
1.5D BASED INVERSION OF LOGGINGWHILEDRILLING RESISTIVITY MEASUREMENTS IN 3D FORMATIONS
(201706)This manuscript describes an extension of a computer method developed for the fast inversion of loggingwhiledrilling (LWD) resistivity measurements Pardo and TorresVerdín (2015); Bakr et al. (2016). The method enables ...

1D Painless Multilevel Automatic GoalOriented h and p Adaptive Strategies Using a PseudoDual Operator
(20220101)The main idea of our GoalOriented Adaptive (GOA) strategy is based on performing global and uniform h or prefinements (for h and padaptivity, respectively) followed by a coarsening step, where some basis functions are ...

2.5D Deep Learning Inversion of LWD and DeepSensing em Measurements Across Formations with Dipping Faults
(20220101)Deep learning (DL) inversion of induction logging measurements is used in well geosteering for realtime imaging of the distribution of subsurface electrical conductivity. We develop a DL inversion workflow to solve 2.5D ...

3D hpAdaptive Finite Element Simulations of Bend, Step, and MagicT Electromagnetic Waveguide Structures
(201403)Metallic rectangular waveguides are often the preferred choice on telecommunication systems and medical equipment working on the upper microwave and millimeter wave frequency bands due to the simplicity of its geometry, ...

Adjointbased formulation for computing derivatives with respect to bed boundary positions in resistivity geophysics
(201902)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 gradientbased inversion ...

An AgentOriented Hierarchic Strategy for Solving Inverse Problems
(20151231)The paper discusses the complex, agentoriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of twophase global optimization algorithms. The global ...

Approximations for traveltime, slope, curvature, and geometrical spreading of elastic waves in layered transversely isotropic media
(202110)Each seismic body wave, including quasi compressional, shear, and converted wave modes, carries useful subsurface information. For processing, imaging, amplitude analysis, and forward modeling of each wave mode, we need ...

Arithmetic method of doubleinjectionelectrode model for resistivity measurement through metal casing
(20101231)Throughcasing resistivity (TCR) measurement instruments such as Cased Hole Formation Resistivity are extensively used for the dynamic monitoring of oil reservoirs during the production phase in oil wells to evaluate the ...

Asymptotic Models for the Electric Potential across a Highly Conductive Casing
(201807)We analyze a configuration that involves a steelcased borehole, where the casing that covers the borehole is considered as a highly conductive thin layer. We develop an asymptotic method for deriving reduced problems ...

Automatic RedChannel underwater image restoration
(20151231)Underwater images typically exhibit color distortion and low contrast as a result of the exponential decay that light suffers as it travels. Moreover, colors associated to different wavelengths have different attenuation ...

Bearing assessment tool for longitudinal bridge performance
(202009)This work provides an unsupervised learning approach based on a singlevalued performance indicator to monitor the global behavior of critical components in a viaduct, such as bearings. We propose an outlier detection ...

Borehole Resistivity Simulations of OilWater Transition Zones with a 1.5D Numerical Solver
(2020)When simulating borehole resistivity measurements in a reservoir, it is common to consider an oilwater contact (OWC) planar interface. However, this consideration can lead to an unrealistic model since in the presence of ...

Compensation effect analysis in DIE method for throughcasing measuring formation resistivity
(201108)The measuring technique based on DoubleInjectionElectrodes (DIE) and its compensation arithmetic method have been proven to be very useful for eliminating the errors caused by electrodescale mechanical tolerances in ...

Computational cost estimates for parallel shared memory isogeometric multifrontal solvers
(20141231)In this paper we present computational cost estimates for parallel shared memory isogeometric multifrontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as $\mathcal{O}( ...

Computational cost of isogeometric multifrontal solvers on parallel distributed memory machines
(20151231)This paper derives theoretical estimates of the computational cost for isogeometric multifrontal direct solver executed on parallel distributed memory machines. We show theoretically that for the $C^{p1}$ global continuity ...

A Deep Double Ritz Method (D2RM) for solving Partial Differential Equations using Neural Networks
(20230215)Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddlepoint (min–max) problem over the ...

A Deep Learning Approach to the Inversion of Borehole Resistivity Measurements
(202004)Borehole resistivity measurements are routinely employed to measure the electrical properties of rocks penetrated by a well and to quantify the hydrocarbon pore volume of a reservoir. Depending on the degree of geometrical ...

Deep learning driven selfadaptive hp finite element method
(202106)The fi nite element method (FEM) is a popular tool for solving engineering problems governed by Partial Di fferential Equations (PDEs). The accuracy of the numerical solution depends on the quality of the computational ...

Deep learning enhanced principal component analysis for structural health monitoring
(20220101)This paper proposes a Deep Learning Enhanced Principal Component Analysis (PCA) approach for outlier detection to assess the structural condition of bridges. We employ partially explainable autoencoder architecture to ...

A Deep Neural Network as Surrogate Model for Forward Simulation of Borehole Resistivity Measurements
(202001)Inverse problems appear in multiple industrial applications. Solving such inverse problems require the repeated solution of the forward problem. This is the most timeconsuming stage when employing inversion techniques, ...

Design of Loss Functions for Solving Inverse Problems using Deep Learning
(202005)Solving inverse problems is a crucial task in several applications that strongly a ffect our daily lives, including multiple engineering fields, military operations, and/or energy production. There exist different methods ...

Dimensionally adaptive hpfinite element simulation and inversion of 2D magnetotelluric measurements
(20160901)Magnetotelluric (MT) problems often contain different subdomains where the conductivity of the media depends upon one, two, or three spatial variables. Traditionally, when a MT problem incorporates a threedimensional (3D) ...

Direct solvers performance on hadapted grids
(20151231)We analyse the performance of direct solvers when applied to a system of linear equations arising from an $h$adapted, $C^0$ finite element space. Theoretical estimates are derived for typical $h$refinement patterns arising ...

A DPGbased timemarching scheme for linear hyperbolic problems
(202011)The Discontinuous PetrovGalerkin (DPG) method is a widely employed discretization method for Partial Di fferential Equations (PDEs). In a recent work, we applied the DPG method with optimal test functions for the time ...

Energynormbased and goaloriented automatic hp adaptivity for electromagnetics: Application to waveguide Discontinuities
(20081231)The finiteelement method (FEM) enables the use of adapted meshes. The simultaneous combination of h (local variations in element size) and p (local variations in the polynomial order of approximation) refinements, i.e., ...

Enhanced variational image dehazing
(20151231)Images obtained under adverse weather conditions, such as haze or fog, typically exhibit low contrast and faded colors, which may severely limit the visibility within the scene. Unveiling the image structure under the haze ...

Equivalence between the DPG method and the Exponential Integrators for linear parabolic problems
(202011)The Discontinuous PetrovGalerkin (DPG) method and the exponential integrators are two well established numerical methods for solving Partial Di fferential Equations (PDEs) and sti ff systems of Ordinary Di fferential ...

Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements
(202011)Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of ...

Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements
(202005)Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of ...

Error representation of the timemarching DPG scheme
(20220301)In this article, we introduce an error representation function to perform adaptivity in time of the recently developed timemarching Discontinuous Petrov–Galerkin (DPG) scheme. We first provide an analytical expression for ...

ExplicitinTime GoalOriented Adaptivity
(20190415)Goaloriented 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 ...

Exploiting the Kronecker product structure of φ−functions in exponential integrators
(20220515)Exponential time integrators are wellestablished discretization methods for time semilinear systems of ordinary differential equations. These methods use (Formula presented.) functions, which are matrix functions related ...

Fast 1D Inversion of LoggingWhileDrilling Resistivity Measurements for Improved Estimation of Formation Resistivity in HighAngle and Horizontal Wells
(201412)We have developed an efficient inversion method to estimate layerbylayer electric resistivity from loggingwhiledrilling electromagnetic induction measurements. The method assumes a 1D model based on planarly layered ...

Fast 2.5D Finite Element Simulations of Borehole Resistivity Measurements
(20180529)We develop a rapid 2.5dimensional (2.5D) finite element method for simulation of borehole resistivity measurements in transversely isotropic (TI) media. The method combines arbitrary highorder $H^1$  and $H$ (curl)conforming ...

FAST AND AUTOMATIC INVERSION OF LWD RESISTIVITY MEASUREMENTS FOR PETROPHYSICAL INTERPRETATION
(201507)This paper describes an extension of a recently developed fast inversion method (Pardo and TorresVerdÍn (2015)) for estimating a layerbylayer electric resistivity distribution from loggingwhiledrilling (LWD) electromagnetic ...

Fast inversion of loggingwhiledrilling resistivity measurements acquired in multiple wells
(201610)This paper introduces a new method for the fast inversion of borehole resistivity measurements acquired in multiple wells using loggingwhiledrilling (LWD) instruments. There are two key novel contributions. First, we ...

Fast Simulation of 2.5D LWD Resistivity Tools
(201706)As a first step towards the fast inversion of geophysical data, in this work we focus on the rapid simulations of 2.5D loggingwhiledrilling (LWD) borehole resistivity measurements. Given a commercial logging instrument ...

Fast simulation of throughcasing resistivity measurements using semianalytical asymptotic models. Part 1: Accuracy study
(20141231)When trying to obtain a better characterization of the Earth's subsurface, it is common to use borehole throughcasing resistivity measurements. It is also common for the wells to be surrounded by a metal casing to protect ...

Finite element approximation of electromagnetic fields using nonfitting meshes for Geophysics
(201807)We analyze the use of nonfitting meshes for simulating the propagation of electromagnetic waves inside the earth with applications to borehole logging. We avoid the use of parameter homogenization and employ standard edge ...

A Finite Element based Deep Learning solver for parametric PDEs
(2021)We introduce a dynamic Deep Learning (DL) architecture based on the Finite Element Method (FEM) to solve linear parametric Partial Differential Equations(PDEs). The connections between neurons in the architecture mimic the ...

Finite Element Simulations of LoggingWhileDrilling and ExtraDeep Azimuthal Resistivity Measurements using NonFitting Grids
(20180427)We propose a discretization technique using nonfitting grids to simulate magnetic fieldbased resistivity logging measurements. Nonfitting grids are convenient because they are simpler to generate and handle than fitting ...

ForwardinTime GoalOriented Adaptivity
(201903)In goaloriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In timedependent problems, this adaptive ...

Fourier finite element modeling of light emission in waveguides: 2.5dimensional FEM approach
(20151231)We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the threedimensional (3D) coupled waveguideemitter system can ...

Fusionbased variational image dehazing
(20170201)We propose a novel imagedehazing technique based on the minimization of two energy functionals and a fusion scheme to combine the output of both optimizations. The proposed fusionbased variational imagedehazing (FVID) ...

Goaloriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
(202103)We propose a goaloriented meshadaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuousGalerkin norms. By solving a saddlepoint problem, this residual minimization delivers ...

Goaloriented adaptivity using unconventional error representations for the 1D Helmholtz equation
(20151231)In this work, the error of a given output functional is represented using bilinear forms that are different from those given by the adjoint problem. These representations can be employed to design novel h, p, and hp ...

Goaloriented adaptivity using unconventional error representations for the multidimensional Helmholtz equation
(20170627)In goal‐oriented adaptivity, the error in the quantity of interest is represented using the error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element‐wise error ...

GoalOriented pAdaptivity using Unconventional Error Representations for a 1D Steady State ConvectionDiffusion Problem
(2017)This work proposes the use of an alternative error representation for GoalOriented Adaptivity (GOA) in context of steady state convection dominated diffusion problems. It introduces an arbitrary operator for the computation ...

Highaccuracy adaptive modeling of the energy distribution of a meniscusshaped cell culture in a Petri dish
(20151231)Cylindrical Petri dishes embedded in a rectangular waveguide and exposed to a polarized electromagnetic wave are often used to grow cell cultures. To guarantee the success of these cultures, it is necessary to enforce that ...

A hybrid method for inversion of 3D DC resistivity logging measurements
(20141231)This paper focuses on the application of hp hierarchic genetic strategy (hpHGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration ...

ICCS 2017 Workshop on AgentBased Simulations, Adaptive Algorithms and Solvers
(2017)This workshop seeks to integrate results from different domains of computer science, computational science, and mathematics. We welcome simulation papers, either hard simulations using finite element or finite difference ...

Influence of boreholeeccentred tools on wireline and loggingwhiledrilling sonic logging measurements
(201306)We describe a numerical study to quantify the influence of tooleccentricity on wireline and loggingwhiledrilling (LWD) sonic logging measurements. Simulations are performed with a hpadaptive Fourier FiniteElement ...

Largeoffset Pwave traveltime in layered transversely isotropic media
(20210501)Largeoffset seismic data processing, imaging, and velocity estimation require an accurate traveltime approximation over a wide range of offsets. In layered transversely isotropic media with a vertical symmetry axis, the ...

Massive Database Generation for 2.5D Borehole Electromagnetic Measurements using Refined Isogeometric Analysis
(202106)Borehole resistivity measurements are routinely inverted in realtime during geosteering operations. The inversion process can be efficiently performed with the help of advanced artificial intelligence algorithms such as ...

Modeling extradeep electromagnetic logs using a deep neural network
(202105)Modern geosteering is heavily dependent on realtime interpretation of deep electromagnetic (EM) measurements. We have developed a methodology to construct a deep neural network (DNN) model trained to reproduce a full set ...

Modeling of bone conduction of sound in the human head using hpfinite elements: Code design and verification
(20111231)We focus on the development of a reliable numerical model for investigating the boneconduction of sound in the human head. The main challenge of the problem is the lack of fundamental knowledge regarding the transmission ...

A multidomain decompositionbased Fourier finite element method for the simulation of 3D marine CSEM measurements
(20170101)We introduce a multidomain decomposition Fourier finite element (MDDFFE) method for the simulation of threedimensional (3D) marine controlled source electromagnetic measurement (CSEM). The method combines a 2D finite ...

Multiobjective hierarchic memetic solver for inverse parametric problems
(20151231)We propose a multiobjective approach for solving challenging inverse parametric problems. The objectives are misfits for several physical descriptions of a phenomenon under consideration, whereas their domain is a common ...

A multiobjective memetic inverse solver reinforced by local optimization methods
(20160901)We propose a new memetic strategy that can solve the multiphysics, complex inverse problems, formulated as the multiobjective optimization ones, in which objectives are misfits between the measured and simulated states ...

New post processing method for interpretation of through casing resistivity (TCR) measurements
(201103)We propose a new iterative method for post processing through casing resistivity (TCR) measurements. This method can be seen as a correction or extension of Kaufman´s theory to more complex scenarios, in which the casing ...

Nonhyperbolic normal moveout stretch correction with deep learning automation
(20220215)Normalmoveout (NMO) correction is a fundamental step in seismic data processing. It consists of mapping seismic data from recorded traveltimes to corresponding zerooffset times. This process produces wavelet stretching ...

A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
(20180614)In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a ...

On quadrature rules for solving Partial Differential Equations using Neural Networks
(20220401)Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature ...

Optimally refined isogeometric analysis
(201706)Performance of direct solvers strongly depends upon the employed discretization method. In particular, it is possible to improve the performance of solving Isogeometric Analysis (IGA) discretizations by introducing multiple ...

A Painless Automatic hpAdaptive Strategy for Elliptic Problems
(202001)In this work, we introduce a novel hpadaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping close to optimal numerical ...

A painless multilevel automatic goaloriented hpadaptive coarsening strategy for elliptic and nonelliptic problems
(20221101)This work extends an automatic energynorm $hp$adaptive strategy based on performing quasioptimal unrefinements to the case of nonelliptic problems and goaloriented adaptivity. The proposed approach employs a multilevel ...

Parallel refined Isogeometric Analysis in 3D
(201811)We study threedimensional isogeometric analysis (IGA) and the solution of the resulting system of linear equations via a direct solver. IGA uses highly continuous $C^{p1}$ basis functions, which provide multiple benefits ...

Performance of a multifrontal parallel direct solver for hpfinite element method
(20091231)In this paper we present the performance of our parallel multifrontal direct solver when applied to solve linear systems of equations resulting from discretizations of a hp Finite Element Method (hpFEM). The hpFEM ...

A QuadratureFree Method for Simulation and Inversion of 1.5D Direct Current (DC) Borehole Measurements
(201612)Resistivity inverse problems are routinely solved in order to characterize hydrocarbon bearing formations. They often require a large number of forward problems simulations. When considering a one dimensional (1D) planarly ...

Quantities of interest for surface based resistivity geophysical measurements
(20151231)The objective of traditional goaloriented strategies is to construct an optimal mesh that minimizes the problem size needed to achieve a user prescribed tolerance error for a given quantity of interest (QoI). Typical ...

Refined Isogeometric Analysis for a Preconditioned Conjugate Gradient Solver
(20180615)Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces $C^0$ hyperplanes that act as separators for the direct LU factorization solver. As a result, ...

Refined Isogeometric Analysis for fluid mechanics and electromagnetism
(201903)Starting from a highly continuous isogeometric analysis discretization, we introduce hyperplanes that partition the domain into subdomains and reduce the continuity of the discretization spaces at these hyperplanes. As the ...

Refined isogeometric analysis for generalized Hermitian eigenproblems
(202104)We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku = λMu). rIGA conserves the desirable properties of maximumcontinuity isogeometric analysis (IGA) while it reduces the solution ...

Refined isogeometric analysis of quadratic eigenvalue problems
(20220716)Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve quadratic eigenproblems. rIGA discretization, while ...

A Secondary Field Based hpFinite Element Method for the Simulation of Magnetotelluric Measurements
(20151231)In some geophysical problems, it is sometimes possible to divide the subsurface resistivity distribution as a one dimensional (1D) contribution plus some two dimensional (2D) inhomogeneities. Assuming this scenario, we ...

Semianalytical response of acoustic logging measurements in frequency domain
(20151231)This work proposes a semianalytical method for simulation of the acoustic response of multipole eccentered sources in a fluidfilled borehole. Assuming a geometry that is invariant with respect to the azimuthal and vertical ...

Sensitivity Analysis for the Appraisal of Hydrofractures in Horizontal Wells with Borehole Resistivity Measurements
(201306)This paper numerically evaluates the possibility of using borehole electromagnetic (EM) measurements to diagnose and quantify hydraulic fractures that have been arti ficially generated in a horizontal well. Hydrofractures ...

Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lockin Thermography for Crack Characterization
(202009)This work focuses on the characterization of narrow vertical cracks of nite size using optically excited lockin thermography (OLT). To characterize these cracks, we need to solve an illposed inverse problem. As a previous ...

Sensitivity study of boreholetosurface and crosswell electromagnetic measurements acquired with energized steel casing to water displacement in hydrocarbonbearing layers
(20081231)We study the theoretical response of electromagnetically energized steel casing in the presence of subsurface variations of electrical resistivity. Casing is energized with a finitesize solenoid antenna located along the ...

A Simulation Method for the Computation of the E
(202103)We propose a set of numerical methods for the computation of the frequencydependent eff ective primary wave velocity of heterogeneous rocks. We assume the rocks' internal microstructure is given by microcomputed tomography ...

Simulation of DC duallaterolog measurements in complex formations: A Fourierseries approach with nonorthogonal coordinates and selfadapting finite elements
(20091231)Dual laterolog (DLL) makes use of a galvanic conduction principle to focus electrical currents into rock formations, thereby minimizing shoulder and borehole effects in the measurement of formation resistivity. The tool ...

Simulation of marine controlled source electromagnetic measurements using a parallel fourier hpfinite element method
(20111231)We introduce a new numerical method to simulate geophysical marine controlled source electromagnetic (CSEM) measurements for the case of 2D structures and finite 3D sources of electromagnetic (EM) excitation. The method ...

Source time reversal (STR) method for linear elasticity
(2018)We study the problem of source reconstruction for a linear elasticity problem applied to seismicity induced by mining. We assume the source is written as a variable separable function $\mathbf{f(x)}\>g(t)$ . We first present ...

A source time reversal method for seismicity induced by mining
(20170101)In this work, we present a modified TimeReversal Mirror (TRM) Method, called Source Time Reversal (STR), to find the spatial distribution of a seismic source induced by mining activity. This methodology is based on a known ...

Supervised Deep Learning with Finite Element simulations for damage identification in bridges
(20220415)This work proposes a supervised Deep Learning approach for damage identification in bridge structures. We employ a hybrid methodology that incorporates Finite Element simulations to enrich the training phase of a Deep ...

TimeDomain GoalOriented Adaptivity Using PseudoDual Error Representations
(201712)Goaloriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudodual problems for goaloriented adaptivity in the ...

Uncertainty Quantification on the Inversion of Geosteering Measurements using Deep Learning
(20211101)We propose the use of a Deep Learning (DL) algorithm for the realtime inversion of electromagnetic measurements acquired during geosteering operations. Moreover, we show that when the DL algorithm is equipped with a ...

Unified modeling language description of the objectoriented multiscale adaptive finite element method for stepandflash imprint lithography simulations
(20141231)In the first part of the paper we present the multiscale simulation of the StepandFlash Imprint Lithography (SFIL), a modern patterning process. The simulation utilizes the hp adaptive Finite Element Method (hpFEM) ...

The value of continuity: Refined isogeometric analysis and fast direct solvers
(20160923)We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) ...

Variational Formulations for Explicit RungeKutta Methods
(201908)Variational spacetime formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop meshadaptive algorithms. Since it is known ...

VibrationBased SHM Strategy for a Real Time Alert System with Damage Location and Quantification
(20210111)We present a simple and fully automatable vibrationbased Structural Health Monitoring (SHM) alert system. The proposed method consists in applying an Automated Frequency Domain Decomposition (AFDD) algorithm to obtain the ...

VibrationBased SHM Strategy for a Real Time Alert System with Damage Location and Quantification
(202101)We present a simple and fully automatable vibrationbased Structural Health Monitoring (SHM) alert system. The proposed method consists in applying an Automated Frequency Domain Decomposition (AFDD) algorithm to obtain the ...