SUMMARY: The Born approximation offers a computationally efficient alternative to full electromagnetic (EM) forward modelling, but suffers from limited accuracy due to its reliance on a fixed background conductivity. In this work, we develop an adaptive Born approximation that treats the background medium as a tunable parameter to enhance accuracy in a goal-oriented manner. The background conductivity is selected locally for each measurement configuration using spatial sensitivity functions, enabling accurate modelling in both isotropic and anisotropic media. In this study, we primarily focus on horizontally layered earth models penetrated by a vertical well to investigate the fundamental behaviour of the approximation in a simplified setting. We formulate our approach to be applicable to general anisotropic media by using the Green’s function defined for a homogeneous medium. Furthermore, the approach extends to cases where the background conductivity is isotropic while the actual medium is anisotropic. For a layered medium, the orientation of induced current densities relative to the layering provides physical intuition for background selection, drawing analogies to Voigt- and Reuss-type bounds. While these analogies offer useful guidance, our numerical results do not always conform to the expectations derived from them. Among the averaging schemes evaluated, arithmetic averaging generally yields the most accurate results. Numerical experiments indicate that the adaptive approach significantly outperforms fixed-background models across a range of frequencies, spacings and conductivity contrasts. Furthermore, an example with a 3-D structure illustrates the method’s broader applicability beyond the horizontally layered earth setting. This framework provides a principled and efficient path toward fast, accurate EM borehole modelling for real-time well geosteering and subsurface electrical imaging.

As seismic migration is increasingly applied to more and more complex media, more sophisticated imaging techniques are required to generate accurate images of the subsurface. Currently, the best results for imaging are achieved by least-squares migration methods, such as least-squares reverse time migration and full-wavefield migration (FWM). These methods iteratively update the image to minimize the misfit between the forward modelled wavefield and the recorded data at the surface. However, a key challenge for these techniques is the speed of convergence. To accelerate the speed of convergence, pre-conditioning is commonly applied. The most common pre-conditioner is the reciprocal of the Hessian operator. However, this operator is computationally expensive to calculate, making it difficult to apply directly. In this paper, we present a novel, alternative, pre-conditioner for FWM. This pre-conditioner is based on applying Galerkin projections to a linear system, which projects the system onto a set of known basis vectors. To find an appropriate set of basis vectors for this approach we apply proper orthogonal decomposition (POD) to a set of partial solutions of the linear system. The resulting method gives an approximation to the pseudo-inverse based on these basis vectors. To test this technique, which we name model-order reduced FWM (MOR-FWM), we apply it to the synthetic Marmousi model as well as to field data from the Vøring basin in Norway. For these examples, we show that MOR-FWM yields an improved data-misfit compared to the standard FWM approach. In addition, we show that the result for the field data case can be improved by normalizing the partial solutions before applying POD.

Structural information about the subsurface near the borehole can be obtained from reconstructed conductivity distributions. These distributions may be reconstructed via the inversion of deep-sensing electromagnetic induction log data. Unfortunately, these complex media often display anisotropy and structural variations in both horizontal and vertical directions, making the three-dimensional inversion computationally demanding and ill-posed. To address these challenges, we introduce a sequential inversion strategy of deep-sensing electromagnetic induction logging data that is measured while drilling. For the inversion at each logging position, we employ a matrix-free implementation of the adjoint integral equation method and a quasi-Newton algorithm. To tackle the ill-posed nature of the problem, we regularize the inverse problem by employing a multi-dimensional inversion parameter technique that shifts from zero- to three-dimensional parameterization. The model derived from the inversion of the data at multiple positions is incrementally integrated by utilizing the sensitivity data at each logging position. To validate our approach, we tested our method on simulated data using an anisotropic model. These experiments show that this approach produces a good reconstruction of the true conductivity for the whole track while only doing the inversion at a single position at a time.

As seismic imaging moves towards the imaging of more complex media, properly modelling elastic effects in the subsurface is becoming of increasing interest. In this context, elastic wave conversion, where acoustic, pressure (P-) waves are converted into elastic, shear (S-) waves, is of great importance. Accounting for these wave conversions, in the framework of forward and inverse modelling of elastic waves, is crucial to creating accurate images of the subsurface in complex media. The underlying mechanism of wave conversion is well understood and described by the Zoeppritz equations. However, as these equations are highly nonlinear, approximations are commonly used. The most well-known of these approximations is Shuey’s approximation. However, this approximation only holds for small angles and small contrasts, making it insufficient for realistic forward and inverse modelling scenarios, where angles and contrasts may be large. In this paper we present a novel set of approximations, based on Taylor expansions of the Zoeppritz equations, which we name the extended Shuey approximations. We examine the quality of these approximations to the Zoeppritz equations and compare them to existing approximations described in literature. We then apply these extended Shuey approximations to the elastic full-wavefield modelling algorithm for a simple, synthetic, 1.5-D example, where we show that we can accurately model the P- and S-wavefields in a forward modelling case. Finally, we apply our approximations to the elastic full-wavefield migration algorithm for a simple, synthetic, 1.5-D example, where we show that we can recover an accurate image in an inverse modelling case.

3D ultrasound computed tomography (3D USCT) requires precise transducer positioning and knowledge of the background speed of sound (SoS). However, factors such as channel-to-channel variability introduced by multiplexer switching, temperature-induced SoS drift, and mechanical misalignment degrade image quality in large apertures. We present a robust linear projection method that operates below the noise level and can detect crosstalk. With spherical back-projection, all A-scans are linearly processed and matched-filtered, then projected into a three-dimensional spatial domain without explicit time-of-flight (ToF) picking. The resulting 3D response maps the origin (emitter) or sink (receiver) of the wave in a linear, pseudo-probabilistic representation, enabling separate examination of transmit and receive paths and isolation of hardware effects. Multiple maxima can be associated with distinct sources such as electrical crosstalk. On a prototype system, 82.4 % of transducers matched expected positions (median deviation ≈1 mm); six transducer-array systems were detected as rotated by 118°, later confirmed mechanically. The method provides robust system analysis, fault detection, and additional system-health information for low-SNR arrays.

The deployment of electromagnetic (EM) induction tools while drilling is one of the standard routines for assisting the geosteering decision-making process. The conductivity distribution obtained through the inversion of the EM induction log can provide important information about the geological structure around the borehole. To image the 3-D geological structure in the subsurface, 3-D inversion of the EM induction log is required. Because the inversion process is mainly dependent on forward modelling, the use of a fast and accurate forward modelling tool is essential. In this paper, we present an improved version of the integral equation (IE) based modelling technique for general anisotropic media with domain decomposition pre- conditioning. The discretized IE after domain decomposition equals a fixed-point equation that is solv ed iterativ ely with either the block Gauss-Seidel or Jacobi pre-conditioning. Within each iteration, the inverse of the block matrix is computed using a Krylov subspace method instead of a direct solver. An additional reduction in computational time is obtained by using an adaptive relative residual stopping criterion in the iterativ e solv er. Using this domain decomposition scheme, numerical experiments show computation time reductions by factors of 1.97-2.84 compared to solving the full-domain IE with a GMRES solver and a contraction IE pre- conditioner. Additionally, the reduction of memory requirement for covering a large area of the induction tool sensitivity enables acceleration with limited GPU memory. Hence, we conclude that the domain decomposition method is improving the efficiency of the IE method by reducing the computation time and memory requirement.

Multi-modality or multi-physics imaging is gaining interest beacuase it overcomes the limitations of a single imaging modality, as each modality typically suffers from its own application specific limitations. Different imaging techniques are developed to combine the outcome of both modalities; varying from image fusion up to the usage of prior information obtained from one imaging modality and used as input for the other one. In this work an alternative approach is presented. The method employs a multi-physics Born inversion algorithm where structural similarity is used as regularization parameter to align the acoustic and electromagnetic contrast interfaces with each other. To align the interfaces the gradients of the acoustic and electromagnetic contrast functions are used. Two approaches are tested successfully on a synthetic profile; one where the cross-product of the two gradients and one where the gradient differences are considered. Both approaches work but the gradient-difference approach outperforms the cross-gradient one. Overall, it is shown that multi-physics Born inversion both approaches reveals details in the electromagnetic contrast function that would have been missed by only employing electromagnetic inversion. This improvement is obtained at the cost of an increase in computational complexity compared to single modality inversion.

We present an iterative nonlinear inverse scattering algorithm for high-resolution acoustic imaging of density and velocity variations. To solve the multi-parameter nonlinear direct scattering problem, the acoustic wave equation for inhomogeneous media in the frequency domain is transformed into a vectorial integral equation of the Lippmann-Schwinger type for the combined pressure and pressure-gradient field. To solve the multi-parameter nonlinear inverse scattering problem, we use the Newton-Kantorovich method in conjunction with matrix-free representations of the Fréchet derivative operators and their adjoints. The approximate Hessian information that is accounted for in our iterative solution of the (nonlinear) multi-parameter inverse scattering problem is essential for the mitigation of multi-parameter cross talk effects. Numerical examples related to seismic and medical ultrasound breast imaging illustrate the performance of the new algorithm for multi-parameter acoustic imaging.

Objective. The image reconstruction of ultrasound computed tomography is computationally expensive with conventional iterative methods. The fully learned direct deep learning reconstruction is promising to speed up image reconstruction significantly. However, for direct reconstruction from measurement data, due to the lack of real labeled data, the neural network is usually trained on a simulation dataset and shows poor performance on real data because of the simulation-to-real gap.Approach. To improve the simulation-to-real generalization of neural networks, a series of strategies are developed including a Fourier-transform-integrated neural network, measurement-domain data augmentation methods, and a self-supervised-learning-based patch-wise preprocessing neural network. Our strategies are evaluated on both the simulation dataset and real measurement datasets from two different prototype machines.Main results. The experimental results show that our deep learning methods help to improve the neural networks' robustness against noise and the generalizability to real measurement data.Significance. Our methods prove that it is possible for neural networks to achieve superior performance to traditional iterative reconstruction algorithms in imaging quality and allow for real-time 2D-image reconstruction. This study helps pave the path for the application of deep learning methods to practical ultrasound tomography image reconstruction based on simulation datasets.

Quantitative images showing the speed of sound proffle of the breast may be obtained by employing full-waveform inversion (FWI) methods on the measured data. These reconstruction methods work well for both dense and normal breasts. Contrast source inversion (CSI) is a frequency domain FWI method. In literature, many examples of successful application of CSI for breast imaging can be found. However, all these works are based on simulated data. In this work, we will present our first results obtained with employing CSI on experimental data. CSI was developed by Delft University of Technology and the experimental data was provided by FUJIFILM Healthcare Corporation. The experimental data is obtained using a ring-shaped transducer which scans a breast-mimicking gelatine phantom. Our initial results obtained with CSI look promising; all inclusions within the phantom are accurately reconstructed.

Imaging by inversion of acoustic or electromagnetic wave fields have applications in a wide variety of areas, such as non-destructive testing, biomedical applications, and geophysical exploration. Unfortunately, each modality suffers from its own application-specific limitations, typically being difficulties in distinguishing different materials/tissues from each other in the case of acoustic wave fields and a low spatial resolution in the case of electromagnetic wave fields. To exploit the advantages of both imaging modalities, we present a Born inversion method where we use an additive regularization term based on structural similarity between the acoustic and electromagnetic contrast. To validate our approach, we compare separate with joint inversion results for one particular example. The results for this example clearly show that separate inversion succeeds in reconstructing the acoustic contrast, but fails to properly reconstruct the electromagnetic contrast. Fortunately, with the joint inversion method, both the acoustic and electromagnetic contrast functions are reconstructed successfully.

Conventional Full Wavefield Migration (FWM) is a full-wavefield inversion method based on recursively applying one-way convolutional propagation and reflection operators in the space-frequency domain at every depth level. Therefore, it struggles to model diving waves and image steep reflectors accurately. In this paper, the Interface Contrast imaging technique, an imaging technique based on the scattering integral developed in the context of medical ultrasound, is presented and used to provide a natural omni-directional extension to the conventional FWM method. The resulting algorithm is applied to a synthetic 2D model featuring a steep reflector. The results of these simulations are given and show that the technique can successfully image steep reflectors. This result yields a proof-of-concept for further research into this algorithm, where including internal scattering is a top priority.

With full waveform inversion (FWI) all available information enclosed in the recorded wavefield - including multiple scattering, dispersion, and diffraction - is used to obtain accurate images showing quantitative information of the tissue parameters. These non-linear inversion methods are implemented either in the time or in the frequency domain. Unfortunately, selecting which implementation should be used for a specific problem is not trivial. To ease the selection process, we compare the performance of one time-domain inversion (TDI) and one frequency-domain inversion (FDI) - also known as Contrast Source Inversion - to provide insights into the strengths and weaknesses of each FWI method. In this contribution, we investigate the effect of the (i) bandwidth, (ii) problem complexity, (iii) number of sources and receivers, and (iv) initial speed-of-sound model on the performance of each FWI method by comparing the resulting reconstructions. Both methods are tested for the same configuration: a 2-D tomographic scan of a cancerous breast model. To avoid an inverse crime, TDI is tested on synthetic data obtained using a frequency-domain forward solver and CSI on data from a time-domain forward solver.

Reverse time migration (RTM) is a method developed for performing non-invasive physical imaging. It aims to generate diagnostic images based on forward and backward modeling of waves, which can be solved with different type of techniques. A widely used one is Finite Differences (FD) due to its low computational cost and its simplicity, as compared to other methods, to implement. In this work we show how to implement RTM with curved coordinates using FD. In particular we focus on the application of curved coordinates to improve the quality of the resulting images and reduce the computational cost of RTM. Here, we apply a strategy to curve coordinates during the wave propagation modeling stage for a modified version of the Marmousi model. The results show that it is completely feasible the redistribution of grid nodes to locally improve quality of the migrated models and reduce the number of grid nodes at the same time. We also found that typical issues associated to the imaging condition and FD scheme remain.

Deep neural networks have proven to excel classical medical image reconstruction techniques. Some networks are based on fully connected (FC) layers to achieve domain transformation such as from the data acquisition domain to the image domain. However, FC layers result in huge numbers of parameters which take a lot of GPU memory. Hence, they do not scale well, and the overall performance is limited. For ultrasound computed tomography (USCT) application, we propose a memory-efficient convolutional network that reconstructs images from the frequency domain to image domain with much less parameters compared with multilayer perceptron, by using data-driven learning. Extensive experiments demonstrate that our method achieves high reconstruction quality. It improves the structural similarity measure (SSIM) from 0.73 to 0.99 when compared with state-of-the-art reconstruction methods in this field while reduces 2/3 parameters when compared with deep neural network with FC layers to reconstruct images from frequency domain to image domain.