., 1990, Magnetic interpretation in three dimensions using Euler deconvolution, Geophysics, 55, 80-91.
Salem, A. and Ravat, D., 2003, A combined analytic signal and Euler method ANEUL for automatic interpretation of magnetic data, Geophysics, 68, 1952-1961.
Salem, A., Ravat, D., Smith, R. and Ushijima, K., 2005, Interpretationof magnetic data using an enhanced local wavenumber (ELW) method, Geophysics, 70, 141-151.
Salem, A., Williams, S., Fairhead, D., Smith, R. and Ravat, D., 2008, Interpretation of magnetic data using tilt-angle derivatives,Geophysics, 73, L1-L10.
Silva, J. B. C. and Barbosa, V. C. F. 2003, 3D Euler deconvolution: theoretical basis for automatically selecting good solutions, Geophysics, 68, 1962-1968.
Smellie, D. W., 1956, Elementary approximations in aeromagnetic interpretation, Geophysics, 21, 1021-1040.
Smith, R. S., Thurston, J. B., Dai, T. and MacLeod, I. N., 1998, iSPI- the improved source parameter imaging method, Geophysical Prospecting, 46, 141-151.
Stavrev, P. and Reid, A. B., 2007, Degrees of homogeneity ofpotential fields and structural indices of Euler deconvolution, Geophysics, 72, L1-L12.
Thompson, D. T., 1982, EULDPH: a new technique for making computer assisted depth estimates from magnetic data, Geophysics, 47, 31-37.
Thurston, J. B. and Smith, R. S., 1997, Automatic conversion of magnetic data to depth, dip, susceptibility contrast using the SPI method, Geophysics, 62, 807-813.