Abstract
This paper presents a Straightforward Inversion Scheme (SIS) for interpreting one-dimensional magnetotelluric sounding data. The basic steps of SIS are (i) parameterization of the layered model such that the layer thickness, expressed in units of its skin depth, is a constant (α); (ii) expansion of the reflection function at each interface as a power series in parameter u = exp(-2(1 +j)α√f);(iii) development of a recurrence relation between the coefficients of the same powers ofu in the power series of reflection functions of any two successive layers; (iv) estimation of the impedance power series coefficients using regressed minimum norm estimator; and (v) evaluation of layer resistivities and thicknesses using the inverse recurrence relation. The power of SIS is established by inverting four synthetic data sets and two field data sets. The effect of noise is extensively studied on a synthetic data set, deliberately corrupted with increasing levels of Gaussian random noise up to 25%. It is found that the scheme can retrieve broad features of the true model even with noise levels as high as 25%. On the basis of findings of different experiments conducted on SIS, it is concluded that SIS is an efficient, robust algorithm with high resolving power. Further, being linear, it is non-iterative and it dispenses with the requirement of having to choose an initial guess model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adam A 1990 Personal communication.
Anderssen R S 1975 On the inversion of global electromagnetic data;Phys. Earth Planet. Int. 10, 292–298
Backus G E and Gilbert J E 1970 Uniqueness in the inversion of inaccurate gross earth data;Philos. Trans. R. Soc. London,266, 123–192
Barcilon V 1982 An explicit method for solving the geomagnetic induction problem;Geophys. J. R. Astron. Soc. 70, 205–215
Berdichevsky M N and Zhdanov M S 1984,Advanced theory of deep geomagnetic sounding, Elsevier.
Bostick F X Jr 1977 A simple almost exact method of MT analysis; inWorkshop on electrical methods in geothermal exploration (Univ. of Utah, Salt Lake City)
Cagniard L 1953 Basic theory of the magnetotelluric method of geophysical Prospecting;Geophysics,18, 605–635
Chave A D and Booker J R 1987 Electromagnetic induction studies;Rev. Geophys. 25, 989–1003
Fischer G, Schnegg P A, Peuiron M and Liquang B V 1981 An analytic one-dimensional magnetotelluric inversion scheme;Geophys. J. R. Astron. Soc. 67, 257–278
Gelfand I M and Levitan R M 1955 On the determination of a differential equation by its spectral function;Am. Math. Soc. Trans. Series 2,1, 253–304
Gupta P K, Sri Niwas and Gaur V K 1996 Straightforward inversion of vertical electrical sounding data;Geophysical Prospecting (communicated)
Hermance J F 1983 Electromagnetic induction studies;Rev. Geophys. 21, 652–664
Hohmann, G W and Raiche, A P 1988 Inversion of controlled source electromagnetic data, in Electromagnetic methods in applied geophysics Nabhighian, M N (ed),Theory, Soc. Expl. Geophys. Vol.1
Kunetz G 1972 Processing and interpretation of magnetotelluric soundings;Geophysics,37, 1005–1021
Larsen J C 1975 Low frequency (0.1–0.6c pd) electromagnetic study of deep mantle electrical conductivity beneath the Hawaiian islands;Geophys. J. R. Astron. Soc. 43, 17–46
Loewenthal D 1975 Theoretical uniqueness of the magnetotelluric inverse problem for equal penetration discretizable models;Geophys. J. R. Astron. Soc. 43, 897–903
Manglik A 1988 Backus-Gilbert magnetotelluric inversion, M.Tech. Dissertation, University of Roorkee, Roorkee
Naresh Kumar 1989 Occam’s inversion of geoelectrical data of Saurashtra region, India: M. Tech Dissertation, University of Roorkee
Oldenburg D W 1979 One-dimensional inversion of natural source magnetotelluric observations;Geophysics. 44, 1218–1244
Oldenburg D W 1990 Inversion of electromagnetic data: An overview of new techniques;Surv. Geophys. 11, 231–170
Parker R L 1977 Understanding inverse theory;Annu. Rev. Earth Planet. Sci. 5, 35–64
Parker R L 1980 The inverse problem of electromagnetic induction: Existence and construction of solutions based upon incomplete data;J. Geophys. Res. 85, 4421–4428
Parker R L and Whaler K A 1981 Numerical methods for establishing solutions to the inverse problem of electromagnetic induction,J. Geophys. Res. 86, 9574–9584
Patrick F W and Bostick F X Jr 1969 Magnetotelluric modelling technique, Rep. 59;Elec. Geophys. Res. Lab. University of Texas, Austin
Pedersen J and Hermance J F 1986 Least square inversion of one-dimensional magnetotelluric data: An assessment of procedures employed by Brown University;Surv. Geophys. 8, 187–231
Porstendorfer G 1975 Principles of magnetotelluric prospecting (Berlin; Borntraeger)
Sabatier P C 1974 Remarks on approximation methods in geophysical inverse problem;Proc R. Soc. London,A 337, 49–71
Spies B R and Eggers D E 1986 The use and misuse of apparent resistivity in electromagnetic method;Geophysics 51, 1462–1471
Sri Niwas and Kumar P 1991 Resolving power of direct current and magnetotelluric resistivity soundings in exploring thick sedimentary horizons;Acta. Geod. Geoph. Mont. Hung. 26, 435–452
Varentsov I V M 1983 Modern trends in the solution of forward and inverse 3-D electromagnetic problems,Geophys. Surv. 6, 55–78
Vozoff K 1986 Magnetotelluric methods; Geophysical reprint series No.5,Soc. Expl. Geophys.
Weidelt P 1972 The inverse problem of geomagnetic induction;Z. fur. Geophys. 38, 257–289
Whittall K P and Oldenburg D W 1986 Inversion of magnetotelluric data using a practical inverse scattering formulation;Geophysics 51, 383–395
Whittall K P and Oldenburg D W 1990 Inversion of magnetotelluric data over one-dimensional earth, in SEG Monograph, edited by P Wannamaker
Wu F T 1968 The inverse problems of magnetotelluric sounding;Geophysics,33, 972–978
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gupta, P.K., Niwas, S. & Gaur, V.K. Straightforward inversion scheme (SIS) for one-dimensional magnetotelluric data. Proc. Indian Acad. Sci. (Earth Planet Sci.) 105, 413–429 (1996). https://doi.org/10.1007/BF02842313
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02842313