determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

on continuous dependence for an inverse initial boundary value problem for the wave equation abstract we show that the bounded coefficient q x of the wave equation u tt u qu x t 0 t u x 0 u t x 0 0 x u v x x x t 0 t can be continuously determined by its neumann to dirichlet map in certain function spaces

simultaneous multifrequency inversion of full waveform seismic data we present a simultaneous multifrequency inversion approach for seismic data interpretation this algorithm inverts all frequency data components simultaneously a data weighting scheme balances the contributions from different frequency data components so the inversion process does not become dominated by high frequency data components which produce a velocity image with many artifacts a gauss newton minimization approach achieves a high convergence rate and an accurate reconstructed velocity image by introducing a modified adjoint formulation we can calculate the jacobian matrix efficiently allowing the material properties in the perfectly matched layers pmls to be updated automatically during the inversion process this feature ensures the correct behavior of the inversion and implies that the algorithm is appropriate for realistic applications where a priori information of the background medium is unavailable two different regularization schemes an l2 norm and a weighted l2 norm function a

borcherds products and arithmetic intersection theory on hilbert modular surfaces we prove an arithmetic version of a theorem of hirzebruch and zagier saying that hirzebruch zagier divisors on a hilbert modular surface are the coecients of an elliptic modular form of weight two moreover we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its petersson metric on a regular model of a hilbert modular surface and study faltings heights of arithmetic hirzebruch zagier divisors

three dimensional earth conductivity inversion abstract we have constructed two inverse algorithms using tikhonov regularization one follows the well known method of solving the linearized data model relation subject to some regularizing operator which forces the solution to satisfy some desirable features we refer to the other more novel approach as the inverse scattering currents method this procedure uses the linear relation between data and scattering currents induced in an inhomogeneous structure and the relation between the scattering currents and the unknown conductivity the inverse problem is solved iteratively using these two relations

stability of the inversion of 3d fixed frequency scattering data abstract numerical methods for solving 3d inverse scattering problems with fixed energy data are described exact inversion formulas are given stability of the inversion methods based on these formulas is investigated an explicit formula is given for construction of the dirichlet to neumann map from the scattering amplitude this formula is used as a basis for another numerical approach to the inverse scattering problem several open problems are formulated

the effect of local distortions on time domain electromagnetic measurements based on the time domain integral equation we derive expressions for the effect of an anomalous body close to the receiver or close to the transmitter on transient electromagnetic measurements similar to magnetotellurics the distortion of electric fields at late times can be described by a constant distortion tensor relating the secondary electric field to the primary field components that would be obtained in the absence of the body the distortion of a single electric field transient is a static shift only for particular configurations over a layered half space in the general case the perturbation is time dependent because the direction of the total electric field vector varies with time the theory nicely explains spatial variations in electric field transients measured during a high redundancy long offset transient electromagnetics lotem survey over an underground gas storage site an inversion example with synthetic data illustrates how distortion can be corrected the elements of the distortion tensor are determined simultaneously with the model parameters ambiguity is reduced by a regularization of the distortion parameters in the example the background model is recovered well even for the difficult case where only one transmitter is used the distortion of the magnetic field time derivatives caused by bodies close to the receiver is proportional to the time derivative of the primary electric step response the distortion is generally not limited to early times and cannot be neglected in general transmitter overprint effects resulting in static shifts of vertical magnetic field time derivatives may also be understood from the theory

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors

degenerate principal series and local theta correspondence following our previous paper lz which deals with the groupu n n we study the structure of certain howe quotients p q and p q 1 which are natural sp 2n r modules arising from the oscillator representation associated with the dual pair o p q sp 2n r by embedding them into the degenerate principal series representations of sp 2n r studied in l2

pullbacks of saito kurokawa lifts pullbacks of siegel eisenstein series have been studied by garrett 17 18 bocherer 6 7 heim 26 and play a key role in the proof of the algebraicity of critical values of certain automorphic l functions more generally one might consider pullbacks of siegel cusp forms for example ikeda 30 gave a conjectural formula for pullbacks of ikeda lifts 29 in terms of critical values of l functions for spn gl2 also the gross prasad conjecture 22 23 8 27 8 would relate pullbacks of siegel cusp forms of degree 2 to central critical values of l functions for gsp2 gl2 gl2 indeed bocherer furusawa and schulze pillot 8 gave an explicit formula for pullbacks of yoshida lifts 57 in this paper we give an explicit formula for pullbacks of saito kurokawa lifts and prove the algebraicity of central critical values of certain l functions for sp1 gl2 to be precise let be an odd positive integer let f s2 sl2 z be a normalized hecke eigenform and h s 1 2 0 4 a hecke eigenform associated to f by the shimura correspondence let f s 1 sp2 z be the saito kurokawa lift of h for each normalized hecke eigenform g s 1 sl2 z we consider the period integral f h h g g given by f h h g g

on some degenerate principal series representations of u n n we study the infinitesimal action of u n n on the degenerate principal series representations of u n n associated with a parabolic subgroup which stabilizes a maximal isotropic subspace of c2n relative to the indefinite hermitian form with signature n n this allows us in particular to determine the reducibility socle series and unitarity of these representations

development of a boundary element method for time dependent planar thermoelasticity abstract a new boundary element method is developed for two dimensional quasistatic thermoelasticity this time domain formulation involves only surface quantities consequently volume discretization is completely eliminated and the method becomes a viable alternative to the usual finite element approaches after presenting a brief overview of the governing equations boundary integral equations for coupled quasistatic thermoelasticity are derived by starting with existing fundamental solutions along with an appropriate reciprocal theorem details of a general purpose numerical implementation are then discussed next boundary element methods for the two more practical theories uncoupled quasistatic and steady state thermoelasticity are developed directly from limiting forms of the coupled formulation several numerical examples are provided to illustrate the validity and attractiveness of the boundary element approach for this entire class of problems

the inverse scattering problem for time harmonic acoustic waves in an inhomogeneous medium with complex refraction index abstract the inverse scattering problem of determining the complex refraction index of a compact inhomogeneous medium from a knowledge of the far field patterns of the scattered fields corresponding to many incident time harmonic plane acoustic waves is solved by using the colton monk method again by using the same method the analogue of karp s theorem for the scattering of acoustic waves through an inhomogeneous medium with compact support is proven

inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection the problem of determining an unknown pair gamma lambda mu of lame parameters inside a body by its dirichlet to neumann data map lambda gamma is considered using explicit exact solutions for the case of constant gamma it is seen that the deflection h between gamma h and gamma is uniquely determined by the first order approximation of lambda gamma h at gamma

multidimensional inverse problems and completeness of the products of solutions to pde a method is given for proving uniqueness theorems for some inverse problems the method is based on a result on completeness of the products of solutions to pde as an example the following uniqueness theorems are proved 1 the scattering amplitude a k known for all s2 and a fixed k 0 determines the compactly supported q x l2 d uniquely 2 the surface data u x y k known for all x y p x x3 0 and a fixed k 0 determine the compactly supported x l2 d d r 3 x x3 0 is arbitrarily small determine aj x j 1 2 uniquely here 2u k2u k2a1x a2 x u x y in r3 a1 l2 d a2 h2 d the same conclusion holds if the surface data are known at two distinct frequencies 4 the surface data u x y k known for all x y p and all k 0 determine v x and h k uniquely here 2 k2 k2 x u x y h k x l2 d h k is fourier transform of a wavelet of compact support 5 the conductivity x w2 2 d x c 0 is uniquely determined by the measurements of u and un on d here n is the outward normal to d d r3 is a bounded domain with a smooth boundary d x u 0 in d 6 necessary and sufficient conditions are given for a function a k s2 k 0 is fixed to be the scattering amplitude corresponding to a local potential from a certain class

the regularized siegel weil formula the second term identity and the rallis inner product formula in this paper we establish the second term identity of the siegel weil formula in full generality and derive the rallis inner product formula for global theta lifts for any dual pair as a corollary we resolve the non vanishing problem of global theta lifts initiated by steve rallis

necessary and sufficient condition for l to have property c abstract let l m j 0aj j be a formal differential operator with constant coefficients in r n n 2 j is a multi index we say that l has property c iff for any bounded domain d r n the set of products uw u w nd l u l u 0 in d u hm d is complete in l2 d here hm d is the sobolev space a necessary and sufficient condition is given for l to have property c

superconnections theta series and period domains abstract we use superconnections to define and study some natural differential forms on the period domain d that parametrizes polarized hodge structures of given type on a rational quadratic vector space v these forms depend on a choice of vectors v 1 v r v and have a gaussian shape that peaks on the locus where v 1 v r become hodge classes we show that they can be rescaled so that one can form theta series by summing over a lattice l r v r these series define differential forms on arithmetic quotients d we compute their cohomology class explicitly in terms of the cohomology classes of hodge loci in d when the period domain is a hermitian symmetric domain of type iv we show that the components of our forms of appropriate degree recover the forms introduced by kudla and millson in particular our results provide another way to establish the main properties of these forms

enhancing the resolving power of least squares inversion with active constraint balancing most geophysical inverse problems are solved using least squares inversion schemes with damping or smoothness constraints to improve stability and convergence rate since the lagrangian multiplier controls resolution and stability of the inverse problem we always want to use the optimum multiplier which is not easy to get and is usually obtained by experience or a time consuming optimization process we present a new regularization approach in which the lagrangian multiplier is set as a spatial variable at each parameterized block and automatically determined via the parameter resolution matrix and spread function analysis for highly resolvable parameters a small value of the lagrangian multiplier is assigned and vice versa this approach named active constraint balancing acb tries to balance the constraints of the least squares inversion according to sensitivity for a given problem so that it enhances the resolution as well as the stability of the inversion process we demonstrate the performa

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

stability of the solution to 3d fixed energy inverse scattering problem let sup s2 a a 0 is a given number b a r3 ba 0 is a small number a numerical method is given to calculate a stable approximation q to the fourier transform q of q x an estimate of the error of the approximation is given for q qq and q qa l ba

advanced development of the boundary element method for steady state heat conduction considerable progress has been made in recent years toward advancing the state of the art in solid mechanics boundary element technology in the present work much of this new technology is applied in the development of a general purpose boundary element method bem for steady state heat conduction in particular the bem implementation involves the use of higher order conforming elements self adaptive integration and multi region capability two and three dimensional as well as axisymmetric analyses are incorporated within a unified framework in addition techniques are introduced for the calculation of boundary flux and for the inclusion of thermal resistance across interfaces as a final extension an efficient formulation is developed for the analysis of solid three dimensional bodies with embedded holes for this last class of problems the new bem formulation is particularly attractive since use of the alternatives i e finite element or finite difference methods is not practical a number of detailed examples illustrate the suitability and robustness of the present approach for steady state heat conduction

superconnection currents and complex immersions let i m m be an immersion of complex manifolds and let be a complex of holomorphic hermitian vector bundles on m which provides a projective resolution of the sheaf of sections of a holomorphic vector bundle on m we study the convergence as u of a class of superconnection currents u introduced by quillen and we calculate the limit microlocal estimates of the speed of convergence are also given

on the siegel weil formula for unitary groups following s s kudla and s rallis we extend the siegel weil formula for unitary groups which relates a value of a siegel eisenstein series to the convergent integral of a theta function

formal solutions of inverse scattering problems iv error estimates the formal solutions of certain three dimensional inverse scattering problems presented in papers i iii in this series j math phys 10 1819 1969 17 1175 1976 21 2648 1980 are employed here to obtain quantitative estimates on the error resulting from the use of the born approximations in both direct and inverse potential scattering problems these estimates are uniformly valid at all energies and for all sufficiently weak potentials

numerical recovery of the layered medium from the surface data abstract in this paper an inverse problem is formulated and its numerical solution is given the problem is of interest for example in geophysics numerical results show that the algorithm is efficient for noisy data practical recommendations are given the problem consists of finding n z the refraction coefficient of the medium given the surface data u x k x p x x3 0 and all k 0 k0 where k0 0 is an arbitrary small wave number the governing equation is 2 k2n z u x x x1 x2 z analytical solution to this inverse problem is given a numerical implementation is suggested and the results of the numerical experiments are reported

an inverse problem of the wave equation this paper is organized as follows in sect 1 the statement of the inverse problem is formulated the basic results are formulated and proved in sect 2 some auxiliary material on the x ray transform is given in a self contained way for convenience of the reader this material is used in section one

boundary element methods in three dimensional thermoelasticity abstract a boundary element method is developed for the solution of time dependent problems in three dimensional thermoelasticity the time domain boundary only formulation represents the first of its kind for quasistatic analysis which by definition considers transient heat conduction but ignores the effects of inertia by eliminating the need for volume discretization the method becomes an attractive alternative to finite element analysis for this class of problems additionally because an exact green s function is used in the interior steep thermal gradients can be captured much more readily than with standard domain based methods the presentation includes details of the fundamental solution a derivation of the boundary integral equations and an overview of a general purpose numerical implementation this implementation permits the solution of large multiregion problems with arbitrary geometry and boundary conditions several examples are included to validate the proposed method as well as to highlight its usefulness

theta dichotomy for unitary groups some recent work of gross and prasad 14 suggests that the root numbers attached to certain symplectic representations of the weil deligne group of a local field f control certain branching rules for representations of orthogonal groups over f on a global level this local phenomenon should have implications for the structure of the value at the center of symmetry for certain l functions of arithmetic interest 12 this conjectural picture is based to some extent on the now classic work of tunnell 47 and waldspurger 49 as well as on the case of the triple product l function 13 34 17 in all of these examples the local root number detects the existence of a certain type of invariant linear functional it is possible to set up analogous conjectures for the isometry groups of hermitian or quaternion hermitian forms it turns out that root numbers also play a role in the local and global theta correspondence roughly speaking certain local root numbers should control the occurrence of representations in the local theta correspondence between groups of the same size e g for dual pairs of the form sp n o 2n 1 and u n u n as will be seen the theta correspondence for such pairs is connected with a certain induced representation in s at the point s 0 on the unitary axis by contrast the correspondence for the pairs sp n o 2n and sp n o 2n 2 discussed by prasad 35 is connected to the behavior of a similar induced representation at the points 12 in which case no epsilon factor arises in this paper we consider the local theta correspondence for unitary groups in the non archimedean case let f be a non archimedean local field of characteristic not equal to 2 and let e be a quadratic extension of f for further notation see the notation section at the end of this introduction let v and w be e vector spaces of dimensions m and n equipped respectively with a hermitian form v v e and a skew hermitian form w w e then the isometry groups g v and g w of the spaces v and w form a dual reductive pair in the symplectic group sp w where w v e w viewed as an f vector space of dimension 2mn and equipped with the symplectic form

formula for the radius of the support of the potential in terms of scattering data let q r r x be a real valued square integrable compactly supported function and be the smallest interval containing the support of q r let be the corresponding scattering amplitude at a fixed positive energy let be the phase shifts at k 1 it is proved that provided that q r does not change sign in some arbitrary small neighbourhood of a

boundary control wave field continuation and inverse problems for the wave equation abstract we consider the problem of the wave field continuation and recovering of coefficients for the wave equation in a bounded domain in r n n 1 the inverse data is a response operator mapping neumann boundary data into dirichlet ones the reconstruction procedure is local this means that observing boundary response for larger times we may recover coefficients deeper in the domain the approach is based upon ideas and results of the boundary control theory yielding some natural multidimensional analogs of the classical gel fand levitan krein equations

behavior of the solutions to exterior boundary value problems at low frequencies abstract a simple method is given to study the low frequency behavior of the solutions to exterior boundary value problems for elliptic equations of second order

bott chern currents and complex immersions in the whole paper we will say that i m m is an immersion of smooth manifolds if m is a submanifold of m and if i is the corresponding injection map in particular the topology of m is the topology induced by the topology of m in differential geometry such maps i m m are also called embeddings

nonhomeomorphic conjugates of connected shimura varieties we show that conjugation by an automorphism of bbb c may change the topological fundamental group of a locally symmetric variety over bbb c as a consequence we obtain a large class of algebraic varieties defined over number fields with the property that different embeddings of the number field into bbb c give complex varieties with nonisomorphic fundamental groups

magnetotelluric inversion for minimum structure structure can be measured in terms of a norm of the derivative of a model with respect to a function of depth f z where the model m z is either the conductivity or log an iterative linearized algorithm can find models that minimize norms of this form for chosen levels of chi squared misfit the models found may very well be global minima of these norms since they are not observed to depend on the starting model overfitting data causes extraneous structure some choices of the depth function result in systematic overfitting of high frequencies a blue fit and extraneous shallow structure others result in systematic overfitting of low frequencies a red fit and extraneous deep structure a robust statistic is used to test for whiteness the fit can be made acceptably white by varying the depth function f z which defines the norm an optimum norm produces an inversion which does not introduce false structure and which approaches the true structure in a reasonable way as data errors decrease

straightforward inversion of vertical electrical sounding data a straightforward inversion scheme sis has been developed to interpret vertical electrical sounding data this scheme does not require quasi linearization of the inverse resistivity problem and thereby dispenses with the iterative process and the necessity of guessing the number of layers and their resistivities and thicknesses the entire solution domain is divided into uniform thickness layers whose scale must be judiciously selected for the desired resolution the apparent resistivity formula can now be posed as an underdetermined matrix equation whose minimum norm solution is downward continued to obtain the reflection coefficients which in turn yield the vertical resistivity distribution a recurrence relation has been developed especially for this purpose in general when data are expected to be noisy a regressed minimum norm solution is used exhaustive tests of the algorithm have established its numerical efficiency results of six typical synthetic models representing diverse geological conditions as well as results of two field examples are included to demonstrate this claim

uniqueness theorems for multidimensional inverse problems with unbounded coefficients abstract in a g ramm inverse problems 3 1987 l77 l82 a method to prove uniqueness theorems is given the method uses an estimate of the solution to a partial differential equation with l d coefficients here the estimate is established for l2 d coefficients and the resulting uniqueness theorems are formulated

three dimensional transient thermo elastic analyses by the bie method the proposed method is the direct boundary integral equation bie method applied to three dimensional transient heat transfer analyses and to corresponding elastostatic analyses under thermal loading the mechanical and thermal problems are decoupled for those not familiar with the bie method a short survey of the basic principles is given to help them understand the mathematical treatment which is performed in the frame of distribution theory the tempered elementary solution of the transient heat transfer problem contains time and space variables the numerical treatment of the thermal equation is performed analytically with respect to time and numerically with respect to space in the same way as for steady state equations great care is paid to space integration in order to compute the values of the kernels precisely enough on the surface and inside the volume the computational treatments of both problems are realized in such a way as to minimize computing time differences between transient and steady state analyses on the one hand and between elastostatic analyses with and without thermal loading on the other are emphasized finally an analytical example shows the good behaviour of the proposed method to solve singular thermal problems and an industrial example shows the accuracy of the results obtained by using the bie method to solve three dimensional thermo elastic problems

a homotopy method for nonlinear inverse problems we develop a homotopy method for nonlinear inverse problems where the forward problems are governed by some forms of differential equations a tikhonov style regularization approach yields an optimization problem ordinary iterative methods may fail to solve this problem due to their locally convergent properties then the fixed point homotopy method is introduced to solving the normal equation of the optimization problem and a new and globally convergent algorithm is constructed which is highly effective in the aspects of speed of computation ability of noise suppression and wide region of convergence as a practical application the method is used to solve the inverse problem of 2 d acoustic wave equation we demonstrate the merits and effectiveness of our algorithm on two realistic model problems

green forms and the arithmetic siegel weil formula we construct natural green forms for special cycles in orthogonal and unitary shimura varieties in all codimensions and for compact shimura varieties of type mathrm o p 2 and mathrm u p 1 we show that the resulting local archimedean height pairings are related to special values of derivatives of siegel eisentein series a conjecture put forward by kudla relates these derivatives to arithmetic intersections of special cycles and our results settle the part of his conjecture involving local archimedean heights

a new boundary element formulation for two and three dimensional thermoelasticity using particular integrals new two and three dimensional boundary element formulations are developed for steady state and transient uncoupled thermoelasticity these new procedures differ from previous work in that additional surface or volume integration is not required to incorporate thermal loads in the analysis instead thermal body forces are introduced in the boundary element system via particular integrals the present formulation is implemented in a general purpose multi region system and examples are presented to demonstrate the accuracy and versatility of the method

a special green s function for the biharmonic operator and its application to an inverse boundary value problem abstract a construction of the special green s function for the biharmonic operator is given this result is used to recover the operator a2 v x from its diricldet to neumann map 1 introduction let n 2 and put az e ix a z z ei z for z e c r with z z o since the inverse of the symbol of az is locally absolutely integrable and decays algebraically at infinity its inverse fourier transform defines a tempered distribution which is a fundamental solution of az and called a green faddeev function at z z for the laplace operator this terminology is seen in 1 this function plays an important role in studying several inverse problems for example inverse scattering problems see 1 2 inverse boundary value problems see 3 in short those problems are to determine the coefficients of an elliptic partial differential operator l in r n or a bounded domain f by the scattering datum at izl oo or the cauchy datum on a of the solutions of

a regularized siegel weil formula for unitary groups for the quasi split unitary group u n n we prove a refined analogue of the result of s s kudla and s rallis on an identity a regularized siegel weil formula between a residue of an eisenstein series and the integral of a certain theta function

fixed energy inverse scattering the author s method for solving inverse scattering problem with fixed energy data is described its comparison with the method based on the d n map is given a new inversion procedure is formulated

the inverse problem of resistivity sounding the electric potential due to a single point electrode at the surface of a layered conducting medium is calculated by means of a linear combination of the potentials associated with a set of two layer systems this new representation is called the bilayer expansion for the green s function it enables the forward problem of resistivity sounding to be solved very efficiently even for complicated profiles also the bilayer expansion facilitates the solution of the resistivity inverse problem the coefficients in the expansion are linearly related to apparent resistivity as it is measured and they are readily mapped into parameters for a model specifically i consider models comprising uniformly conducting layers of equal thickness for a given finite data set a quadratic program can be used to find the best fitting model in this class for any specified thickness as the thickness is reduced models of this kind can approximate arbitrary profiles with unlimited accuracy if there is a model that satisfies

confluent hypergeometric functions on tube domains our problem specialized to the case of the siegel upper half space h of degree m concerns the fourier expansion of a series s z fl det z a det a a l here z is a variable on h l is a lattice in the space v of all real symmetric matrices of size m and fl ec it can be shown that this is convergent if re f l m and also that if re m 2 and r e f l m 2 it has a fourier expansion of the form

property c and an inverse problem for a hyperbolic equation let utt u q x t u 0 in d 0 t where d r3 is a bounded domain with a smooth boundary d t d d diam d q x t c 0 t l d suppose that for every u d f x t c1 d 0 t the value un d h s t is known where n is the outer normal to d u solves and and satisfies the initial conditions u ut 0 at t 0 then q x t is uniquely determined by the data f h f c1 d 0 t in the subset s of d 0 t consisting of the lines which make 45 with the t axis and which meet the planes t 0 and t t outside d 0 t provided that q x t is known outside s here d is the closure of d

occam s inversion a practical algorithm for generating smooth models from electromagnetic sounding data the inversion of electromagnetic sounding data does not yield a unique solution but inevitably a single model to interpret the observations is sought we recommend that this model be as simple or smooth as possible in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models to obtain smooth models the nonlinear forward problem is linearized about a starting model in the usual way but it is then solved explicitly for the desired model rather than for a model correction by parameterizing the model in terms of its first or second derivative with depth the minimum norm solution yields the smoothest possible model rather than fitting the experimental data as well as possible which maximizes the roughness of the model the smoothest model which fits the data to within an expected tolerance is sought a practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models resulting in a stable and rapidly convergent algorithm the inversion of both magnetotelluric and schlumberger sounding field data and a joint magnetotelluric resistivity inversion demonstrate the method and show it to have practical application

finding conductivity from surface measurements abstract a method is given to determine conductivity of a body from the measurements of the potential and either normal component of the current on the surface of the body or the normal derivative of the potential on and the value of conductivity at a single point on

occam s inversion to generate smooth two dimensional models from magnetotelluric data magnetotelluric mt data are inverted for smooth 2 d models using an extension of the existing 1 d algorithm occam s inversion since an mt data set consists of a finite number of imprecise data an infinity of solutions to the inverse problem exists fitting field or synthetic electromagnetic data as closely as possible results in theoretical models with a maximum amount of roughness or structure however by relaxing the misfit criterion only a small amount models which are maximally smooth may be generated smooth models are less likely to result in overinterpretation of the data and reflect the true resolving power of the mt method the models are composed of a large number of rectangular prisms each having a constant conductivity apriori information in the form of boundary locations only or both boundary locations and conductivity may be included providing a powerful tool for improving the resolving power of the data joint inversion of te and tm synthetic data generated from known models al

symmetry properties of scattering amplitudes and applications to inverse problems abstract for the transformations of the potential q q l where l is one of the following transformations rotation scaling or translation the corresponding transformation of the scattering amplitude is given a necessary and sufficient condition on the scattering amplitude for the scatterer to be spherically symmetric is derived as an application of the above results

regularization in model updating this paper presents the theory of sensitivity based model updating with a special focus on the properties of the solution that result from the combination of optimization of the response prediction with a priori information about the uncertain parameters model updating together with the additional regularization criterion is an optimization with two objective functions and must be linearized to obtain the solution structured solutions are obtained based on the generalized singular value decomposition gsvd and specific features of the parameter and response paths as the regularization parameter varies are explored the four different types of spaces that arise in the solution are discussed together with the characteristics of the regularized solution families these concepts are demonstrated on a simulated discrete example and on an experimental case study copyright 2007 john wiley sons ltd

a hybrid regularization scheme for the inversion of magnetotelluric data from natural and controlled sources to layer and distortion parameters magnetotelluric mt radiomagnetotelluric rmt and in particular controlled source audiomagnetotelluric csamt data are often heavily distorted by near surface inhomogeneities we developed a