A multi-domain decomposition-based Fourier finite element method for the simulation of 3D marine CSEM measurements

We introduce a multi-domain decomposition Fourier finite element (MDDFFE) method for the simulation of three-dimensional (3D) marine controlled source electromagnetic measurement (CSEM). The method combines a 2D finite element (FE) method in two spatial dimensions with a hybrid discretization based on a Fourier FE method along the third dimension. The method employs a secondary field formulation rather than the total field formulation. We apply the MDDFFE method to several synthetic marine CSEM examples exhibiting bathymetry and/or multiple 3D subdomains. Numerical results show that the use of the MDDFFE method reduces the problem size by as much as 87 % in terms of the number of unknowns, without any sacrifice in accuracy

Simulation of marine controlled source electromagnetic measurements using a parallel fourier hp-finite element method

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 of solution is based on a spatial discretization that combines a 1D Fourier transform with a 2D self-adaptive, goal-oriented, hp-Finite element method. It enables fast and accurate simulations for a variety of important, challenging and practical cases of marine CSEM acquisition. Numerical results confirm the high accuracy of the method as well as some of the main physical properties of marine CSEM measurements such as high measurement sensitivity to oil-bearing layers in the subsurface. In our model, numerical results indicate that measurements could be affected by the finite oil-bearing layer by as much as 104% (relative difference). While the emphasis of this paper is on EM simulations, the method can be used to simulate different physical phenomena such as seismic measurements

Quantities of interest for surface based resistivity geophysical measurements

The objective of traditional goal-oriented 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 geophysical resistivity measurement acquisition systems can easily record electromagnetic (EM) fields. However, depending upon the application, EM fields are sometimes loosely related to the quantity that is to be inverted (conductivity or resistivity), and therefore they become inadequate for inversion. In the present work, we study the impact of the selection of the QoI in our inverse problem. We focus on two different acquisition systems: marine controlled source electromagnetic (CSEM), and magnetotellurics (MT). For both applications, numerical results illustrate the benefits of employing adequate QoI. Specifically, the use as QoI of the impedance matrix on MT measurements provides significant computational savings, since one can replace the existing absorbing boundary conditions (BCs) by a homogeneous Dirichlet BC to truncate the computational domain, something that is not possible when considering EM fields as QoI

A summary of my twenty years of research according to Google Scholars

I am David Pardo, a researcher from Spain working mainly on numerical analysis applied to geophysics. I am 40 years old, and over a decade ago, I realized that my performance as a researcher was mainly evaluated based on a number called \h-index". This single number contains simultaneously information about the number of publications and received citations. However, dif- ferent h-indices associated to my name appeared in di erent webpages. A quick search allowed me to nd the most convenient (largest) h-index in my case. It corresponded to Google Scholars. In this work, I naively analyze a few curious facts I found about my Google Scholars and, at the same time, this manuscript serves as an experiment to see if it may serve to increase my Google Scholars h-index

A summary of my twenty years of research according to Google Scholars

I am David Pardo, a researcher from Spain working mainly on numerical analysis applied to geophysics. I am 40 years old, and over a decade ago, I realized that my performance as a researcher was mainly evaluated based on a number called \h-index". This single number contains simultaneously information about the number of publications and received citations. However, dif- ferent h-indices associated to my name appeared in di erent webpages. A quick search allowed me to nd the most convenient (largest) h-index in my case. It corresponded to Google Scholars. In this work, I naively analyze a few curious facts I found about my Google Scholars and, at the same time, this manuscript serves as an experiment to see if it may serve to increase my Google Scholars h-index

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

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 adjoint-based formulation for computing the derivatives of the electromagnetic fields withrespect 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

Three-dimensional modelling and inversion of controlled source electromagnetic data

The marine Controlled Source Electromagnetic (CSEM) method is an important and almost self-contained discipline in the toolkit of methods used by geophysicists for probing the earth. It has increasingly attracted attention from industry during the past decade due to its potential in detecting valuable natural resources such as oil and gas. A method for three-dimensional CSEM modelling in the frequency domain is presented. The electric field is decomposed in primary and secondary components, as this leads to a more stable solution near the source position. The primary field is computed using a resistivity model for which a closed form of solution exists, for example a homogeneous or layered resistivity model. The secondary electric field is computed by discretizing a second order partial differential equation for the electric field, also referred in the literature as the vector Helmholtz equation, using the edge finite element method. A range of methods for the solution of the linear system derived from the edge finite element discretization are investigated. The magnetic field is computed subsequently, from the solution for the electric field, using a local finite difference approximation of Faraday’s law and an interpolation method. Tests, that compare the solution obtained using the presented method with the solution computed using alternative codes for 1D and 3D synthetic models, show that the implemented approach is suitable for CSEM forward modelling and is an alternative to existing codes. An algorithm for 3D inversion of CSEM data in the frequency domain was developed and implemented. The inverse problem is solved using the L-BFGS method and is regularized with a smoothing constraint. The inversion algorithm uses the presented forward modelling scheme for the computation of the field responses and the adjoint field for the computation of the gradient of the misfit function. The presented algorithm was tested for a synthetic example, showing that it is capable of reconstructing a resistivity model which fits the synthetic data and is close to the original resistivity model in the least-squares sense. Inversion of CSEM data is known to lead to images with low spatial resolution. It is well known that integration with complementary data sets mitigates this problem. It is presented an algorithm for the integration of an acoustic velocity model, which is known a priori, in the inversion scheme. The algorithm was tested in a synthetic example and the results demonstrate that the presented methodology is promising for the improvement of resistivity models obtained from CSEM data

Controlled-source electromagnetics for reservoir monitoring on land

The main goal of exploration geophysics is to obtain information about the subsurface that is not directly available from surface geological observations. The results are primarily used for finding potential reservoirs that contain commercial quantities of hydrocarbons. A number of possible geophysical methods exists these days to achieve such a goal. One of them is the controlled-source electromagnetic (CSEM) method. CSEM data can provide resistivity maps of the subsurface. Because the bulk resistivity depends on the resistivity of the pore fluid, these maps may enable us to estimate the nature of the fluid content in the reservoir. The CSEM method exploits electromagnetic fields to remotely characterize the nature of the fluid content in the pores. When a dipole current source is stuck into the ground or placed in the seawater, current flows from one pole to the other through the sediments, creating an electrical field in the subsurface. If highly resistive bodies are present in the subsurface, the electrical field measured at some distance from the source will be larger in amplitude than the field in the absence of these bodies. As hydrocarbon-bearing rock is highly resistive, one may link the larger amplitude to the presence of hydrocarbon reservoirs. A logical consequence of this phenomenon is that the CSEM method may also be suited for monitoring a hydrocarbon reservoir during production. The reason is that water flooding or steam injection for oil production creates resistivity changes in the reservoir, and if those changes are large enough, we can expect differences in the CSEM response with time-lapse surveys. This consideration led us to further investigate the EM monitoring problem. We tried to answer two questions: are the time-lapse changes in the reservoir detectable, particularly in the presence of noise, and if so, could we use timelapse signals to locate where the time-lapse changes happened in the subsurface? In this thesis, we considered land CSEM and found that the resistivity change due to displacement of oil by brine can produce a small but measurable difference in the CSEM response. Interestingly, those response differences at the surface are confined to the lateral extent of resistivity changes in the subsurface, even in the presence of various kinds of repeatability noise. We found a simple and effective method to remove the repeatability noise due to the airwave. Finally, results obtained when incorporating nonlinear EM inversion into the monitoring problem suggest that this application of the CSEM method has the potential to play a significant role in the oil and gas industry

Gaussian process methodology for multi-frequency marine controlled-source electromagnetic profile estimation in isotropic medium

The marine controlled-source electromagnetic (CSEM) technique is an application of electromagnetic (EM) waves to image the electrical resistivity of the subsurface underneath the seabed. The modeling of marine CSEM is a crucial and time-consuming task due to the complexity of its mathematical equations. Hence, high computational cost is incurred to solve the linear systems, especially for high-dimensional models. Addressing these problems, we propose Gaussian process (GP) calibrated with computer experiment outputs to estimate multi-frequency marine CSEM profiles at various hydrocarbon depths. This methodology utilizes prior information to provide beneficial EM profiles with uncertainty quantification in terms of variance (95% confidence interval). In this paper, prior marine CSEM information was generated through Computer Simulation Technology (CST) software at various observed hydrocarbon depths (250–2750 m with an increment of 250 m each) and different transmission frequencies (0.125, 0.25, and 0.5 Hz). A two-dimensional (2D) forward GP model was developed for every frequency by utilizing the marine CSEM information. From the results, the uncertainty measurement showed that the estimates were close to the mean. For model validation, the calculated root mean square error (RMSE) and coefficient of variation (CV) proved in good agreement between the computer output and the estimated EM profile at unobserved hydrocarbon depths

Theoretical Developments in Electromagnetic Induction Geophysics with Selected Applications in the Near Surface

Near-surface applied electromagnetic geophysics is experiencing an explosive period of growth with many innovative techniques and applications presently emergent and others certain to be forthcoming. An attempt is made here to bring together and describe some of the most notable advances. This is a difficult task since papers describing electromagnetic induction methods are widely dispersed throughout the scientific literature. The traditional topics discussed herein include modeling, inversion, heterogeneity, anisotropy, target recognition, logging, and airborne electromagnetics (EM). Several new or emerging techniques are introduced including landmine detection, biogeophysics, interferometry, shallow-water electromagnetics, radiomagnetotellurics, and airborne unexploded ordnance (UXO) discrimination. Representative case histories that illustrate the range of exciting new geoscience that has been enabled by the developing techniques are presented from important application areas such as hydrogeology, contamination, UXO and landmines, soils and agriculture, archeology, and hazards and climat