Colin Farquharson

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• Professor at Memorial University of Newfoundland

Seismic surveys are a key method for monitoring CO₂ storage. Seismic Full Waveform Inversion (FWI) is an advanced approach that reconstructs a detailed subsurface model using seismic data. Due to its ill-posed and non-unique nature, quantifying uncertainty is essential for evaluating model confidence and guiding decision-making. Bayesian inference...

We consider application of full-waveform inversion (FWI) to radio-frequency electromagnetic (EM) data. Radio-frequency imaging (RIM) is a cross-borehole technique to image EM subsurface properties from measurements of transmitted radio-frequency waves. It is used in coal seam imaging, ore exploration and various engineering and civil engineering ap...

Minimum-structure, or Occam’s style of, inversion introduces a regularization function into the underdetermined geophysical inverse problems to stabilize the inverse problem and mitigate its non-uniqueness. The regularization function is typically designed such that it can incorporate a priori information into the inversion framework, thus construc...

CALL FOR PAPERS _________________________________________________________________________________ The editors of this special section are: * Colin Farquharson (Memorial University, Newfoundland and Labrador), * Sihong Wu (University of Houston), * Sizhuang Deng (Chevron), * Xiaolong Wei (Stanford University), * Muhammad Rizwan Asif (Aarhus Uni...

We investigate an emerging method called surface geometry inversion (SGI) for the inversion of transient electromagnetic (TEM) data. Conventional minimum-structure inversion methods parameterize the Earth model with many mesh cells within which the physical properties are constant and construct a physical property model that is usually smoothly var...

Trial-and-error modeling may provide some level of interpretation of the subsurface while sacrificing certainty, and certainty it is a viable alternative for precise three-dimensional (3D) interpretation of real ground-airborne frequency-domain electromagnetic (GAFEM) data. Therefore, a semiautomatic trial-and-error modeling approach has been prese...

This paper proposes a procedure of forward modeling three-dimensional frequency-domain wire-source electromagnetic data using the meshless generalized finite-difference (MGFD) method. This method is based on Taylor series expansions and the weighted least squares method, and its basic principle is to express the partial derivatives of the unknown f...

An effective solver for the direct-current (DC) resistivity forward-modeling problem should be capable of accommodating arbitrary electrode layouts, adapting the mesh to topography and complex geologic structures, and adaptively refining the mesh to ensure high solution accuracy. We use the capability of the mimetic finite-difference method in natu...

To effectively and efficiently interpret or invert controlled-source electromagnetic (CSEM) data which are recorded in areas with the kind of complex geological environments and arbitrary topography that are typical, three-dimensional (3D) CSEM forward modeling software that can quickly solve large-scale problems, provide accurate electromagnetic r...

The use of drones fo r geophysical data acquisition and artificial intelligence (AI) for geophysical data processing, imaging, and interpretation are active focus areas in current industry and academic applications. Unlocking their cumulative potential in single-focus applications can have a transformative impact, possibly leading to dramatic cost...

Current “visual” integration approaches to map geology from geophysics are challenging, biased toward user assumptions, and time consuming. Applying a supervised machine learning Random Forest method to airborne geophysical data sets is an alternative solution to quickly generate interpretative maps, which can later be validated through targeted an...

Three-dimensional (3D) airborne electromagnetic (AEM) inversions have been restricted by the modeling efficiency resulted from the complex geology in exploration areas and massive amount of data collected by AEM systems. In order to improve the modeling efficiency, we develop an algorithm that combines the hexahedral vector finite-element (FE) with...

Investigation of three-dimensional forward modeling for the ground-airborne frequency-domain electromagnetic (GAFEM) method and the characterization of its responses are presented. The electric field Helmholtz equation in the frequency domain is discretized by the Galerkin weighted residual method. The secondary electric field is the unknown to be...

An investigation of forward modeling 3‐D wire source electromagnetic data in the frequency domain using nodal and edge finite‐element basis functions is presented. The equations solved are those for the coupled secondary vector‐scalar potentials (i.e., magnetic vector potential A and electric scalar potential φ) which give rise to a less ill‐condit...

The northern Wuyi area, which is located in the northernWuyi metallogenic belt, has superior mineralization conditions. The Pingxiang‐Guangfeng‐Jiangshan‐Shaoxin fault (PSF) extends across the whole region regardless of whether or how the PSF relates to the near‐surface mineralization. We carried out an MT survey in the region and obtained a reliab...

3D Image reconstruction with Deep Learning AI on hi resolution drone magnetometer

Seafloor massive sulfide deposits form in remote environments, and the assessment of deposit size and composition through drilling is technically challenging and expensive. To aid the evaluation of the resource potential of seafloor massive sulfide deposits, three‐dimensional inverse modeling of geophysical potential field data (magnetic and gravit...

We have developed a two-dimensional (2D) anisotropic magnetotelluric (MT) inversion algorithm that uses a limited-memory quasi-Newton (QN) method for bounds-constrained optimization. This algorithm solves the inverse problem, which is non-linear, by iterative minimization of linearized approximations of the classical Tikhonov regularized objective...

We present a general scheme for 3D geophysical inversion using a deep learning convolutional neural network that enables three-dimensional inversions of useful size to be solved on laptops and desktops. A priori constraints of maximum smoothness or compactness on model parameters used during conventional geophysical inversion are not necessary. In...

Uranium exploration in the Athabasca Basin, Canada, relies heavily on ground-based transient electromagnetic (TEM) surveys to target thin, steeply dipping graphitic conductors that are often closely related to the uranium ore deposits. The interpretation of TEM data is important in identifying the locations and trends of conductors in order to guid...

The spectral-element (SE) method, which is based on the Galerkin technique, has been gradually implemented in geophysical electromagnetic (EM) three-dimensional (3D) simulation. The accuracy and efficiency of this approach, implemented for both deformed hexahedral and regular meshes, has been verified for airborne EM forward modeling. One advantage...

Gravity and magnetic data have unique advantages for studying the lateral extents of geological bodies. There is a class of methods for edge recognition called the maximum-edge-recognition methods that use their extreme values to locate the edges of geological bodies. These methods include the total horizontal derivative, the analytic signal amplit...

Self-organizing maps (SOMs) are a type of unsupervised artificial neural networks clustering tool. SOMs are used to cluster large multi-variate datasets. They can identify patterns and trends in the geophysical maps of an area and generate proxy geology maps, known as remote predictive mapping. We applied SOMs to magnetic, radiometric and gravity d...

Electromagnetic (EM) methods are important geophysical tools for mineral exploration. Forward and inverse computer modeling are commonly used to interpret EM data. Real-life geology can be complex, and our computer modeling tools need to faithfully represent subsurface features to achieve accurate data interpretation. Traditional rectilinear meshes...

The Zhuxi tungsten deposit is the largest tungsten deposit in the world. A mineral prospectivity analysis of the areas surrounding this deposit has the potential to identify further resources, and thus, it is important to conduct such an analysis. Therefore, a mineral prospectivity was performed on the results of completed 3D geological modeling of...

Magnetic and gravity data are used in the early stages of exploration for uranium deposits in the Athabasca Basin of Canada, just as for many other mineral exploration scenarios. Uranium mineralization in the Athabasca Basin is located where faults in the basement intersect the unconformity between the basement and the overlying sandstones. Both th...

Although most electromagnetic (EM) data can be inverted to actual resistivity, ways of quickly getting a real‐time interpretation of a data set are still valuable. Such methods are useful when we are testing instrumentation or assessing data quality during a survey, or when we need to get a general understanding of the geological structure during a...

Two-dimensional (2D) marine magnetotelluric (MT) observations are useful for offshore geological studies, such as natural resource exploration, fault mapping, fluid estimation at subduction zones, and the delineation of the lithosphere-asthenosphere boundary beneath the seafloor. Earth structures are often assumed to be 2D, which allows MT data to...

Hydrothermal fluid circulation beneath the seafloor is an important process for chemical and heat transfer between the solid Earth and overlying oceans. Discharge of hydrothermal fluids at the seafloor supports unique biological communities and can produce potentially valuable mineral deposits. Our understanding of the scale and geometry of subseaf...

Canadian Malartic is an Archean low-grade bulk tonnage native gold deposit. The deposit is mostly located in altered clastic metasedimentary rocks, mafic-ultramafic dykes and monzodioritic porphyry intrusions. Airborne magnetic and frequency-domain electromagnetic (EM) data were inverted to reconstruct the geological units associated with the miner...

Unstructured grids are capable of faithfully representing real-life geological models and topography with relatively small numbers of mesh cells. We present a finite-volume solution to the 3D time-domain electromagnetic forward modeling problems using unstructured Delaunay-Voronoï dual meshes. We consider both the Helmholtz equation for the electri...

Geologists’ interpretations about the Earth typically involve distinct rock units with contacts between them. 3D geological models typically comprise surfaces of tessellated polygons that represent the contacts. In contrast, geophysical inversions are typically performed on voxel meshes comprising space-filling elements. Standard minimum-structure...

A workflow for constructing realistic mesh-based magnetotelluric (MT) models from 3D geological models is introduced. The routine is developed for unstructured meshes that adapt to the complex shapes of geological bodies including three-dimensional surfaces and volumes in realistic modelling scenarios. The methodology is applied to the complexly-al...

A probabilistic approach is presented for jointly inverting gravity gradient and magnetic data for 3D subsurface distributions of density and magnetic susceptibility. The coupling of the physical property models is incorporated in the inversion by using a cross-covariance matrix of density and magnetic susceptibility. This enables structural simila...

Gravity signatures from features associated with the footprints of uranium deposits within the sandstones and basement of the Athabasca Basin are masked in the measured gravity by the contribution from glacial sediments (overburden), in particular by the variable thickness of the overburden. 2D inversions of seismic refraction and gravity data are...

Reduction to pole and other transformations of total field magnetic intensity data are often challenging to perform at low magnetic latitudes, when remanent magnetization exists, and when large topographic relief exists. Several studies have suggested use of inversion‐based equivalent source methods for performing such transformations under those c...

We evaluated imaging alteration associated with porphyry copper style mineralisation using aeromagnetic data in the Highland Valley Copper (HVC) district as part of the Natural Sciences and Engineering Research Council of Canada (NSERC) and Canada Mining Innovation Council (CMIC) Footprints project. The first step of the investigation involved cons...

Studying how to improve the boundary recognition ability and resolution of anomalies is of great significance in the electromagnetic prospecting method. This paper analyzes the response characteristics of gradient data from the frequency-domain controlled-source electromagnetic method. A survey geometry that has one transmitter and many receiver lo...

The investigation of using a novel radial-basis-function-based mesh-free method for forward modelling magnetotelluric data is presented. The mesh-free method, which can be termed as radial-basis-function-based finite difference (RBF-FD), uses only a cloud of unconnected points to obtain the numerical solution throughout the computational domain. Un...

As part of the Natural Sciences and Engineering Research Council of Canada–Canada Mining Innovation Council (NSERC-CMIC) Mineral Exploration Footprints project, three selected magnetic inversion programs (VPmg, MAG3D and VINV) were used to process the same aeromagnetic data set from the Highland Valley Copper district, British Columbia, Canada. In...

The rational Krylov subspace method enables the time integration required to calculate responses directly in the time-domain to be computed accurately and more efficiently than by regular time-stepping methods. In this study, the optimal rational Krylov subspace approach is used for the forward modeling of data from the grounded electric source air...

In transient electromagnetic (TEM) methods, the full transmitting-current waveform, not just the abrupt turn-off, can have effects on the measured responses. A 3D finite-element time-domain forward-modeling solver was used to investigate these effects. This was motivated by an attempt to match, via forward-modeling, real data from the Albany graphi...

Muography is a relatively new geophysical imaging method that uses muons to provide estimates of average densities along particular lines of sight. Muography can only see above the horizontal elevation of the detector and it is therefore attractive to attempt a joint inversion of muography data with gravity data, which is also responsive to density...

Magnetic and gravity inversions are used to create 2D or 3D models of the magnetic susceptibility and density, respectively, using potential field data. Unconstrained inversions generate an output based on mathematical constraints imposed by the inversion algorithm. Constrained inversions integrate lithological, structural, and petrophysical inform...

We have studied the Mesozoic Budgell Harbour Stock (BHS), a gabbroic intrusion in north-central Newfoundland, Canada, using 3-D inversion of airborne gravity gradiometry data based on a probabilistic inversion method. Significantly, differences were observed between results when inverting the single Tzz component and when inverting the five-compone...

We have developed a new constrained inversion method that is based on a probabilistic approach for resolving crustal structure from regional gravity data. The smoothness of estimated structures is included in the inversion by using a model covariance matrix, and the sparse boundary information obtained from seismic data is incorporated in the inver...

A study is presented using a mesh-free approach and a radial basis function generated finite difference (RBF-FD) method for numerically modelling 3-D gravity data. The gravity responses, that is, vertical gravity and gravity gradients, are obtained by solving the partial differential equation (PDE), that is, the Poisson's equation for gravitational...

Gravity inversion is inherently nonunique. Minimum-structure inversion has proved effective at dealing with this nonuniqueness. However, such an inversion approach, which involves a large number of unknown parameters, is computationally expensive. To improve efficiency while retaining the advantages of a minimum-structure-style inversion, we have d...

Mainstream numerical methods for 3D time-domain airborne electromagnetic (AEM) modeling, such as the finite-difference (FDTD) or finite-element (FETD) methods, are quite mature. However, these methods have limitations in terms of their ability to handle complex geologic structures and their dependence on quality meshing of the earth model. We have...

We present 3-D inversion results of gravity gradiometry data over the Budgell Harbour Stock (BHS) intrusion, in northern-central Newfoundland, Canada, obtained using a probabilistic inversion method. We examine multiple density contrast models obtained by inverting the single component Tzz and by jointly inverting five independent components. The i...

An inversion methodology and algorithm is developed for inverting Magnetotelluric data for threedimensional Earth conductivity models meshed using unstructured grids. The forward modeling subset of the inversion method is implemented using the E-field vectorial finite-element method for layered or homogeneous Earth models and complex target geometr...

In this paper, we propose a new wavelet-based 3-D inversion method for frequency-domain airborne electromagnetic (FDAEM) data. Instead of inverting the model in the space domain using a smoothing constraint, this new method recovers the model in the wavelet domain based on a sparsity constraint. In the wavelet domain, the model is represented by tw...

A finite-element time-domain (FETD) electromagnetic forward solver for a complex-shaped transmitting loop is presented. Any complex-shaped source can be viewed as a combination of electric dipoles (EDs), each of which can be further decomposed into two horizontal EDs along the xand y-directions and one vertical ED along the z-direction. Using this...

The creation of 3D models is commonplace in many disciplines. Models are often built from a collection of tessellated surfaces. To apply numerical methods to such models it is often necessary to generate a mesh of space-filling elements that conforms to the model surfaces. While there are meshing algorithms that can do so, they place restrictive re...

In recent years, marine controlled-source electromagnetic (CSEM) surveying has become an effective supplemental interpretation tool to the seismic reflection method to help mitigate risk in an offshore exploration setting. Interpretation of marine CSEMdata is commonly achieved via finite-difference inversions on rectilinear meshes, which has its me...

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of to...

We have developed a multiple level-set method for simultaneous inversion of gravity and seismic traveltime data. The method recovers the boundaries between regions with distinct physical properties assumed constant and known, creating structurally consistent models of two subsurface properties: P-wave velocity and density. In single level-set metho...

In this paper, we report the advantages of using a stochastic algorithm in the context of mineral exploration based on gravity measurements. This approach has the advantage over deterministic methods in that it allows one to find the solution of the Poisson equation in specified, isolated points without the need of meshing the computational domain...

While seismic methods provide the best geophysical methods for characterizing crustal structure, regional potential field studies and, specifically, constrained 3-D potential field inversion studies, provide an efficient means of bridging between seismic lines and obtaining regional views of deep structure. Most existing potential field inversion c...

A presentation that I gave on a regression code designed to produce a textural index for incorporation into my SOM machine learning strategy. Given at the Geological Association of Canada Newfoundland branches annual meeting.

This paper is concerned with the applicability of Pareto Multi-Objective Global Optimization (PMOGO) algorithms for solving different types of geophysical inverse problems. The standard deterministic approach is to combine the multiple objective functions (i.e. data misfit, regularization and joint coupling terms) in a weighted-sum aggregate object...

Stochastic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The stochastic form of the exact solution of Maxwell's equations is evaluated using Monte-Carlo methods taking into consideration that the domain may be divided into neighboring sub-domains. These...

This study compares two finite–element (FE) and three finite–volume (FV) schemes which use unstructured tetrahedral grids for the modelling of electromagnetic (EM) data. All these schemes belong to a group of differential methods where the electric field is defined along the edges of the elements. The FE and FV schemes are based on both the EM–fiel...