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We have developed an approach for integrating the interdependent information of different geophysical methods to obtain a self-consistent geophysical model in offshore exploration. Electromagnetic (EM) and gravity data complement seismic data by providing information about the physical properties of prospective reservoir rocks. We have combined marine EM and gravity gradiometry geophysical data in joint inversion using a joint focusing stabilizer. The method enforces coupling between different physical models and simultaneously promotes focused images of the targets. We also consider the importance of using robust norms to analyze data collected by marine controlled-source EM surveys. The practical effectiveness of the developed method is illustrated by a case study of integrating and imaging marine multiphysics data collected in the Nordkapp Basin, Barents Sea, Norway.

This paper discusses the physical and mathematical principles of the airborne induced polarization (IP) method. The possibility of extracting information about the IP properties of rocks from airborne survey data has become a subject of active research recently. We introduce a method for the joint inversion of the airborne EM data into the electrical conductivity and IP parameters based on the generalized effective-medium theory of induced polarization (GEMTIP). We also present the results of the inversion of the airborne EM data collected over the Echum Project Area, in Northwestern Ontario, Canada, into 3D conductivity and chargeability models. Obtaining IP physical property models from an airborne geophysical survey may result in a paradigm change in mineral exploration by pulling more information and value from airborne EM surveys.

SUMMARY Joint inversion of multiphysics data is a practical approach to the integration of geophysical data, which produces models of reduced uncertainty and improved resolution. The development of effective methods of joint inversion requires considering different resolutions of different geophysical methods. This paper presents a new framework of joint inversion of multiphysics data, which is based on a novel formulation of Gramian constraints and mitigates the difference in resolution capabilities of different geophysical methods. Our approach enforces structural similarity between different model parameters through minimizing a structural Gramian term, and it also balances the different resolutions of geophysical methods using a multiscale resampling strategy. The effectiveness of the proposed method is demonstrated by synthetic model study of joint inversion of the P-wave traveltime and gravity data. We apply a novel method based on Gramian constraints and multiscale resampling to jointly invert the gravity and seismic data collected in Yellowstone national Park to image the crustal magmatic system of the Yellowstone. Our results helped to produce a consistent image of the crustal magmatic system of the Yellowstone expressed both in low-density and low-velocity anomaly just beneath the Yellowstone caldera.

An efficient solution of the three-dimensional Helmholtz equation is known to be crucial in many applications, especially geophysics. In this paper, we present and test two preconditioning approaches for the discrete problem resulting from the second order finite-difference discretization of this equation. The first approach combines shifted-Laplacian preconditioner with inversion of a separable matrix, corresponding to the horizontally-layered velocity model, using fast Fourier based transforms. The second approach is novel and involves a special transformation resulting in a preconditioner with a contraction operator (CO preconditioner). The two approaches have near the same arithmetical complexity; however, the second approach, developed in this paper, provides a faster convergence of an iterative solver as illustrated by numerical experiments and analysis of the spectral properties of the preconditioned matrices. Our numerical experiments involve parallel modeling of highly heterogeneous lossy and lossless media at different frequencies. We show that the CO-based solver can tackle problems with hundreds of millions of unknowns on a conventional cluster node. The CO preconditioned solver demonstrates a very moderate increase of iteration count with the frequency. We have conducted a comparison of the performance of the developed method versus open-source parallel sweeping preconditioner. The results indicate that, the CO solver is several times faster with respect to the wall-clock time and consumes substantially less memory than the code based on the sweeping preconditioner at least in the example we tested.

Towed streamer electromagnetic (TSEM) survey is an efficient data acquisition technique capable of collecting a large volume of electromagnetic (EM) data over extensive areas rapidly and economically. The TSEM survey is capable of detecting and characterizing marine hydrocarbon (HC) reservoirs. However, interpretation of the TSEM data is still a very challenging problem. We propose solving this problem by migrating the optimal synthetic aperture (OSA) data for the TSEM survey. We first represent the OSA data as a solution of Lippmann–Schwinger equation and then demonstrate that the migration of OSA data is just the inner product of the backward-propagated and forward-propagated EM fields. The migration problem is solved iteratively within the general framework of the reweighted, regularized, conjugate gradient (RRCG) method. The proposed method was tested with two synthetic models. We also applied this method to the TSEM data set collected in the Barents Sea and revealed a resistive layer at a depth of about 500 m.

The synthetic aperture (SA) method has recently found applications in the analysis of the low-frequency marine controlled-source electromagnetic (MCSEM) data. It has been shown that this method can enhance the response from an anomalous target. However, in a SA method, anomalous EM fields and the noise will be equally steered and focused, leading to amplifying the noise and introducing artifacts into the images. In addition, the current realizations of the SA method are very sensitive to the noise in the data and the parameters of the SA. In this article, we address these difficulties by introducing a robust SA (RSA) method. The RSA method consists of three steps, namely, robust smoothing of the background field, robust interpolation of EM fields from the real receiver positions to the virtual receiver positions, and estimating the SA weights with a robust optimization scheme. The synthetic model studies show that this method is stable to noise and has a relatively high spatial resolution. We have also applied this method to the towed streamer data collected in the Barents Sea. The generated pseudo-3-D images accurately reveal the locations of the salt domes and fault structures known from the seismic data.

Geological interpretation based on gravity gradiometry data constitutes a very challenging problem. Rigorous 3D inversion is the main technique used in quantitative interpretation of the gravity gradiometry data. An alternative approach to the quantitative analysis of the gravity gradiometry data is based on 3D smooth potential field migration. This rapid imaging approach, however, has the shortcomings of providing smooth images since it is based on direct integral transformation of the observed gravity tensor data. Another limitation of migration transformation is related to the fact that, in a general case, the gravity data generated by the migration image do not fit the observed data well. In this paper, we describe a new approach to rapid imaging that allows us to produce the density distribution which adequately describes the observed data and, at the same time, images the structures with anomalous densities having sharp boundaries. This approach is based on the basic theory of potential field migration with a focusing stabilizer in the framework of regularized scheme, which iteratively transfers the observed gravity tensor field into an image of the density distribution in the subsurface formations. The results of gravity migration can also be considered as an a priori model for conventional inversion subsequently. We demonstrate the practical application of migration imaging using both synthetic and real gravity gradiometry data sets acquired for the Nordkapp Basin in the Barents Sea.

SUMMARY The finite-element (FE) method is one of the most powerful numerical techniques for modelling 3-D electromagnetic fields. At the same time, there still exists the problem of efficient and economical solution of the respective system of FE equations in the frequency domain. In this paper, we concentrate on modelling with adapted hexahedral or logically rectangular grids. These grids are easy to generate, yet they are flexible enough to incorporate real topography and seismic horizons. The goal of this work is to show how a finite-difference (FD) solver can be used as a pre-conditioner for hexahedral FE modelling. Applying the lowest order Nédélec elements, we present a novel pre-conditioned iterative solver for the arising system of linear equations that combines an FD solver and simple smoothing procedure. The particular FD solver that we use relies on the implicit factorization of the horizontally layered earth matrix. We assessed runtime and accuracy of the presented approach on synthetic and real resistivity models (topography of the Black Sea continental slope). We further compared performance of our program versus publicly available Mare2DEM, ModEM and MUMPS programs/libraries. Our examples involve plane-wave and controlled source modelling. The numerical examples demonstrate that the presented approach is fast and robust for models with moderate contrast, supports highly deformed cells, and is quite memory-economical.

In this paper, we develop a general approach to integrating petrophysical models in three‐dimensional seismic full‐waveform inversion based on the Gramian constraints. In the framework of this approach, we present an example of the frequency‐domain P‐wave velocity inversion guided by an electrical conductivity model. In order to introduce a coupling between the two models, we minimize the corresponding Gramian functional, which is included in the Tikhonov parametric functional. We demonstrate that in the case of a single‐physics inversion guided by a model of different physical type, the general expressions of the Gramian functional and its gradients become simple and easy to program. We also prove that the Gramian functional has a non‐negative quadratic form, so it can be easily incorporated in a standard gradient‐based minimization scheme. The developed new approach of seismic inversion guided by the known petrophysical model has been validated by three‐dimensional inversion of synthetic seismic data generated for a realistic three‐dimensional model of the subsurface.

Potential field migration represents a rapid technique for imaging the subsurface based on gravity data. However, migration transformation usually produces a smooth and unfocused image of the targets due to the diffusive nature of the potential fields. In this paper, we introduce a method of the migration image enhancement and sharpening based on the application of the hybrid focusing stabilizer, which combines the edge-preserving smoothing filter with the minimum support functional. The method is based on the model resolution matrix of the migration operator. We also improve the migration image with a novel target-oriented migration method. The developed method of migration image enhancement and sharpening is illustrated by synthetic model studies and case studies. The case study involves imaging the full tensor gravity gradient data collected in the Nordkapp Basin of the Barents Sea.

The synthetic aperture (SA) method is one of the key techniques in remote sensing using radio frequency signals. Introduced in the early 1950s, Synthetic Aperture Radar, or SAR revolutionized reconnaissance surveying using radio and microwave signals. The key idea of the SAR is based on considering the entire flight path of airborne or spaceborne platform as a huge synthetic antenna, and on processing simultaneously all signals collected along this path. As a result, the clarity and resolution of the images produced by SAR can be improved dramatically.

SUMMARY This paper presents a feasibility study of using the controlled-source frequency-domain electromagnetic (CSEM) method in mineral exploration. The method has been widely applied for offshore hydrocarbon exploration; however, nowadays this method is rarely used on land. In order to conduct this study, we have developed a fully parallelized forward modelling finite-difference (FD) code based on the iterative solver with contraction-operator preconditioner. The regularized inversion algorithm uses the Gauss–Newton method to minimize the Tikhonov parametric functional with the Laplacian-type stabilizer. A 3-D parallel inversion code, based on the iterative finite-difference solver with the contraction-operator preconditioner, has been evaluated for the solution of the large-scale inverse problems. Using the computer simulation for a synthetic model of Sukhoi Log gold deposit, we have compared the CSEM method with the conventional direct current sounding and the CSEM survey with a single remote transmitter. Our results suggest that, a properly designed electromagnetic survey together with modern 3-D inversion could provide detailed information about the geoelectrical structure of the mineral deposit.

Gravity and long-period magnetotelluric data are combined in a joint Gramian inversion to obtain structurally-similar 3D density and electrical resistivity models of the Yellowstone magmatic feeding system. Structural constraints are enforced through a correlation of the model gradients. Gravity data are sensitive to upper-crustal structure, whereas long-period magnetotelluric data are more sensitive to deeper structure. By combining these complementary data, the jointly inverted models provide a consistent image of the partially molten structure underlying the Yellowstone Caldera from the surface to the Moho. Discrete zones of inferred partial melt in the upper and lower crust are fed by a southwest trending plume, and satisfy expectations from modern mantle plume models.

Potential field data form an important frontline exploration tool thanks to the modern-day airborne platforms capable of collecting large amounts of data over large areas. Interpretation of these data using a 3D inversion is still a challenging problem due to the large amount of data and the need to discretize the inversion volume into a huge number of elements.