A dual‐grid nonlinear inversion technique with applications to the interpretation of dc resistivity data

  title={A dual‐grid nonlinear inversion technique with applications to the interpretation of dc resistivity data},
  author={Carlos Torres‐Verd{\'i}n and Vladimir Druskin and Sheng Fang and Leonid A. Knizhnerman and Alberto Malinverno},
We develop a solution to the nonlinear inverse problem via a cascade sequence of auxiliary least‐squares minimizations. The auxiliary minimizations are nonlinear inverse problems themselves, except that they are implemented with an approximate forward problem that is at least an order of magnitude faster to solve than the algorithm used to simulate the measurements. Any given auxiliary minimization in the cascade is fully selfcontained and yields a solution of the unknown model parameters. This… 
An enhanced Gauss-Newton inversion algorithm using a dual-optimal grid approach
Two algorithms for solving the nonlinear electromagnetic inversion problem in the Earth are developed that employ the Gauss-Newton inversion method and the so-called optimal grid technique to speed up the inversion's computational time.
Numerical Simulation and Inversion of Pressure Data Acquired With Permanent Sensors
A new axisymmetric solution for the numerical simulation of single-phase fluid flow in permeable media and an efficient algorithm to quantify the sensitivity of permanent pressure data to lateral and vertical variations in the distribution of permeability around the injection well is constructed.
A data‐adaptive spatial resolution method for three‐dimensional inversion of triaxial borehole electromagnetic measurements
A novel adaptive inversion technique: Data-adaptive Spatial Resolution Inversion (DSRI) method, which eliminates the need to select parameterization prior to inversion, and which constitutes a robust technique for efficient multiparameter inversion of multicomponent electromagnetic measurements.
Fast 2D inversion of large-borehole EM induction data sets with a domain-decomposition method
Inversion methods have become increasingly important to estimate formation resistivity from borehole electromagnetic (EM) measurements. Recent advances in hardware computer resources as well as the
Cascade 3-D Inversion of Magnetotelluric Data
We have developed a new method of cascade threedimensional (3-D) magnetotelluric (MT) inversion which combines the advantages of the rigorous and approximate methods. As the main engine of the
Three-dimensional inversion of static-shifted magnetotelluric data
A practical method for inverting static-shifted magnetotelluric (MT) data to produce a 3-D resistivity model is presented. Static-shift parameters are incorporated into an iterative, linearized
Data-adaptive resolution method for the parametric three-dimensional inversion of triaxial borehole electromagnetic measurements
We develop a new adaptive inversion procedure: Data- adaptive Resolution Inversion (DRI) method, which eliminates the need of selecting a parameterization prior to inversion. Instead, one performs a
Multiscale electrical impedance tomography
[1] Electrical impedance tomography aims to recover the electrical conductivity underground from surface and/or borehole apparent resistivity measurements. This is a highly nonlinear inverse problem,
A dual-grid automatic history-matching technique with applications to 3D formation testing in the presence of oil-based muds
Probe-type formation testers are often used to estimate permeability and permeability anisotropy from pressure transient measurements. The interpretation of these measurements is not trivial in the


Approximate Inverse Mapping Inversion of the COPROD2 Data
The results of the inversion of the COPROD2 magnetotelluric data set are presented using two implementations of the AIM inverse method, and the similarities of the final models give a suggestion of that which might be common to all models which fit the data.
Solution of 2.5‐dimensional problems using the Lanczos decomposition
We consider the problem of electrical conduction in the context of geophysical prospecting and assume that the conductivity of the Earth is constant in a direction perpendicular to the probing plane.
A method for inverting electromagnetic fields induced by a line source in an earth of two-dimensional conductivity structure is developed. Certain unique features of the finite element method are
Three-dimensional magnetotelluric inversion using conjugate gradients
SUMMARY We have developed an inversion procedure that uses conjugate gradient relaxation methods. Although one can generalize the method to all inverse problems, we demonstrate its use to invert
Three-dimensional electromagnetic modeling and inversion on massively parallel computers
This report has demonstrated techniques that can be used to construct solutions to the 3-D electromagnetic inverse problem using full wave equation modeling. To this point great progress has been
Rapid 2.5‐dimensional forward modeling and inversion via a new nonlinear scattering approximation
We introduce a novel approximation to numerically simulate the electromagnetic response of point or line sources in the presence of arbitrarily heterogeneous conductive media. The approximation is
Three-dimensional magnetotelluric modeling using difference equations­ Theory and comparisons to integral equation solutions
We have developed an algorithm for computing the magnetotelluric response of three‐dimensional (3-D) earth models. It is a difference equation algorithm that is based on the integral forms of
Cross-borehole resistivity tomography
Electrical resistivity tomography (ERT) is a method for determining the electrical resistivity distribution in a volume from discrete measurements of current and voltage made within the volume or on
Some factors affecting the resolution and accuracy of resistivity tomography are examined using numerical simulation. The inversion method used is based on smoothness-constrained least-squares and
Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering
The Born and Rytov approximations, widely used for solving scattering problems, are of limited utility for low-frequency electromagnetic scattering in geophysical applications where conductivity can