Summary
The essential component of gravity modeling is an initial model with arbitrary shape having regular geometry. This regular geometry approximates causative body of irregular geometry. For best approximation of causative bodies using regular geometry one requires several polygons represented by many vertices, which are perturbed during global optimization to achieve best model that fits the anomaly. We have circumvented the choice of multi-face regular polygonal initial model by using Lp norm modified Voronoi tessellation. This tessellation scheme provides realistic irregular (fractal) geometry of the causative body using a few parameters known as Voronoi centers, which makes inversion algorithm faster as well as provides an irregular realistic final model for the causative body.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnold JF, Siegert (1942) A mechanical integrator for the computation of gravity anomalies. Geophysics 74: 354–366
Bhattacharya BK, Navolio ME (1976) A fast Fourier transform method for rapid computation of gravity and magnetic anomalies due to arbitrary bodies, Geophys Prosp 20: 633–649
Bott MHP (1960) The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins. GJRAS 3:63–67
Carbato CE (1965) A least squares procedure for gravity interpretation. Geophysics 30:228–233
Dimri VP (1992) Deconvolution and inverse theory. Elsevier Science Publishers, Amsterdam London New York Tokyo
Dimri VP (2000) Fractal dimension analysis of soil for flow studies. In: Application of fractals in earth sciences, edited, V.P. Dimri, pp 189–193, A.A. Balkema, USA
Dimri VP (2000) Crustal fractal magnetisation. In: Application of fractals in earth sciences, edited, V.P. Dimri, pp 89–95, A.A. Balkema, USA
Fortune S (1987) A sweepline algorithm for Voronoi diagrams. Algorithmica 2:153–174
Ferguson JF, Felch RN, Aiken CLV, Oldow JS, Dockery H (1988) Models of the Bouguer gravity and geologic structure at Yucca Flat Navada. Geophysics 53: 231–244
Gregotski ME, Jensen OG, Akrani-Hamed J (1991) Fractal stochastic modeling of aeromagnetic data. Geophysics 56:1706–1715
Gupsi F (1992) Three-dimensional Fourier gravity inversion with arbitrary gravity contrast. Geophysics.57: 131–135
Korvin G (1992) Fractal models in the earth sciences, Elsevier Science Publishers, Amsterdam London New York Tokyo
Lee DT (1982) On k — nearest neighbours Voronoi diagrams in the plane, IEEE Transactions on Computers C-31: 478–487
Li Y, Oldenburg DW (1997) Fast inversion of large scale magnetic data using wavelets. 67th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 490–493
Li Y, Oldenburg DW (1998) 3D inversion of gravity data. Geophysics 63: 109–119
Mandelbrot BB (1983) The Fractal Geometry of Nature. WH Freeman & Company, San Francisco
Maus S, Dimri VP (1994) Fractal properties of potential fields caused by fractal sources. Geophys Res Lett 21: 891–894.
Maus S, Dimri VP (1995) Potential field power spectrum inversion for scaling geology: J Geophys Res 100: 12605–12616
Maus S, Dimri VP (1996) Depth estimation from the scaling power spectrum of potential fields? Geophys J Int 124: 113–120
Moharir PS, Maru VM, Srinivas S (1999) Lemniscates representation for inversion of gravity and magnetic data through nonlocal optimization. Proc Ind Acad Sci (Earth & Planet Sci) 108:223–232
Negi JG, Garde SC (1969) Symmetric matrix method for gravity interpretation. Jour Geophys Res 74: 3804–3807
Nettleton L (1940) Geophysical prospecting for oil. McGraw Hill Book Co.
Nettleton LL (1942) Gravity and magnetic calculations. Geophysics 7:293–310
Oldenburg DW (1974) The inversion and interpretation of gravity anomalies. Geophysics 39:526–536
Okabe A, Barry B, Sugihara K (1992) Spatial tessellations: Concepts and applications of Voronoi diagrams. John Wiley & Sons
Parker RL (1973) The rapid computation of potential anomalies. Geophys J.R. Astr. Soc., 31: 447–455
Pilkington, M., Todoeschuck, J.P.(1993) Fractal magnetization of continental crust. Geophys. Res. Lett., 20: 627–630
Sergio E. Oliva, Claudia L. Ravazzoli (1997) Complex polynomials for the computation of 2D gravity anomalies. Geophys. Pros. 45: 809
Talwani M, Worzel JL, Landisman M (1959) Rapid gravity computations for twodimensional bodies with application to the Mendocino submarine fracture zone. J. Geophys. Res. 64: 49–59
Talwani M, Ewing M (1960) Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape, Geophysics 25: 203–225
Talwani M, Heirtzler J.(1964) Computation of magnetic anomalies caused by 2-D structures of arbitrary shapes. In: Compt. Min. Ind. Part 1, Stanford Univ. Geo.Sci., 9
Tanner, J.G., 1967, An automated method of gravity interpretation, Geophys. J. R. Astr. Soc. 13: 339–347
Tikhonov AN (1963) Solution of incorrectly formulated problems and the regularizations method. Soviet Math. Doklady, 4:1035:1038
Tipper J.C., 1990, A straight forward iterative algorithm for the planar Voronoi diagram, Information Process Letters 34:155–160
Turcotte D., 1997, Fractals and Chaos in Geology and Geophysics, 2nd edition,: Cambridge University Press, Cambridge, New York
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dimri, V.P., Srivastava, R.P. (2005). Fractal Modeling of Complex Subsurface Geological Structures. In: Dimri, V.P. (eds) Fractal Behaviour of the Earth System. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26536-8_2
Download citation
DOI: https://doi.org/10.1007/3-540-26536-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26532-0
Online ISBN: 978-3-540-26536-8
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)