The possibility to have results very quickly after, or even during, the collection of electromagnetic data would be important, not only for quality check purposes, but also for adjusting the location of the proposed flight lines during an airborne time-domain acquisition. This kind of readiness could have a large impact in terms of optimization of the Value of Information of the measurements to be acquired. In addition, the importance of having fast tools for retrieving resistivity models from airborne time-domain data is demonstrated by the fact that Conductivity-Depth Imaging methodologies are still the standard in mineral exploration. In fact, they are extremely computationally efficient, and, at the same time, they preserve a very high lateral resolution. For these reasons, they are often preferred to inversion strategies even if the latter approaches are generally more accurate in terms of proper reconstruction of the depth of the targets and of reliable retrieval of true resistivity values of the subsurface. In this research, we discuss a novel approach, based on neural network techniques, capable of retrieving resistivity models with a quality comparable with the inversion strategy, but in a fraction of the time. We demonstrate the advantages of the proposed novel approach on synthetic and field datasets.
Inversions of airborne EM data are often an iterative process, not only requiring that the researcher be able to explore the impact of changing components such as the choice of regularization functional or model parameterization, but also often requiring that forward simulations be run and fields and fluxes visualized in order to build an understanding of the physical processes governing what we observe in the data. In the hope of facilitating this exploration and promoting reproducibility of geophysical simulations and inversions, we have developed the open source software package, SimPEG. Th…
Airborne electromagnetic surveys may consist of hundreds of thousands of soundings. In most cases, this makes 3D inversions unfeasible even when the subsurface is characterized by a high level of heterogeneity. Instead, approaches based on 1D forwards are routinely used because of their computational efficiency. However, it is relatively easy to fit 3D responses with 1D forward modelling and retrieve apparently well-resolved conductivity models. However, those detailed features may simply be caused by fitting the modelling error connected to the approximate forward. In addition, it is, in prac…
Full 3D inversion of time-domain Airborne ElectroMagnetic (AEM) data requires specialists' expertise and a tremendous amount of computational resources, not readily available to everyone. Consequently, quasi-2D/3D inversion methods are prevailing, using a much faster but approximate (1D) forward model. We propose an appraisal tool that indicates zones in the inversion model that are not in agreement with the multidimensional data and therefore, should not be interpreted quantitatively. The image appraisal relies on multidimensional forward modelling to compute a so-called normalized gradient. …
Airborne transient electromagnetic (TEM) is a cost-effective method to image the distribution of electrical conductivity in the ground. We consider layered earth inversion to interpret large data sets of hundreds of kilometre. Different strategies can be used to solve this inverse problem. This consists in managing the a priori information to avoid the mathematical instability and provide the most plausible model of conductivity in depth. In order to obtain fast and realistic inversion program, we tested three kinds of regularization: two are based on standard Tikhonov procedure which consist …
Detection of induced polarisation (IP) effects in airborne electromagnetic (AEM) measurements does not yet have an established methodology. This contribution develops a Bayesian approach to the IP-detectability problem using decoupled transdimensional layered models, and applies an approach novel to geophysics whereby transdimensional proposals are used within the embarrassingly parallelisable and robust static Sequential Monte Carlo (SMC) class of algorithms for the simultaneous inference of parameters and models. Henceforth referring to this algorithm as Reversible Jump Sequential Monte Carl…
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent wavelet-based L1-regularization term to cure the ill-posedness of the airborne (time-domain) electromagnetic induction inverse problem. The regularization term is flexible, as it can recover blocky, smooth and tunable in-between inversion models, based on a suitable wavelet basis function. For each orientation, a different wavelet basis function can be used, …
Electromagnetics has an important role to play in solving the next generation of geoscience problems. These problems are multidisciplinary, complex, and require collaboration. This is especially true at the base scientific level where the underlying physical equations need to be solved, and data, associated with physical experiments, need to be inverted. In this paper, we present arguments for adopting an open-source methodology for geophysics and provide some background about open-source software for electromagnetics. Immediate benefits are the reduced time required to carry out research, bei…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in high-dimensional parameter spaces. Existing approaches are largely based on deterministic gradient-based methods, which are limited by nonlinearity and nonuniqueness of the inverse problem. Probabilistic inversion methods, despite their great potential in uncertainty quantification, still remain a formidable computational task. In this paper, I explore the pot…
Frequency-domain electromagnetic (FDEM) data of the subsurface are determined by electrical conductivity and magnetic susceptibility. We apply a Kalman Ensemble generator (KEG) to one-dimensional probabilistic multi-layer inversion of FDEM data to derive conductivity and susceptibility simultaneously. The KEG provides an efficient alternative to an exhaustive Bayesian framework for FDEM inversion, including a measure for the uncertainty of the inversion result. Additionally, the method provides a measure for the depth below which the measurement is insensitive to the parameters of the subsurfa…
The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability of the inversion and, based on Occam's razor principle, a smoothing constraint is typically used. However, the conductivity profiles are not always expected to be smooth. Here, we develop a new inversion scheme in which we transform the model to the wavelet space and impose a sparsity constraint. This sparsity constrained inversion scheme will minimize an objective function with a least-squares data misfit and a sparsity measure of the model in the wavelet do…
Curtin University（科廷大学）；Colorado School of Mines（科罗拉多矿业学院）
Inversion of electromagnetic data finds applications in many areas of geophysics. The inverse problem is commonly solved with either deterministic optimization methods (such as the nonlinear conjugate gradient or Gauss-Newton) which are prone to getting trapped in a local minimum, or probabilistic methods which are very computationally demanding. A recently emerging alternative is to employ deep neural networks for predicting subsurface model properties from measured data. This approach is entirely data-driven, does not employ traditional gradient-based techniques and provides a guess to the m…
Simulations and inversions of electromagnetic geophysical data are paramount for discerning meaningful information about the subsurface from these data. Depending on the nature of the source electromagnetic experiments may be classified as time-domain or frequency-domain. Multiple heterogeneous and sometimes anisotropic physical properties, including electrical conductivity and magnetic permeability, may need be considered in a simulation. Depending on what one wants to accomplish in an inversion, the parameters which one inverts for may be a voxel-based description of the earth or some parame…
Electromagnetic induction methods are a common means for geophysical survey. For soil structures that are invariant in one spatial dimension such as trench structures, we propose a fast forward model based on a 2D response function, taking into account sharp horizontal and vertical transitions in the electrical conductivity. The 2D model is used to invert trench structures from a synthetic dataset. The propsed method can determine trench parameters (width, height, steepness of the slope) more accurately than methods based on regularization of the 1D response function.
Feature-based Inversion of 2.5D Controlled Source Electromagnetic Data using Generative Priors
Department of Electronic Engineering, Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University（电子工程系，北京信息科学与技术国家研究中心（BNRist），清华大学）；Faculty of Math and Computer Science, Weizmann Institute of Science（数学与计算机科学学院，魏兹曼科学研究所）
Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a two-dimensional (2D) pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model …
Small-loop frequency-domain electromagnetic (FDEM) devices measure a secondary magnetic field caused by the application of a stronger primary magnetic field. Both the in-phase and quadrature component of the secondary field commonly suffer from systematic measurement errors, which would result in a non-zero response in free space. The in-phase response is typically strongly correlated to subsurface magnetic susceptibility. Considering common applications on weakly to moderately susceptible grounds, the in-phase component of the secondary field is usually weaker than the quadrature component, m…
The three electromagnetic properties appearing in Maxwell's equations are dielectric permittivity, electrical conductivity and magnetic permeability. The study of point diffractors in a homogeneous, isotropic, linear medium suggests the use of logarithms to describe the variations of electromagnetic properties in the earth. A small anomaly in electrical properties (permittivity and conductivity) responds to an incident electromagnetic field as an electric dipole, whereas a small anomaly in the magnetic property responds as a magnetic dipole. Neither property variation can be neglected without …
The advent of fast sensing technologies allows for real-time model updates in many applications where the model parameters are uncertain. Bayesian algorithms, such as ensemble smoothers, offer a real-time probabilistic inversion accounting for uncertainties. However, they rely on the repeated evaluation of the computational models, and deep neural network (DNN) based proxies can be useful to address this computational bottleneck. This paper studies the effects of the approximate nature of the deep learned models and associated model errors during the inversion of extra-deep borehole electromag…
Marine Controlled Source Electromagnetic (CSEM) is employed both in large-scale geophysical applications as well as within exploration of hydrocarbons and gas hydrates. Due to the diffusive character of the EM field only very low frequencies are used leading to inversion results with rather low resolution. In this paper, we calculate the resolution matrix associated with the inversion and derive the corresponding point spread functions (PSFs). The PSFs give information about how much the actual inversion has been blurred, and use of space-varying deconvolution can therefore further improve the…
We introduce a novel approach to waveform inversion, based on a data driven reduced order model (ROM) of the wave operator. The presentation is for the acoustic wave equation, but the approach can be extended to elastic or electromagnetic waves. The data are time resolved measurements of the pressure wave gathered by an acquisition system which probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity estimation by minimizing the square misfit between the ROM computed from the recorded data and the ROM computed from the modeled …
3-D Magnetotelluric Deep Learning Inversion Guided by Pseudo-Physical Information
Key Laboratory of Earth Exploration and Information Techniques of Ministry of Education, College of Geophysics, Chengdu University of Technology（教育部地球探测与信息技术重点实验室，成都理工大学地球物理学院）；College of Computer Science and Cyber Security, Chengdu University of Technology（成都理工大学计算机科学与网络security学院）
Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed problem. In the framework of Tikhonov regularization theory, in order to replace an ill-posed problem by a well-posed one and to get a unique and stable solution, a stabilizing functional (stabilizer) has to be introduced. The stabilizer selects the desired solution from a class of solutions with a specific physical and/or geometrical property; e.g., the exi…
We present a wave-equation inversion method that inverts skeletonized data for the subsurface velocity model. The skeletonized representation of the seismic traces consists of the low-rank latent-space variables predicted by a well-trained autoencoder neural network. The input to the autoencoder is the recorded common shot gathers, and the implicit function theorem is used to determine the perturbation of the skeletonized data with respect to the velocity perturbation. The final velocity model is the one that best predicts the observed latent-space parameters. Empirical results suggest that th…
