Dimensionally adaptive hp-finite element simulation and inversion of 2D magnetotelluric measurements

Álvarez-Aramberri, Julen; Pardo, David

doi:10.1016/j.jocs.2016.07.014

Cited by 19 publications

(19 citation statements)

References 36 publications

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“…Goal-oriented adaptive algorithms address the accuracy requirements of some engineering problems, where it is crucial to accurately approximate some physical features of the solution [12][13][14][15][16][17][18][19]. These relevant features are called quantities of interest and they are usually represented by output functionals computed from the solution.…”

Section: Introductionmentioning

confidence: 99%

Explicit-in-time goal-oriented adaptivity

Muñoz‐Matute

Calo

Pardo

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of interest as an integral over the whole space-time domain. A full space-time variational formulation allows such representation. Most authors employ implicit time marching schemes to perform goal-oriented adaptivity as it is known that they can be reinterpreted as Galerkin methods. In this work, we consider variational forms for explicit methods in time. We derive an appropriate error representation and propose a goal-oriented adaptive algorithm in space. For that, we derive the forward Euler method in time employing a discontinuous-in-time Petrov-Galerkin formulation. In terms of time domain adaptivity, we impose the Courant-Friedrichs-Lewy condition to ensure the stability of the method. We provide some numerical results in 1D space + time for the diffusion and advection-diffusion equations to show the performance of the proposed explicit-in-time goal-oriented adaptive algorithm.

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Section: Introductionmentioning

confidence: 99%

Explicit-in-time goal-oriented adaptivity

Muñoz‐Matute

Calo

Pardo

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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“…with z i = (3,5,7). For this problem, we consider the attenuation and the phase 500 kHz difference of the magnetic field between the two receivers.…”

Section: Model Problem C: Multi-layer Mediamentioning

confidence: 99%

“…We consider resistivity measurements to characterize the electrical properties of the subsurface. There exist: (a) on surface resistivity measurements acquisition systems such as controlled source electromagnetic (CSEM) [1][2][3][4] and Magnetotellurics (MT) [5,6], and (b) borehole logging measurements such as those obtained with logging-while-drilling (LWD) devices [7][8][9], including the so-called deep and extra-deep [10,11] logging devices used for geosteering purposes. Recently developed LWD resistivity measurements are able to measure all nine components of the magnetic field, namely H xx , H xy , H xz , H yx , H yy , H yz , H zx , H zy , H zz , where the first and second sub-indexes indicate the orientation of the transmitter and the receiver, respectively.…”

Section: Introductionmentioning

confidence: 99%

Adjoint-based formulation for computing derivatives with respect to bed boundary positions in resistivity geophysics

2019

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In inverse geophysical resistivity problems, it is common to optimize for specific resistivity values and bed boundary positions, as needed, for example, in geosteering applications. When using gradient-based inversion methods such as Gauss-Newton, we need to estimate the derivatives of the recorded measurements with respect to the inversion parameters. In this article, we describe an adjointbased formulation for computing the derivatives of the electromagnetic fields with respect to the bed boundary positions. The key idea to obtain this adjoint-based formulation is to separate the tangential and normal components of the field, and treat them differently. We then apply this method to a 1.5D borehole resistivity problem. We illustrate its accuracy and some of its convergence properties via numerical experimentation by comparing the results obtained with our proposed adjoint-based method vs. both the analytical results when available and a finite differences approximation of the derivative.

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“…To numerically solve equation (10), we employ the self-adaptive multigoal oriented hp-FEM, which have already being successfully employed to obtain accurate MT measurements [43,44]. After numerically computing E y , we calculate H x from Maxwell's equations via postprocessing using the formula H x (ρ) = (jωµ) −1 (∂E y (ρ)/∂z).…”

Section: Magnetotelluric Inverse Problemmentioning

confidence: 99%