We present 2.5D fast and rigorous forward inversion algorithms for deep electromagnetic (EM) applications that include crosswell controlled-source EM measurements. The algorithm is based on a finite-difference approach in which multifrontal LU decomposition simulates multisource experiments at nearly the cost of simulating one single-source experiment each frequency operation. When size linear system equations large, use this noniterative solver impractical. Hence, we optimal grid technique...

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This based a near-best uniform rational interpolant the inverse square root function union negative and positive real interval, designed with help classical result by Zolotarev. Using Krein's interpretation Stieltjes continued fraction, this can be converted into three-term finite difference discretization perfectly matched layer which converges exponentially fast in...

A technique derived from two related methods suggested earlier by some of the authors for optimization finite-difference grids and absorbing boundary conditions is applied to discretization perfectly matched layer (PML) wave equations in Cartesian coordinates. We formulate simple sufficient optimality implement them. It found that minimal error can be achieved using pure imaginary coordinate stretching. As such, PML algebraically equivalent rational approximation square root on [0,1]...

The interpretation of long‐offset transient electromagnetic (LOTEM) data is usually based on layered earth models. Effects lateral conductivity variations are commonly explained qualitatively, because three‐dimensional (3-D) numerical modeling not readily available for complex geology. One the first quantitative 3-D interpretations LOTEM carried out using measurements from Münsterland basin in northern Germany. In this survey area, four sets show effects including a sign reversal measured...

Abstract Resistivity anisotropy in both laminated shale-sand and clean sand formations is well documented. Tools that are sensitive to formation also documented, the leading contender for this type of measurement transverse induction array. Such an array, whose transmitter generates currents plane borehole axis, has a good sensitivity vertical resistivity formation, Rv. Invasion mud filtrate into permeable long complicated wireline log analysis. Interpretation anisotropic will be no...

We suggest an approach to grid optimization for a second order finite-difference scheme elliptic equations. A model problem corresponding the three-point semidiscretization of Laplace equation on semi-infinite strip is considered. relate approximate boundary Neumann-to-Dirichlet map rational function and calculate steps our using Padé--Chebyshev approximation inverse square root. It increases convergence from exponential without increasing stencil losing stability.

We develop a parametric inversion algorithm to determine simultaneously the horizontal and vertical resistivities of both formation invasion zones, radius, bed boundary upper location thickness, relative dip angle from electromagnetic triaxial induction logging data. This is full 3D inverse scattering problem in transversally isotropic media. To acquire sufficient sensitivity invert for all these parameters, we collect data using multicomponent, multispacing array. For each...

We introduce a novel inversion algorithm for electrical impedance tomography in two dimensions, based on model reduction approach. The reduced models are resistor networks that arise five point stencil discretizations of the elliptic partial differential equation satisfied by electric potential, adaptive grids computed as part problem. prove unique solvability problem broad class measurements Dirichlet-to-Neumann map. size is limited precision measurements. resulting naturally refined near...

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by application controlled source electromagnetic exploration, where unknown subsurface electrical resistivity and data are time resolved surface measurements magnetic field. presented in this paper considers one two dimensions. reduced obtained with rational interpolation frequency (Laplace) domain Krylov subspace projection...

We present two‐and‐half‐dimensional (2.5D) forward and inversion algorithms for the interpretation of Marine controlled‐source electromagnetic (CSEM) data. The algorithm employs a frequency domain finite difference solution Maxwell equation. Fast computational times are achieved through use a) optimal grid techniques to extend boundaries mesh outwards from region interest along invariant direction b) direct stiffness matrix technique that allows us obtain field all source excitations...

We introduce an inversion algorithm for electrical impedance tomography (EIT) with partial boundary measurements in two dimensions. It gives stable and fast reconstructions using sparse parameterizations of the unknown conductivity on optimal grids that are computed as part inversion. follow approach Borcea et al (2008 Inverse Problems 24 035013) Vasquez (2006 PhD thesis Rice University, Houston, TX, USA) connects inverse discrete problems resistor networks to continuum EIT problems, grids....

The Krylov subspace projection approach is a well-established tool for the reduced-order modeling of dynamical systems in time domain. In this paper, we address main issues obstructing application powerful to time-domain solution exterior wave problems. We use frequency-independent perfectly matched layers simulate extension infinity. Pure imaginary stretching functions based on Zolotarev's optimal rational approximation square root are implemented leading with controlled accuracy over...

Transient data controlled-source electromagnetic measurements are usually interpreted via extracting few frequencies and solving the corresponding inverse frequency-domain problem. Coarse frequency sampling may result in loss of information affect quality interpretation; however, refined increases computational cost. Fitting directly time domain has similar drawbacks, i.e., its large cost, particular, when Gauss-Newton (GN) algorithm is used for misfit minimization. That cost mainly...

.Data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of inverse scattering problems with applications to seismic and sonar imaging. One requirement this approach is that it uses full square multiple-input/multiple-output (MIMO) matrix-valued transfer function data multidimensional problems. The synthetic aperture radar (SAR), however, limited single-input/single-output (SISO) measurements corresponding diagonal matrix function. Here we present...

We present a 2.5D inversion algorithm for the interpretation of electromagnetic data collected in cross‐well configuration. Some results from simulated as well field measurements are presented order to show efficiency and robustness algorithm.

We developed two algorithms for solving the nonlinear electromagnetic inversion problem in Earth. To achieve a balance between efficiency and robustness, both employ Gauss-Newton method. Moreover, to speed up inversion's computational time, so-called optimal grid technique is utilized. The first algorithm uses forward solver with very coarse calculate Jacobian matrix. Hence, this scheme we different sets of grids. One set used compute data mismatch be minimized other construct In second...

Abstract Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback this approach is that it was limited to measurement arrays with reciprocally collocated transmitters and receivers, is, square symmetric matrix (data) transfer functions. To relax limitation, we use our previous work Druskin et al (2021 Inverse Problems 37 075003), where ROMs were combined Lippmann–Schwinger integral equation produce a direct...

Abstract Reservoir simulation models often require grids sufficiently resolved to capture the complexities of geological structures present so that pressure and saturation profiles are deemed reasonable enough for decisions be made with confidence. However, high resolution implies long run times, which is compounded in optimization problems. problems usually involve localized decisions, e.g., production control a specific time-dependent objective function. With this tighter focus on...