Abstract for Session 8: Title: 8.1 COMPARISON OF ELECTRIC FIELDS OBTAINED FROM 3D MAGNETIC FIELD CALCULATIONS ON FIXED AND STAGGERED GRIDS Authors: A.K. Agarwal and J.T. Weaver (Department of Physics & Astronomy and School of Earth & Ocean Sciences, University of Victoria, B.C., Canada, V8W 3P6: numod@uvvm.uvic.ca and weaver@uvphys.phys.uvic.ca). Computation of the electric field on fixed grids, either by a simple numerical differentiation of the magnetic field, or by the method commonly employed with staggered grids---integration over the volume of a surface cell to get the electric field at its centre followed by an interpolation to the surface---can sometimes yield inaccurate and erratic results for fixed grid calculations, especially near conductivity boundaries where the contrast is great. In a recent investigation of an E-polarization problem in two dimensions, this problem was overcome by integration around a vertical rectangular column extending from the surface node to the bottom of the grid. With this approach it was found that the computed surface electric field was in excellent agreement with that obtained on a staggered grid. This approach has been generalized to the 3D case to obtain either the surface electric field at the centre of the surface cell or the electric field/current density at the node itself. The method is illustrated by computing electric fields for various models, including some with high conductivity contrasts, and comparisons are made with corresponding results obtained using staggered grids. Good agreement is obtained between the two methods. Title: 8.2 A SPECTRAL APPROACH TO 3D ELECTROMAGNETIC INVERSION Authors: Colin Brown (1) and Grant Caldwell (2) 1 Applied Geophysics Unit, National University Ireland, Galway, Ireland Colin.Brown@ucg.ie 2 Institute of Geological and Nuclear Sciences, Wellington, New Zealand G.Caldwell@gns.cri.nz The paradox in some conventional solutions to the 3D EM inverse problem is that the underlying forward problem requires many small cells over a large volume then an iterative inversion essentially minimises the effective number of parameters describing the conductivity by finding the smoothest distribution commensurate with the data. We are developing a direct inversion of electric and magnetic transfer functions to circumvent the computational burden in these techniques. We expand the differential equations for plane wave excitation in terms of analytic basis functions. This results in a system of equations that relates conductivity to horizontal and vertical derivatives of the transfer functions.We choose orthonormal Hermite and orthogonal Laguerre polynomials as basis functions. The Hermite polynomials are convenient for computing horizontal derivatives and moving between the spatial and wave-number domain. The vertical derivatives are evaluated using an integral equation which incorporates an analytic Green's function. The computation of the integral equation uses a quasi-linear approximation for the Neumann series expansion (electrical reflectivity tensor). The Laguerre polynomials facilitate the computation of Laplace Transforms arising from this integral equation. The inversion is controlled using a singular value decomposition to identify the most significant components needed to represent the conductivity distribution. We will show some theoretical examples. Title: 8.3 2.5D Conductivity Inversion of Airborne EM data Authors: Jiuping Chen, Art Raiche, Fred Sugeng, and James Macnae Cooperative Research Centre for Australian Mineral Exploration Technologies (CRC AMET) School of Earth Sciences, Macquarie University, North Ryde, NSW, Australia, 2109 jchen@laurel.ocs.mq.edu.au We present an inversion method for generating a two-dimensional electrical conductivity model from airborne electromagnetic measurements either in the frequency or time domain. The inversion process is classified as 2.5D, since the two-dimensional conductivity model is excited by a three-dimensional dipolar field. The forward model computation is based on an isoparametric finite-element formulation with quadratic basis and test functions, thus allowing complex structures, including topography, to be included if necessary. A direct frontal solution method is used to solve for the along-strike components of magnetic and electric fields in the Fourier domain. Thus the response of each additional transmitter position can be computed in about five percent of the time required by the first. The sensitivity matrix computation is based on an adjoint equation method which requires one additional source computation for each receiver position. Thus the forward model and sensitivity matrix computation for an entire line of say N positions can be computed in (1 + 0.1 N) times the time required for a single source forward model. A damped eigenparameter approach is utilised to regularise the inversion process, rather than forcing adherence to a priori geological constraints. A test with a set of synthetic AEM data with 3% Gaussian noise demonstrates the viability of this inversion program. Title: 8.5 GENERAL SCHEME OF STABLE NONLINEAR INVERSION OF EM DATA WITHIN PIECE-WISE CONTINUOUS GEOELECTRIC MEDIA Authors: N.G. Golubev, Iv.M. Varentsov (Geoelectromagnetic Research Institute RAS, Troitsk, Russia; e-mail: igemi1@pop.transit.ru) A number of general problems how to achieve both resolution and stability is studied within new algorithms of EM data inversion in models containing both traditional "fixed geometry" parametrization and "scanning windows" with arbitrary conductivity distributions estimated. These distributions are approximated by sets of independent or pseudo-correlated cells and Strakhov's finite functions. The optimization technique for the joint space of data and model parameters is constructed in terms of Tikhonov's regularization within robust functional metrics. Newtonian schemes with adaptive stabilization are involved. Flexible finite difference solutions are presented for the simulation of EM responses and model sensitivities with regulated accuracy. The effective use of a priori information is discussed and a posteriori accuracy estimates are developed. Several 2D schemes and a full 3D approach are considered in details. Title: 8.6 Using Homotopy for Inversion of EM data Authors: Marion Jegen Institute of Theoretical Geophysics Department of Earth Sciences University of Cambridge Downing St. Cambridge, CB2 3EQ U.K. email: jegen@esc.cam.ac.uk Adam Schultz Institute of Theoretical Geophysics Department of Earth Sciences University of Cambridge Downing St. Cambridge, CB2 3EQ U.K. email: adam@esc.cam.ac.uk Most conventional inversion algorithms for EM data use linearised, iterative schemes to minimise the misfit between EM data and forward modeling solutions. Everett (1996) showed that homotopic methods provide an alternate approach for EM inversion, and this was applied to the 2D MT problem. For a discretized earth model, Everett formulated the inverse problem as a solution to a system of polynomial equations. The variables in this system are the conductivities at the grid points; and the coefficients governing the system are functions of the boundary conditions, and include the measured electric and magnetic field data on the model's surface. Using homotopy one can test for the existence of real, positive grid conductivities and also generate the entire list of possible solutions. Unlike other inversion algorithms this method is neither linearised nor dependent on the starting model. We will show how homotopic algorithms can be implemented for real-world EM data, and discuss inversion by homotopy for one- and multi-dimensional earth models. We employ a modern (fortran90) parallelisable homotopic solver, and discuss the advantages and limitations of homotopic inversion for increasingly large and noisy systems. Title: 8.7 Modelling of Complex Electromagnetic Targets using Non-Linear Approximator Techniques Authors: I. R. Murray, C. Alvarez and R. W. Groom PetRos EiKon Incorporated, Georgetown, Ontario, Canada The development of rapid O(N) numerical techniques, initiated by the pioneering of the Localized Non-Linear (LN) Approximator in 1991, offers seemingly endless possibilities for the simulation of realistic electromagnetic situations. Very rapid calculation times and minimal memory requirements offer the potential to simulate more complex and thus more geologically meaningful models than through the use of conventional techniques. Many developments in the LN technique have been attempted, with varying degrees of success, at PetRos EiKon. We will provide an overview of the research and development associated with extending the LN technique to inductive modes, induced polarization, fully rotational prismatic and polyhedral-based primitives, multiple interactions between scatterers, strong DC magnetic effects, combined conductivity, permeability and permittivity contrasts, controlled conversion, and automated gridding of scattering objects. Accuracy of such approximate techniques is a key issue, and the methods have been seen to sometimes far surpass traditional techniques in this regard. As model complexity increases, a need to further accelerate the numerical calculations to meet production situations in exploration environments becomes critical. Since the majority of the model calculation time is in assembling the required Green's functions, techniques will be described for their ge neration over regular grids in conjunction with interpolation algorithms and databasing to reduce modelling times. Title: 8.8 Three-dimensional Magnetotelluric Inversion using Non-Linear Conjugate Gradients Authors: Gregory A. Newman and David L. Alumbaugh Email ganewma@sandia.gov Advanced Geophysical Technology Department, Sandia National Laboratories P.O. Box 5800 Albuquerque NM 87185-0750 A three-dimensional (3D) magnetotelluric (MT) inverse solution is formulated using non-linear conjugate gradients. To develop the solution, finite difference methods are used to efficiently compute predicted data and functional gradients from the forward problem. It is shown that only six forward modeling applications per frequency are typically required to produce the model update at each iteration of the scheme. This efficiency is achieved by incorporating a crude line search procedure that calls for a sufficient reduction in cost functional, instead of an exact determination of its minimum along a given decent direction. Additional efficiencies in the scheme are sought by incorporating preconditioning to accelerate solution convergence. A critical test of the inversion scheme is presented by inverting data produced with a forward modeling code that differs fundamentally from that employed in the inversion algorithm. This check provides independent verification of the scheme since the two forward modeling algorithms are prone to different types numerical errors. Field data collected over a geothermal prospect in Indonesia is being analyzed with the scheme. Computation times for the data set are approximately three weeks on a single processor workstation. To reduce run times to within 12 hours we are now implementing the scheme on a massively parallel computing platform. Title: 8.9 Application of Genetic Algorithms for 2D interpretation of the Okabe Data as well as a geothermal field in Central America Authors: M.A. Perez-Flores (*) & A. Schultz Institute of Theoretical Geophysics Department of Earth Sciences University of Cambridge Downing St. Cambridge, CB2 3EQ U.K. email: mperez@geofisica.cicese.mx adam@esc.cam.ac.uk Genetic Algorithms (GAs) have an increasing impact in inversion of seismic data, but have not been fully exploited by workers in that field as a means of nonlinear hypothesis testing. Within EM induction, efficient inversion and hypothesis testing requires extremely high accuracy in the forward solution, as well as rapid calculation of responses for multiple frequencies in a highly inhomogeneous Earth. The work reported here is the second generation of application of GAs to magnetotellurics. We have improved the convergence speed by changing the mutation process and we have defining a suitable objective function for the 2D MT problem. We have also examined several methods of forward solution and have selected Weaver & Agarwal's adaptive grid implementation as representing the best combination of speed and accuracy for highly heterogeneous models. We have accelerated the algorithm by partitioning the finite difference grid into subgrids for low periods. This improved version of GA was applied to the central sections of the Okabe data set to obtain 2D models of the area. Also it was applied to a MT section from a geothermal zone located in El Salvador. Title: 8.10 Complex image method for calculating electric and magnetic fields produced by a 3-D ionospheric current system Authors: Risto Pirjola(1), Ari Viljanen(1) and David Boteler(2) 1 Finnish Meteorological Institute, Geophysical Research Division 2 Geological Survey of Canada, Geomagnetic Laboratory The electromagnetic field due to three-dimensional ionospheric-magnetospheric currents has to be known when evaluating space weather effects at the earth's surface, like geomagnetically induced currents (GIC) in technological systems. Forecasting of space weather effects is time-critical, so the calculation of the fields has to be fast but accurate. Even for a layered earth, the contribution of the induction leads to complicated integrals for the total fields resulting in time-consuming computations. An approximate method of calculation based on replacing the earth by an image current which has a complex location yields closed-form expressions, and the computation becomes much faster. We consider the complex image method (CIM) in the case of a realistic auroral electrojet system consisting of horizontal finite-length current filaments with accompanying vertical currents above a layered earth. We prove that the cur-rent system can be replaced by a horizontal current distribution which is equivalent regarding the total (= primary + induced) magnetic field and the total horizontal electric field at the earth's surface, and so earlier CIM results derived for a horizontal source are available. Numerical calculations demonstrate that CIM is very accurate and several magnitudes faster than the ex-act conventional approach. Title: 8.11 TWO-DIMENSIONAL INVERSION OF VLF DATA Authors: Markku Pirttijarvi, Pertti Kaikkonen, Shashi P. Sharma and Sven-Erik Hjelt Department of Geophysics Institute of Geosciences University of Oulu FIN-90570, Oulu Finland mpi@babel.oulu.fi pjk@babel.oulu.fi sharma@babel.oulu.fi seh@babel.oulu.fi Session: Session 8: Progress in 3D modelling and inversion Type: Oral presentation For over three decades the VLF method has been successfully used in geophysical investigations, such as environmental studies, structural mapping as well as mineral exploration. Quite often, however, the interpretation of the measurements is left at the stage of qualitative interpretation. Lately, the progress in computational methods and computer hardware has made it possible to develop practical inversion programs for microcomputer environment. We have developed an inversion program for the interpretation of VLF and VLF-R profile data using a two-dimensional (2-D) model. The method is based on a linearized inversion scheme where the singular value decomposition (SVD) with an adaptive damping method is used. The model consists of several dyke-like bodies embedded in conductive two-layer Earth. The parameters of the model are: the overburden resistivity and thickness, the host resistivity, the x- and z-positions of the top center of the body, the width, the height, the dip angle and the resistivity of the body. The forward computation is based on integral equation method and only the E-polarization mode is considered. The performance of the inversion scheme is demonstrated using both synthetic and field data. Additional information about the model parameters derived by the SVD analysis is also shown. oral session: Progress in 3D modelling and inversion Title: 8.12 Inversion of electrical soundings by neural networks Authors: Joel E. Rodriguez, Francisco J. Esparza, and E. Gomez-Trevino, CICESE, Km 107 Carretera Tijuana-Ensenada, Ensenada, B.C., Mexico e-mail: fesparz@cicese.mx, Session 8 In this work we present a method of inversion which uses artificial neural networks. The data to be considered are the apparent resistivity obtained by means of the Schlumberger array. During initial testing, it was found that the numerical algorithm CASCOR is the most appropriate algorithm for the learning of the inverse mapping. The learning phase consists in presenting to the network curves of apparent resistivity and electric resistivity of the subsurface. The models used in this phase corresponds to three layer models in which the electric resistivities of the second and third layer were randomly varied, the thickness of the first and second layer were varied randomly as well. In the first network trained the four kinds of models (A, K, H, and Q) were used, also a network trained with sets corresponding to every kind of model was considered. By means of a learning analysis in each network, it is concluded that the networks learned more easily the ascendant and descendent step models. The models with a maximum or a minimum were best assimilated by the specialized network. The application of the inversion algorithm includes interpretation of field data from a farming region located near Ensenada, Mexico. The models estimated with the inversion algorithm show a remarkable similitude with those computed by means of Occam's method. Title: 8.13 COSY-B Intercomparison Experiment: Accuracy in 3D Forward Solvers Authors: A. Schultz (1), D. Avdeev (2), M. Everett (3), A. Flosadottir (4), I. Fujii (1,5), H. Igel (1), M. Jegen (1), T. Koyama (5), A. Kuvshinov (2), Z. Martinec (6), O. Pankratov (2), P. Tarits (7), H. Utada (5), M. Uyeshima (5), C. Weiss (3) 1: Institute of Theoretical Geophysics Department of Earth Sciences University of Cambridge Downing St. Cambridge, CB2 3EQ U.K. email: adam@ ikuko@ heiner@ jegen@esc.cam.ac.uk 2: Geoelectromagnetic Research Institute Russian Academy of Sciences PO Box 30 142092 Troitsk Troitsk, Moscow Region Russia email: avdeev@gemri.msk.ru akuvsh@igemiras.msk.ru pankratov@igemr.msk.ru 3: Department of Geology and Geophysics Texas A&M University College Station Texas 77843 U.S.A. email: colt45@ guinness@beerfrdg.tamu.edu 4: JISAO/PMEL Box 357941 University of Washington Seattle, WA98115, USA. email: agusta@pmel.noaa.gov 5: Earthquake Research Institute University of Tokyo Tokyo Japan email: koyama@ utada@ uyeshima@utada-sun.eri.u-tokyo.ac.jp 6: Department of Geophysics Charles University V Holesovickach 2 180 00 Prague 8 Czech Republic email: zdenek@hervam.troja.mff.cuni.cz 7: UBO - IUEM UMR ' Domaines Oceaniques ' Place Nicolas Copernic F-29280 Plouzane France email: tarits@univ-brest.fr An ad hoc group of researchers has been formed with the aim of developing reliable and accurate global-scale 3D forward solvers for the problem of EM induction in the spherical earth. Philosophically, this is a natural extension of the previous COMMEMI projects, but differs in that the target is arbitrary 3D heterogeneous models in spherical coordinates. There are strong links to a parallel effort in comparing forward solvers for the full 3D seismic elastodynamic equations in a spherical earth. The project is known as COSY - COmparison of SYnthetics, and is organised into Group A (seismology) and Group B (EM induction). Within Group B, a set of forward solvers is being cross validated, and also compared against a set of quasi-analytical solutions for specific model geometries. The Group B membership extends to all those working in the area of global scale 3D forward solvers in spherical geometry. The forward solvers currently being validated include finite element, staggered grid finite difference, staggered grid integral formulation, spectral element method, spectral method, multi-shell integral equation formulation, iterative dissipative method, eccentrically-nested spheres, and perturbation expansion (Born approximation) techniques. A set of common models against which quasi-analytical solutions are known have been run using one or more of these techniques. A geodynamical reference model based on H-P Bunge's mantle convection simulation has also been used to generate a target 3D EM and seismic forward model. A review of preliminary COSY-B results is given. Title: 8.14 BAYESIAN INVERSION WITH MARKOV CHAINS: THE THIN SHEET APPROXIMATION FOR A VERTICAL MAGNETIC DIPOLE CONTROLLED SOURCE Authors: Stefan Sineux(1,2), Michel Menvielle(2), Michel Roussignol(3) (1) Institut fuer Geophysik und Meteorologie, TU Braunschweig, Germany (2) Centre d'etude des Environnements Terrestre et Planetaires, St.-Maur-des-Fosses, France (3) Equipe d'Analyse et de Mathematiques Appliquees, Universite de Marne la Vallee, France Bayesian inversion with Markov chains has turned out to be a good means to interpret electromagnetic measurements in the magnetotelluric case. This paper aims to present the progress in using this method for the case of a vertical magnetic dipole controlled source. The Bayesian approach requires an a priori knowledge, described by an a priori probability distribution over the parameters, which is updated by the inversion. The solution of the inversion can be expressed by an a posteriori law over the parameters. We consider a heterogeneous 2-D domain limited in space, for which the thin sheet approximation is valid. This domain is divided in homogeneous square cells. Thus, the conductances of each cell become the parameters of the model. By limiting the possible number of conductance values, the a priori and the a posteriori law are digitized. The Markov chain is based on scannings of the considered domain. The conductances are successively updated for the actual cell, while the values of the other cells are supposed to be known and fixed. At each step the direct problem is entirely solved by the Vasseur & Weidelt algorithm. The transition probabilities of the Markov chain to the distinct conductance values are the a posteriori law for the considered cell. Results from synthetic models are presented and discussed. Oral Session: 8 Title: 8.15 Modelling the transient EM responses of complex 3D geological structures using the 3D full-domain hexahedral edge-element finite-element technique. Author: F.Sugeng CRC for Australian Mineral Exploration Technologies Earth Sciences, Macquarie University, NSW, 2109, Australia. fsugeng@laurel.ocs.mq.edu.au The finite-element method (FEM) has been used as a powerful method for solving complex electromagnetic modeling problems. The method is attractive, because of its flexibility to model any complicated geometries and it becomes the appropriate tool to model the curvature variations in the topography of the geological structures without the fine level of discretisation. Its system matrix is symmetric and sparse, which can be solved very fast by using the iterative solver such as the conjugate gradient method. The straightforward approach in applying the conventional finite-element method to EM problem is to apply the FEM to the Maxwell's equation directly and solve for the electric or the magnetic fields at the each nodes of the finite-element mesh. The method is called the node (scalar) basis function FEM and it requires the fields to be continuous across the inter-element boundaries. This continuity requirement generates a problem in the EM modelling, because it requires inherent constraints in the electric and magnetic fields approximation, such as the discontinuity of the normal and the continuity of the tangential component of the electric and magnetic fields at the inter-element boundary. The edge basis function (vectorial) FEM overcomes the problem, because it takes the whole vector of the field components in the approximation as one entity instead of independently. In this paper, an accurate approach to model the transient EM response of geological structures based on the 3D hexahedral edge finite-element technique is presented. The approach works accurately well in broad contrast range from low to very high conductivity contrasts (up to 100,000:1) and it is capable to model complex 3D earth geological structures efficiently. Title: 8.16 Keyhole imaging Authors: Laszlo SZARKA Geodetic and Geophysical Research Institute of the Hungarian Academy of Sciences, Sopron, Hungary (szarka@ggki.hu) and Universite Paris Sud, France Michel MENVIELLE Centre d'Etude des Environnements Terrestres et Planetaires, CNRS/UVSQ, Saint Maur (michel.menvielle@cetp.ipsl.fr) and Universite Paris Sud, France Vjacheslav SPICHAK Geophysical Research Centre, Moscow, Russia (spichak@dol.ru) In a very narrow period range within the short-period domain of the sounding curves the anomaly maps are much more closely related to the detailed geometry of high-conductivity 3D thin-sheet models than in the commonly used period domain. The existence of this "keyhole" period range was already shown both with CSAMT analogue modelling experiments and with MT numerical modelling results. The phenomenon is detectable in different interpretation parameters, and the keyhole period range corresponds always to the end of overshooting period domain, associated with the actual parameter. In the keyhole range the electromagnetic image of the investigated models does not vary with the rotation of the inducing field. This latter property means that in such conditions locally one-dimensional responses are obtained over 3D models. In this paper we give an insight into the physics of this short-period phenomenon. We do it by means of analytical studies of layered 1D earth models, and by using 2D and 3D numerical modelling results. Although the lateral variations in the keyhole range are relatively small, the "keyhole" imaging might meet application in some special exploration problems. Related papers: Szarka L, 1991, Acta Geod. Geoph. Mont. Hung., 26, 273-285. Szarka L and Menvielle M, 1997, EAGE, Geneva, paper F007, submitted to Geophysical Prospecting Szarka, 1997, Geophysical Prospecting, 45, 763-777. Title: 8.17 Geoelectromagnetic induction in a heterogeneous sphere: a new 3-D forward solver using a staggered-grid integral formulation Authors: M. Uyeshima(1) and A. Schultz(2) (1): Earthquake Research Institute, University of Tokyo address: 1-1-1, Yayoi, Bunkyo, Tokyo, 113-0032 Japan E-mail: uyeshima@utada-sun.eri.u-tokyo.ac.jp (2): Institute of Theoretical Geophysics, Department of Earth Sciences, University of Cambridge address: Downing Street, Cambridge, CB2 3EQ, England E-mail: adam@esc.cam.ac.uk A staggered grid numerical method is presented for computing the electromagnetic induction response of an arbitrary heterogeneous conducting sphere by external current excitation. This method is appropriate as the forward solution for the problem of determining the electrical conductivity of the Earth's deep interior. The solution is derived from that originally presented by Mackie et al. (1994) for Cartesian geometry. The difference equations that we solve are second order in the magnetic field H, and are derived from the integral form of Maxwell's equations on a staggered grid in spherical coordinates. The resulting matrix system of equations possesses the same general structure as that for Mackie's Cartesian case - the matrix is sparse, symmetric, is real everywhere except along the diagonal, and is ill-conditioned. The system is solved using the minimum residual conjugate gradient method with preconditioning by incomplete Cholesky decomposition of the diagonal subblocks of the coefficient matrix. In order to ensure there is zero H divergence in the solution, corrections are made to the H field every few iterations. In order to validate the code, we check against an integral equation solution for an azimuthally symmetric, buried thin spherical shell model (Kuvshinov and Pankratov, 1994), and against a quasi-analytic solution for an azimuthally nonsymmetric configuration of eccentrically nested spheres (Martinec, 1998). Title: 8.18 Electromagnetic induction in a layered earth with arbitrary anisotropy Authors: Changchun Yin and Peter Weidelt Institute of Geophysics and Meteorology Technical University of Braunschweig D-38106 Braunschweig, Germany E-mail: yin@geophys.nat.tu-bs.de To interprete geoelectromagnetic data in regions with distinct dipping stratification it is useful to extend the traditional layered isotropic model to a layered earth with arbitrary anisotropy, such that to each layer is assigned a symmetrical 3x3 resistivity tensor. - Two scalar potentials are introduced to solve Maxwell's equations for the EM fields, which describe the poloidal and toroidal part of the magnetic field, respectively. In order to stabilize the computation, the calculation is divided in the wavenumber domain into two parts. Whereas the EM fields with small wavenumbers are calculated through the continuation of EM fields with the boundary conditions from layer to layer, a Green's function approach is used for great wavenumbers. Considered are both harmonic and transient EM fields. Title: 8.20p Frequency Domain Three-Dimensional Modelling of Airborne Electromagnetic Responses Authors: Dmitry B. Avdeev^, Alexei V. Kuvshinov^, Oleg V. Pankratov^, Gregory A. Newman^^ ^Geoelectromagnetic Research Institute, Russian Academy of Sciences, Troitsk Moscow Region, Russia ^^Sandia National Laboratories, Albuquerque NM, U.S.A. avdeev@gemri.msk.ru Progress in 3D modelling and inversion poster Airborne electromagnetic (AEM) frequency domain responses have been simulated for commercially available helicopter and aircraft EM systems. To simulate the responses our integral equation three-dimensional (3D) modelling code (1997) has been modified and used. We have considered three types of the earth's models of practical interest: (1) 3D elongated body (dyke) residing in a layered section; (2) faulted half-space (vertical contact) with and (3) without topography. At these models the code has been compared with staggered grid finite-difference solution by Newman and Alumbaugh (1995) and is found to produce results in excellent agreement. We believe that our solution is an efficient tool for AEM modelling and inversion; as an example, for a model of 1 ohmm body in a 100 ohmm half-space the code takes 8 minutes on PC Pentium-100MHz per AEM system position when the body is discretized by 1500 cells. Title: 8.21p Modelling of Direct Currents in Laterally Inhomogeneous Anisotropic Structures Authors: Vaclav Cerv(1) and Josef Pek(1) (1) Geophysical Institute, Acad. Sci. Czech Rep., Bocni II/1401, CZ-14131 Prague 4, Czech Republic e-mail: vcv@ig.cas.cz, jpk@ig.cas.cz Well-known Dey & Morrison's finite difference (FD) algorithm for the 2-D modelling of direct currents is modified for generally anisotropic 2-D structures. By Fourier transforming the general current conservation equation with respect to the strike co-ordinate, the original 2.5-D problem for the potential of a single feeding electrode is decomposed into an infinite number of 2-D problems in the wave number domain. Applying the area discretization scheme to the transformed 2-D PDEs, a 9-point FD stencil is obtained at each mesh node within the anisotropic structure, with generally complex elements for the direct neighbours of the central node. The resulting FD matrix is banded, 9-diagonal, complex and non- symmetric, but Hermitian. Slightly modified version of the Gaussian elimination for real, symmetric and banded matrices is used to solve for the wave number potential components. Numerical tests and modelling examples of 2-D anisotropic structures are presented. Extension of the technique to 3-D models with anisotropy is discussed. Title: 8.22p APPROXIMATE MODELING AND IMAGING APPLIED TO HIGH-FREQUENCY INDUCTION LOGGING Author: Cheryauka A.B., Epov M.I., Martakov S.V. Institute of Geophysics, 3, Pr. Koptyug, Siberian Branch of RAS, Novosibirsk, Russia fax: +7 383 333432, e-mail: acher@uiggm.nsc.ru Institute of Mathematics, 4, Pr. Koptyug, Siberian Branch of RAS, Novosibirsk, Russia Interpretation models of electromagnetic logging for thin-layered formation with non-uniform invasion zones and tilted-subhorisontal intervals with asymmetry of properties are really multi-dimensional. Methods of imitation modeling and approximate inversion have been developed using approaches of surface and volume integral equations. For model which contains boundaries of regular curvatures we employ surface grid variant with equivalent continuous kernels. Express-modeling of massive log data is carried out by codes based on linear and localized-nonlinear perturbations. Under condition of quasi-propagation feature of high-frequency process the approximate technique are effective for correction of relative amplitude-phase functions. Reconstruction of geoelectric image is derived by using of linearized inverse scheme and least squares method. Solution regularization is reduced to evaluation of its r-importance in the basis of eigenvectors. Computation approach operates with adaptive apertures of induction array and restores complex resistivity image of given resolution. Title: 8.23p EXPERIMENTS ON QUASI-1D INVERSION OF MT DATA Authors: V.I.Dmitriev, M.N.Berdichevsky, E.E.Pozdnjakova, V.V.Pastutsan Moscow State University, Moscow, Russia E-mail: dmitriev@cs.msu.su Method of quasi-1D inversion of MT data has been suggested by V.Dmitriev and independently by D.Oldenburg and R.Ellis. It reduces the 2D or 3D inversion to iterative sequence of the 1D inversions corrected by the 2D or 3D misfits. The iteration formula for any observation site takes the form Z(cor,k)=Z(obs)-Z(2D/3D,k-1)+Z(1D,k-1), where k is the number of iteration, Z(cor,k) is the impedance corrected at the k-th iteration, Z(obs) is the impedance observed, Z(2D/3D,k-1) is the impedance of a 2D or 3D model synthesized from the 1D inversion of the impedances corrected at the (k-1)-th iteration, Z(1D,k-1) is the local 1D impedance of the (k-1)-th synthesized model. The iterations are fini- shed when the misfit m(k)=Z(obs)-Z(2D/3D,k-1) is sufficiently small and the corrected impedance Z(cor,k) approaches the local impedance Z(1D,k-1). For the sake of simplicity we can apply the iteration formula to one of the principal values of tensor Z. The main advantage of this technique is that the inversion consists of algebraic operations and does not need differentiation or integration procedures.It has been proved that if horizontal variation in conductivity are sufficiently slow, then the iterations converge to the exact solution. Up to now, there has been no work done to adopt these ideas in modern MT practice. It would be natural to begin this work with the 2D interpretation. Recently such a program has been elaborated at Moscow university. We tested the program using some 2D models of horst- and graben-type. Our experiments showed that the quasi-1D inversion may give rather high accuracy of interpretation ,even though the conduct- ivity changes sharply in horizontal direction. Title: 8.24p THREE DIMENSIONAL MODELLING FOR HIGH CONDUCTIVITY CONTRAST STRUCTURES. Authors: Elena Yu. Fomenko (Geoelectromagnetic Research Institute, Troitsk, RUSSIA) Toru Mogi (Kyushu University, Fukuoka, JAPAN) We have developed a new 3D modeling scheme for MT problem. The scheme based on the staggered grid finite difference formulation with continuous components of the electrical fields at the center of the edges of each cell, opposite in many known program codes with discontinuous E-field at the face of the cells. To apply resonably for the high conductivity contrast problem, we improved a condition number of the global matrix using an effective, simple, memory economical SSOR pre - conditioner. We introduced stable solver based on the bicongugate gradient method with QMR reqularization. The great acceleration in convergence and accuracy was achieved due to correction of E-field in accordance with conservative law in order to make a current J divergence free, especially at the low frequiencies. We applied the scheme to the practically important issues such as the island effect and topographic distorsion on the apparent resistivity and phase. These issues must be deal with high conductivity contrast and were difficult to discuss using numerical models. We estimated that these effect is severe at some frequencies relating to the scale of the structure. Title: 8.25p Calculation of electromagnetic sensitivities in the time-domain Authors: Andreas Hoerdt, University of Cologne Electromagnetic sensitivities are crucial for inversion of electromagnetic data and for the evaluation of the resolution properties of a method. Several methods exist to calculate sensitivities in the frequency domain, most of them are based on the reciprocity theorem. This paper presents a method to calculate sensitivities for time-domain methods by applying the reciprocity theorem directly in the time domain. The sensitivities are obtained by convolving the electric field in the subsurface due to a transmitter at the surface with the electric field impulse response due to another transmitter, which replaces the original receiver. The method uses the Druskin and Knizhnerman time domain finite difference code and avoids fourier transforming of frequency domain responses, which requires a wide frequency band. The acceleration compared to the classical perturbation method is approximately R/P, where P is the number of model parameters and R is the number of receiver positions. If the sensitivity has to be calculated very close to the receiver, approximate sensitivities can be obtained using an integral condition. Comparisons with the classical perturbation approach show that the method gives accurate results. Examples using transmitter-receiver configurations from a long-offset transient electromagnetics survey demonstrate the usefulness of sensitivities for the evaluation of resolution properties. Andreas Hoerdt University of Cologne Institute for Geophysics and Meteorology Albertus Magnus Platz 50933 Koeln Germany Tel.: 49-221-470-5477 Fax: 49-221-470-5481 email: hoerdt@ageo.uni-koeln.de Title: 8.26p Electromagnetic Modelling in a Spherical Earth with Surface and Deep Conducting Inhomogeneities: Multi-Shell Solution. Authors: Alexei V. Kuvshinov, Dmitry B. Avdeev, and Oleg V. Pankratov Geoelectromagnetic Research Institute, Russian Academy of Sciences 142092 Troitsk, Moscow Region Russia akuvsh@igemiras.msk.ru We present numerical solution of Maxwell's equations in a spherical Earth consisting of a number of conducting inhomogeneous shells embedded into radially-symmetric section. The numerical solution is based on integral equation concept by Singer (1995) and allows to simulate electromagnetic (EM) fields in multi-shell models with large lateral contrast of shells conductance. EM field can be generated by external (e.g. Sq and Dst) or by internal (e.g. water motion induced current) sources. For a number of simplified Earth's models incorporating surface and deep inhomogeneous shells and excited by Dst source, our solution has been checked against a three-dimensional cartesian solution. Excellent agreement is obtained for the regions analysed. When shell conductance has contrast of 400 and both spherical shells are discretized onto 90 x 45 cells each, the solution on PC/Pentium-100MHz takes 1.2 hour per period and excitation. Title: 8.27p 3D Finite Difference Simulation for High Frequency Induction Logging Authors: S.Martakov ^1, M.Epov ^2, A.Cheryauka ^2 ^1 - Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia Address: Pr. akad. Koptyuga, 4, Novosibirsk, 630090, Russia E-mail: martakov@math.nsc.ru ^2 - Institute of Geophysics, SB of RAS, Novosibirsk, Russia Abstract: Progress in directed drilling technology requires adequate modeling technique. To explain 3D effects in dipping or horizontal wells we need numerical algorithm which is capable to calculate signals in essentially 3D formation. We offer finite difference algorithm for high frequency electromagnetic field simulation based on methods derived in fluid dynamics for hyperbolic systems. To approximate Maxwell's equations on Cartezian non-homogeneous grid we use directed differencies of high order and matrix decompozition by eigenvalues. An implicit iterative scheme is applied to solve the obtained linear system by stabilization method. The algorithm has been tested by comparison of its solution with independent numerical solutions calculated due to other technigue: analytical (in case of cylindrically-layered medium), finite differences for elliptic equation (case of axial symmetry), integral equation method (borehole is parallel to layer boundary). Calculation results are presented for a number of real 3D models. Title: 8.28p 3-D AIRBORN ELECTROMAGNETIC AND MAGNETIC DATA INTEGRAL INVERSION Authors: P.S. Martyshko, A.L.Rublev (Institute of Geophysics, Ural Branch of Russian Academy of Science. 620016, Ekaterinburg, Amundsen str. 100, Russia) Phone: +7 3432 678883 Fax: +7 3432 678872 e-mail: pmart@igeoph.mplik.ru The interpretation of data obtained by EM methods involves considerable difficulties because in a general case the inverse problem is reduce to an operator equation of the first kind with an implicitly stipulated operator. The numerical solution of such equations requires considerable expenditures of computer time. We have obtained the new inverse problem equations of electromagnetic fields. There are the first generation equations with explicit operators. The primary field sourse can be arbitrary type. We've used representations of field functions through the values of the functions themselves and the derivatives at the boundary of the anomaly-forming object The method for solving of 3-D nonlinear electromagnetic and magnetic inverse problem was diviced (in the cases potential and monochromatic fields). It's based on the algorithm for solving explicit equations of the 3-D inverse problem. The algorithm was successfully tested on a number of model examples. We apply the Tikhonov regularization method to 3-D EMD inversion. We do AEM and/or magnetics data inversion by two-stage interpretation method: 1) approximation of the observed data with the fields of singular sourses; 2) construction of equivalent objects with different physical parameters values. As a result of interpretation we obtain the bodies stellate relative to some point with different values of conductivity (permeability) which generated the same ( electrical or magnetic) field. We have studied the possibilities for solution uniqueness seeking on the based joint interpretation of different EMD (Airborne EM and magnetics data, charge method and so on). We have some examples with good results of interpretation. ----------------------------------------------------------------------------- Title: 8.29p Three Dimensional Magnetotelluric Survey for Hydrocarbon Exploration on the overthrust area in Japan. Authors: Koichi Matsuo (matsuo-k@jnoc.go.jp), Masato Minegishi (minegs-m@jnoc.go.jp) Japan National Oil Corporation( JNOC ) 2-2, Hamada 1-chome, Mihama-ku, CHIBA, JAPAN 167 sites MT data were acquired in the 40km2(10km x 4km) area using the satellite synchronized MT system for the availability test to the complex geological structure. The in-line spacing is 250m-500m(18 to 22 sites per line) and 500m intervals for cross lines(8 survey lines). The data quality is quite good in spite of the high cultural noise area by trains, industries, many traffics and high voltage power lines. This survey field was one of oil and gas produced area in the northern part of Japan and characterized by prevalence of N-S trending reverse faults and folds. Three dimensional seismic survey also has been conducted in the same area by JNOC. Surface geological survey information and well logging data are available for investigation of the geological structure. We applied two dimensional inversion with smoothness constraint for each lines. The resistivity sections are coincident with the geological faults and folds structure of this area. Moreover we applied three dimensional MT modeling and conclude the results. Title: 8.30p Simulating MT Responses in Three-Dimensional Conductivity Anisotropic Models Authors: Oleg V. Pankratov, Alexei V. Kuvshinov, and Dmitry B. Avdeev Geoelectromagnetic Research Institute, Russian Academy of Sciences 142092 Troitsk, Moscow Region Russia pankratov@igemr.msk.ru Inconsistency in E- and B-polarized magnetotelluric (MT) responses is observed in many regions. It is often explained by anisotropy of electrical conductivity of subsurface structures. So, while interpreting MT responses, the modelling tool must incorporate both heterogeneity of conductivity and its anisotropy. We modified integral equation three-dimensional (3D) numerical solution by Avdeev et al. (1997) to include conductivity anisotropy and applied it to carry out simulations for a number of earth's models with anisotropic 3D targets which are excited by a MT source. The modelled responses were compared with the ones observed in the Rhine Graben area. Title: 8.31p Modelling the EM System Response of Geological Complexity Accurately. Authors: Art Raiche, Fred Sugeng, Zonghou Xiong CRC for Australian Mineral Exploration Technologies Earth Sciences, Macquarie University, NSW, 2109 art.raiche@mq.edu.au For many years, EM modellers were amongst the strongest proponents of the flat earth society because geological complexities such as topography, irregular bedding dipping faults, curving boundaries and high conductivity contrast were too difficult to model. Using an edge-element method, we have been able to model these effects for 3D models for contrasts as high as 106 to 1. We have also used conventional finite- element methods to model these effects for 2D models activated by 3D sources. The question is: are these results right? Simpler models such as multiple thin sheet structures with arbitrary orientation and multi-block models in layered hosts continue to remain useful for a variety of modelling tasks. These are based on integral equation and hybrid methods. By applying programs based on different mathematical algorithms to similar structures we are able to establish regimes of accuracy for each. This also allows us to establish empirically derived discretisation criteria for model building. Accurate modelling must also account for the EM system effects such as transmitter waveform, stacking algorithms, receiver windows and geometric effects. We present examples of complex model responses, (including the effects of EM system properties) together with accuracy checks based on simpler models. Pierre-Andre Schnegg Geomagnetism Group of the University Rue de l'Observatoire 58 CH-2000 NEUCHATEL Switzerland Phone: +4132 889 68 70 Direct: 889 88 17 Fax: +4132 889 62 81 email: Pierre-Andre.Schnegg@on.unine.ch URL: www-geol.unine.ch/GEOMAGNETISME/HomePage.html 8.32p Scheme for 3D MT modelling using polynomials P.-A. Schnegg Geomagnetism Group, Geological Institute, University of Neuchatel, Switzerland pierre-andre.schnegg@geol.unine.ch Our 3D modelling scheme employs a forward calculation based upon the integral form of Maxwell's equations (Mackie et al. 1993,1994), where accelerated conjugate gradient relaxation is used to solve for Hx, Hy and Hz. To automate the search for the best model, this scheme is included in a main program which launches a search loop. The model conductivity is controlled by polynomial functions of the coordinates. The method is best suited for modelling a conducting slab embedded in a resistive matrix. The depth to the top of the slab, its thickness and its resistivity are typical elements that can be approximated by polynomials. The objective function is minimized in the endless loop by a steepest descent algorithm which automatically modifies the polynomials. Modelling 2D and 3D MT data by hand can be a very wearing task. Quite frequently, automated methods like this one can be used successfully, by feeding the computer programme with a guessed initial model, and leaving the modelling work unattended during several days. Every smooth parametric geological situations can be approximated by simple polynomial expressions. This is the case for structures produced in collisions (or extensions; suture zones, crustal dThetacollements and shear zones) and salt domes. Title: 8.33p Sensitivity studies in magnetotelluric inversion Authors: Katrin Schwalenberg GFZ Potsdam Telegrafenberg 14473 Potsdam Germany E-Mail: katrin@gfz-potsdam.de Volker Rath Institut fuer Geologie, Geophysik und Geoinformatik Fachgebiet Geophysik Haus D Hochschulgelaende Lankwitz Malteserstr. 74-100 D-12249 Berlin Germany E-Mail: volker@geophysik.fu-berlin.de In magnetotelluric modelling one is not only confronted with the question whether the obtained model explains the data, but also whether the data require all or certain features of the model. It is straightforward to calculate the model resolution for small (e.g. 1-D) problems, but already in real-life 2-D cases it is computationally expensive to quantify the resolution of the modeled structures by standard methods (SVD). The sensitivity matrix is a by-product when solving the nonlinear 2-D inverse problem. It will be discussed which information with respect to parameter resolution can directly be extracted from this matrix. Several case studies (synthetic and field data) will be presented to clarify the meaning of the sensitivities and the problems associated with their use. The use of approximate SVD will be discussed, where only a small number of the largest singular values and vectors are computed. This can be done at small computational costs using Lanczos techniques which can favorably be combined with the iterative solution of the linear subproblems of the inversion process. Title: 8.34p ON THE SINGULARITY METHOD FOR HARMONIC ELECTROMAGNETIC FIELDS INTERPRETATION Author: A. F. Shestakov Institute of Geophysics, Ural Branch of Russian Academy of Sciences, Amundsen str.100, Ekaterinburg,620016, Russia The method is based on well-known singularity points conception of analytical functions (related with geophysical fields) which is connected with following: firstly, the anomalous field is defined by it's effective sources in a unique manner and secondly, these singular sources can be detemined from the field data even if the apriori information is absent. This fact allows to state that localisation and parameters singularity points knowledge let us to obtain the objective information about anomalous object, although not define it completely. The singularity method for geophysical fields interpretation allows to identify anomalous object of the following classes: isometric, extentive, plate-similar or prismatic. Localisation of target object in earth's half-space is achieved by the determination and location of singularity points assosiated with it. These points are the following: center of masses - for isometric object, nearest edge to the earth's surface - for extentive object, upper border - for plate-similar or prismatic objects. Initial data of problem are the "Caushy data" measured in restricted part of profil (Dim2) or earth's surface (Dim3). For garmonic electromagnetic field such data are presented by the values of mutual-perpendicular horisontal components of electric and magnetic fields. Model examples were considered to illustrate the singularity method possibilities conformably the magneto-telluric profiling data interpretation. In the first variant model consist of homogeneous half-space with a different resistivity anomalous prismatic bodies, which is excited by the vertically propagating plane wave. Initial data for singularity method was specified on 60 points, located along horisontal rectilinear profile crossing the inhomogeneity strike's direction. In the second variant the model examples were complicated by horisontal layer adding with more strong conductivity than containing half-space. The results of numerical calculations have shown that obtained singularity points parameters gives an accurate correspondence with the singularity method theory. TITLE: 8.35p The method of neuron network in inverse problems MTZ AUTORS: Shimelevitch Mickhail, Obornev Eugeny The algorithm of inverse rational problem solution was designed by the method of neuron networks. Nonlinear function of many variables, displaying a great variety of observed data to multitude sought parameters of geological layer for the fixed type of the cut, is approximated by multilayer perceptron with the hidden layer. The aim (the education) of approximation is reduced to the problem of conditional nonlinear optimization, which is solved by the method of back propagation. After educating the neuron networks, inverse problem of MTZ for given type of the cut is solved in real time. Inaccuracy and stability is being researched. A lot of comparisons with classical inverse of ratio problem are being conducted. Title 3.36p Exact Leontowich's identity for the harmonic electromagnetic fields on closed boundaries Author: V.N.Shuman Department of mathematical Geophysics, Institute of Geophysics of the Ukrainian National Academy of Science, Ukraine. E-mail:earth@igph.kiev.ua As is well-known, Rytov-Leontowich's approximated boundary condition establish the connection not only between the tangential components of the electrical and magnetic field, but also between normal and tangential components of the field. This paper present exact impedance identity for the harmonic electromagnetic fields. Using the known results of Aboul-Atta and Boerner (1975) obtained the exact general impedance conditions between the normal and tangential components of harmonic field on closed boundaries. These identity summarise the approxima- ted results, obtained previously of Rytov and Leontowich (1940,1948) and A.Ku- ckes et.al. (1985). They are of great importance in the description of the formation process of the electromagnetic response in real media and are theo- retical basis of the horizontal gradient and geomagnetic depth sounding methods of the Earth's crust and upper mantle. Mathematical models of local description of magnetotelluric field in the vicinity of an observation point are discussed. As it appears, the many conclusions and recommendations relating to this problem and though to by generally accepted are too optimistic and re- quire re-examination. Title: 8.37p The application of the equivalent wave kinematics: model studies and field examples Authors: V.N.Shuman and T.I.Tsymbal Department of Mathematical Geophysics, Institute of Geophysics of the Ukrainian National Academy Science Ukraine. E-mail:earth@igph.kiev.ua As is known, the transformation of electromagnetic response to an equivalent wave (hyperbolic) domain has considerable promise for the elec- tromagnetic transient-mode data inversion end imaging. The application of the hyperbolic equation to the interpretation of electromagnetic sounding has been widely discussed. However, due attention has non been paid to the difficulties of the method implementation. As a result the method does not find wide prac- tical use. This paper considers some results obtained with particular emphasis on some factors simplifying the problem: we suggested reconstruction of the positions of discontinuities of the wave function of electromagnetic response rather than the function itself, we represented the electromagnetic response as laterally propagating waves. According to V.Fok, the electromagnetic response on the Earth's sur- face or near it in the lower conducting half-space is formed by two types of disturbances. From this point of view numerical results on equivalent wave characteristics and field examples are discussed. As a results a number nume- rical experiments was found a strong similarity between abscissas and ordina- tes of extreme of wave curves and electrical and geometrical characteristics of lower half-space. Title: 8.38p MODELING ELECTROMAGNETIC EFFECTS CAUSED BY INHOMOGENEITIES OF THE CONDUCTIVE SEDIMENTARY COVER AND RESISTIVE EARTH CRUST Authors: B. Sh. Singer (presenting author), CRCAMET, Bldg.E5A, Macquarie University, North Ryde, NSW 2109, Australia, Tel.:(61-2)9850-9281, Fax.:(61-2)9850-8366, E-mail: bsinger@laurel.ocs.mq.edu.au E. B. Fainberg, Institute of Physics of the Earth, Troitsk, Moscow Region 142092, Russia The importance of the effects caused by the inhomogeneities of subsurface sedimentary and / or water cover is well recognized. In the problems that are internally related to appearance of the poloidal currents in the ground, the effects of inhomogeneities of the resistive earth crust can profound as well. Such problems include electromagnetic explorations with a grounded electric dipole, measurement of the electromagnetic fields caused by electrokinetic processes in a volcano magma chamber, and a number of others. We developed an integral equation algorithm for a model that represents the subsurface inhomogeneous layer as a generalized thin sheet of a finite thickness. The integral equation is solved using the iterative dissipative method (IDM) that provides a solution in a wide frequency range. Finiteness of the inhomogeneous layer thickness may be essential for achieving accurate results. On the other hand, no additional computer resources are necessary to account for the layer thickness. The convergence, numerical robustness, and technical aspects that are important for a practical implementation of an efficient IDM-algorithm are discussed. Title: 8.39p BOUNDARY CONDITIONS FOR SOLUTION OF IDM INTEGRAL EQUATION Authors: B. Sh. Singer (presenting author), CRCAMET, Bldg.E5A, Macquarie University, orth Ryde, NSW 2109, Australia, Tel.:(61-2)9850-9281, Fax.:(61-2)9850-8366, E-mail: bsinger@laurel.ocs.mq.edu.au T. Wang, Western Atlas Logging Services, 10205 Westheimer, Houson, Texas 77042, U.S.A. The Iterative Dissipative Method (IDM) by Fainberg & Singer (1980, 1985) is based on a property of the Green's function derived from the energy conservation law. A solution of the integral equation is found by simple iterations that are always convergent. The convergence is optimized by a proper choice of the reference model. With a reference model different from the "normal" conductivity distribution, the integration is spread over the volume where the anomalous current is different from zero. We discuss several approaches to the reduction of the area of the integration. Two of the approaches are based on a presentation of the electromagnetic field outside of the anomaly by the field of a set of unknown electric dipoles. The dipole moments have be found either iteratively (Singer & Pankratov 1990) or directly. In an alternative approach the solution is first approached using an optimal reference model. The approximate solution is further improved using iterations based on a background reference model. This results in a slower convergence of the iterative process. On the other hand, the volume of the integration that has to be covered with a numerical grid reduces to the minimum volume containing the anomaly. Title: 8.40p An Efficient Data Subspace Inversion for MT Data Authors: Weerachai Siripunvaraporn and Gary Egbert College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331 USA. wsiripun@oce.orst.edu; egbert@oce.orst.edu In a data space approach, to regularize 2-D MT inversion, the optimal (norm-minimizing) solution is expressed as a linear combination of N basis functions, i.e. the rows of the NxM sensitivity matrix where N is number of independent data and M is the number of model parameters. The coefficient vector can be obtained by inverting the NxN matrix computed from the inner products of the sensitivity matrix (the representer matrix) instead of MxM matrix inversion required with standard model space approach. Because of data redundancy, basis functions for a subset of the data can be chosen to approximate the optimal solution, and lower the sensitivity matrix size to LxM and the representer matrix size to LxL, where L is the number of selected data. We have found that L can be much smaller than N or M which allowing dramatic reductions in the computational cost without significantly changing the solution. In addition, sensitivities which are localized around the data location can be significantly truncated allowing huge saving in memory and speeding up the computation of the inner products of the representer matrix. With these innovations, inversion of a large MT data set (e.g. 55 stations and 49 frequencies presented here) becomes possible on workstation. Title: 8.41p Three-dimensional interpretation of EM data using Artificial Intelligence paradigm Authors: Vjacheslav Spichak (Geophysical Research Centre, Varshavskoe shosse 8, Moscow, 113105, Russia) and Irina Popova.(Institute of Geoelectromagnetic Investigations, RAS, Troitsk, Moscow region, 142092, Russia) Phone:+7(095)3340906, Fax:+7(096)6014400 popov@ntcstm.msk.ru An approach to 3D inversion of EM based on Neural Network (NN) paradigm is elaborated. The backpropagation scheme and simulated annealing Hopfield network used to this end allows mapping from the input space of EM-data to the output space of unknown parameters of 3D geoelectrical structure. The synthetic data base for training NN is created by means of forward modelings for the 3D conductivity model considered. FFT is used to compress the input synthetic data and to extract their characteristic features. NN is trained then in order to "remember" the correspondence between the unknown parameters of the model and the data images obtained at the previous step. The real data interpretration by means of such NN is actually a recognition procedure the output beeing the unknown values of the target parameters. The ability of the NN trained using noise-free and noisy synthetic data is studied and statistically grounded conclusions are made on the effects of the noise level in training data sets on the quality of the NN - recognition. An example of the data interpretation in terms of 3D conductivity model of the fault located in two-layered earth is given. Fault's depth, width, length, angle of inclination as well as the conductivities of the first layer and of the fault itself are detected basing on apparent resistivities and phases in CSAMT frequency range. Title: 8.42p 3D Resistivity and IP Forward Modeling for Crosshole Techniques Authors: Klaus Spitzer & Michel Chouteau Ecole Polytechnique, Montreal,Quebec, Canada Klaus Spitzer Geowissenschaftliche Gemeinschaftsaufgaben Stilleweg 2 30655 Hannover Germany Tel.: (+49) 511-643-3490 Fax: (+49) 511-643-3665 klaus.spitzer@bgr.de Electrical crosshole techniques can be very useful for mining applications because transmitters and receivers may be positioned close to the target bodies, thereby enhancing the resolution compared to surface methods. However, crosshole methods are difficult to interpret. We present a full 3D finite difference resistivity and IP forward modeling algorithm that is capable of simulating arbitrarily bent and inclined boreholes within arbitrary conductivity structures. The presented algorithm is fast, accurate, and memory efficient. The crosshole method is briefly outlined and its superiority to surface methods depicted by displaying the individual sensitivity distributions and the apparent resistivity responses. Title: 8.43p RESOLUTION STUDY OF 2D/3D INVERSION TECHNIQUES USING IMITATION MODELS Authors: Iv.M. Varentsov, N.V. Baglaenko (Geoelectromagnetic Research Institute RAS, Troitsk, Russia; e-mail: igemi1@pop.transit.ru) A family of MT data inversion algorithms (Golubev, Varentsov, 1988-98) is investigated within a number of synthetic data sets (including those selected for MT-DIW4), generated for known geoelectric structures. This approach allows to measure the achieved resolution directly in the space of model parameters and to check/calibrate internal a posteriory accuracy estimates. Different model parametrization schemes (fixed geometry, independent or correlated cells and finite function approximation) are examined. The main analysis is done for 2D models, but volume 3D solutions are also considered. In the experiments with true data the resolution at the level of 0.1% and even below is usual. The very close accuracy is shown for data with huge, but rear outliers. In the presence of random noise the resolution of significant parameters is estimated within the noise level. Formalized static shift indicators are studied. Resolution effects of different selection of inverted data components as well as of various numerical improvements are studied. Some results for the recent COPROD2 2D inversion comparison project are presented as a supplement. Title: 8.44p Studies of the source effect due to 3-D ionospheric current systems using the complex image method Authors: Ari Viljanen1, Olaf Amm2 and Risto Pirjola1 1Finnish Meteorological Institute, Geophysical Research Division P. O. Box 503, FIN-00101 Helsinki, Finland phone: +358-9-19294652, +358-9-19294668 fax: +358-9-19294603 email: Ari.Viljanen@fmi.fi, Risto.Pirjola@fmi.fi 2Technical University of Braunschweig, Institute of Geophysics and Meteorology Mendelssohnstr. 3, D-38106 Braunschweig, Germany phone: +49-531-391-5221 fax: +49-531-391-5220 email: amm@geophys.nat.tu-bs.de The complex image method (CIM) provides an efficient way to use realistic models of 3-D ionospheric current systems in the auroral region, where the source effect is the most severe. We apply here data-based models of four typical high-latitude ionospheric situations: the electrojet, the westward travelling surge, the Harang discontinuity and the omega band. Ionospheric currents are typically given in a 50 km x 50 km grid covering a region of even 2000 km x 2000 km. This allows for very detailed studies of the spatial structure of the electromagnetic field at the earth's surface, and makes it possible to estimate quantitatively the range of the distortion. These studies serve as a preparatory work for the analysis of the recordings by the BEAR project (Baltic Electromagnetic Array Research). The electric field values at the earth's surface are also applicable to studies of geomagnetically induced currents in technological systems. Title: 8.45p A Study of High Accuracy Methods for Full-domain 3-D Electromagnetic Modelling Author: Zonghou Xiong CRC AMET, Earth Science, Macquarie University, Sydney, NSW, Australia 2109 Using the staggered grid we have developed three 4th-order schemes for three-dimensional electromagnetic modelling in the frequency domain: a complete Galerkin method, an incomplete Galerkin method, and a 4th-order finite difference method. The first two solve Maxwell equations by a Galerkin method on slices of 3x3x3 Yee-cells. While the complete Galerkin method applies the Galerkin process on a 3x3 slice, the incomplete method applies the Galerkin process to the centre cell only. The Galerkin methods treat non-uniform conductivity as part of the weighting function, thus allowing the modelling of arbitrarily shaped targets. The use of higher order Lagrangian interpolants as basis and test functions means that the mesh can be expanded logarithmically to the boundary without loss of accuracy. These three method are compared with two second-order method for a whole space. Results show that the 4th-order finite difference method and the incomplete Galerkin method are the most accurate. The presence of the air contributes significant difficulties in solving the matrix equations by itreative solvers. To solve this problem we have developed a domain decomposition technique with adaptive iterations between the air domain and the earth domain. Title: 8.46p The numerical modeling of low frequency electromagnetic field for 3D spherical model of the Earth. Authors: I. V. Yegorov and N. A. Palshin Shirshov Institute of Oceanology, Russian Academy of Sciences 36 Nakhimov Avenue, 117815 Moscow Russia (yegorov@geo.sio.rssi.ru, palshin@geo.sio.rssi.ru) For the low frequency EM field, the continuity equation of the electric current density, expressed in terms of a scalar potential, could be applied. 3D conductivity model of the Earth is considered as a set of spherical inhomogeneous layers. Relatively conductive layers are approximated by spherical S-sheets, while the relatively resistive layers are described by integral resistivity R. Both S and R are functions of latitude and longitude. The thin-sheet approximation gives the possibility to reduce the 3D problem, corresponding to the general conductivity model, to the solution of a system of 2D elliptic partial differential equations. Global conductivity model consisting of inhomogeneous spherical thin sheets was constructed using the geological and geophysical data available. The numerical modeling was carried out for two types of the sources: (1) equatorial ionosphere currents for simulating the Dst variation and (2) the annual mean global water circulation model for simulation of motionally induced currents. The results of the modeling give a possibility to analyze the spatial distribution of induced electromagnetic field in the global scale. One of the main features of the electromagnetic field (for both types of the source), it's dependence on integral resistivity of the lithosphere, was studied.