A reduced order approach for probabilistic inversions of 3-D magnetotelluric data I: general formulation

Simulation-based probabilistic inversions of 3-D magnetotelluric (MT) data are arguably the best option to deal with the nonlinearity and non-uniqueness of the MT problem. However, the computational cost associated with the modelling of 3-D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT data sets. In this contribution, we present a novel and general inversion framework, driven by Markov Chain Monte Carlo (MCMC) algorithms, which combines (i) an efficient parallel-in-parallel structure to solve the 3-D forward problem, (ii) a reduced order technique to create fast and accurate surrogate models of the forward problem and (iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method. We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parametrizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3-D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth's interior.Fil: Manassero, María Constanza. Macquarie University; AustraliaFil: Afonso, Juan Carlos. Macquarie University; AustraliaFil: Zyserman, Fabio Ivan. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Zlotnik, Sergio. Universidad Politécnica de Catalunya; EspañaFil: Fomin, I.. Macquarie University; Australi

Geophysics for Mineral Exploration

This Special Issue contains ten papers which focus on emerging geophysical techniques for mineral exploration, novel modeling, and interpretation methods, including joint inversions of multi physics data, and challenging case studies. The papers cover a wide range of mineral deposits, including banded iron formations, epithermal gold–silver–copper–iron–molybdenum deposits, iron-oxide–copper–gold deposits, and prospecting forgroundwater resources

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

A reduced order approach for probabilistic inversions of 3-D magnetotelluric data I: general formulation

Simulation-based probabilistic inversions of 3D magnetotelluric (MT) data are arguably the best option to deal with the non-linearity and non-uniqueness of the MT problem. However, the computational cost associated with the modeling of 3D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT datasets. In this contribution, we present a novel and general inversion framework, driven by Markov chain Monte Carlo (MCMC) algorithms, which combines i) an efficient parallel-in-parallel structure to solve the 3D forward problem, ii) a reduced order technique to create fast and accurate surrogate models of the forward problem, and iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method. We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parameterizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth’s interior.Facultad de Ciencias Astronómicas y Geofísica

Joint optimization of geophysical data using multi-objective swarm intelligence

The joint inversion of multiple data sets encompasses the advantages of different geophysical methods but may yield to conflicting solutions. Global search methods have been recently developed to address the issue of local minima found by derivative-based methods, to analyse the data compatibility and to find the set of trade-off solutions, since they are not unique. In this paper, we examine two evolutionary algorithms to solve the joint inversion of electrical and electromagnetic data. These nature-inspired metaheuristics also adopt the principle of Pareto optimality in order to identify the result among the feasible solutions and then infer the data compatibility. Since the joint inversion is characterized by more than one objective, we implemented the algorithm multi-objective particle swarm optimization (MOPSO) to jointly interpret time-domain electromagnetic data and vertical electrical sounding. We first tested MOPSO on a synthetic model. The performance of MOPSO was directly compared with that of a multi-objective genetic algorithm, the non-dominated sorting genetic algorithm (NSGAIII), which has often been adopted in geophysics. The adoption of MOPSO and NSGA-III enabled avoiding both simplification into a single-objective problem and the use of a weighting factor between the objectives. We tested the two methods on real data sets collected in the northwest of Italy. The results obtained from MOPSO and NSGA-III were highly comparable to each other and largely consistent with literature findings. The MOPSO performed a rigorous selection of the best trade-off solutions and its convergence was faster than NSGA-III. The analysis of the Pareto Front reported data incompatibility, which is very common for real data due to different resolutions, sensitivities and depth of investigations. Notwithstanding this, the multi-objective optimizers provided a complementary interpretation of the data, ensuring significant advantages with respect to the separate optimizations we carried out using the single-objective particle swarm optimization algorithm

HIBRIDNI ALGORITAM OPTIMIZACIJE ROJA ČESTICA I OPTIMIZACIJE SIVOGA VUKA ZA JEDNODIMENZIONALNO INVERZNO MODELIRANJE AUDIOFREKVENCIJSKE MAGNETOTELURIKE S KONTROLIRANIM IZVOROM (CSAMT)

The Controlled Source Audio-frequency Magnetotellurics (CSAMT) is a geophysical method utilizing artificial electromagnetic signal source to estimate subsurface resistivity structures. One-dimensional (1D) inversion modelling of CSAMT data is non-linear and the solution can be estimated by using global optimization algorithms. Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO) are well-known population-based algorithms having relatively simple mathematical formulation and implementation. Hybridization of PSO and GWO algorithms (called hybrid PSO-GWO) can improve the convergence capability to the global solution. This study applied the hybrid PSO-GWO algorithm for 1D CSAMT inversion modelling. Tests were conducted with synthetic CSAMT data associated with 3-layer, 4-layer and 5-layer earth models to determine the performance of the algorithm. The results show that the hybrid PSO-GWO algorithm has a good performance in obtaining the minimum misfit compared to the original PSO and GWO algorithms. The hybrid PSO-GWO algorithm was also applied to invert CSAMT field data for gold mineralization exploration in the Cibaliung area, Banten Province, Indonesia. The algorithm was able to reconstruct the resistivity model very well which is confirmed by the results from inversion of the data using standard 2D MT inversion software. The model also agrees well with the geological information of the study area.Audiofrekvencijska magnetotelurika s kontroliranim izvorom (CSAMT) geofizička je metoda koja se koristi izvorom umjetnoga elektromagnetskog signala za procjenu struktura otpornosti ispod površine. Jednodimenzionalno (1D) inverzno modeliranje CSAMT podataka nelinearno je te se rješenje može procijeniti korištenjem algoritama za globalnu optimizaciju. Algoritam roja čestica (PSO) i algoritam sivoga vuka (GWO) dobro su poznati algoritmi koji se temelje na populaciji i imaju relativno jednostavnu matematičku formulaciju i implementaciju. Hibridizacija PSO i GWO algoritama (hibridni PSO-GWO) može poboljšati sposobnost konvergencije prema globalnom rješenju. U ovom istraživanju primijenjen je hibridni PSO-GWO algoritam za 1D CSAMT inverzno modeliranje. Provedeno je testiranje sa sintetičkim CSAMT podatcima povezanim s 3-slojnim, 4-slojnim i 5-slojnim modelima zemlje kako bi se odredile performanse algoritma. Rezultati su pokazali kako hibridni PSO-GWO algoritam ima dobre performanse u postizanju minimalne neusklađenosti u usporedbi s originalnim PSO i GWO algoritmima. Hibridni PSO-GWO algoritam također je primijenjen za inverziju CSAMT terenskih podataka s ciljem istraživanja mineralizacije zlata u području Cibaliung, provincija Banten, Indonezija. Algoritam je uspio vrlo dobro rekonstruirati model otpornosti, što potvrđuju rezultati inverznoga modeliranja korištenjem standardnoga softvera za inverziju 2D magnetotelurskih podataka. Rezultati modela također se dobro podudaraju s geološkim informacijama istraživanoga područja

Utilisation of probabilistic magnetotelluric modelling to constrain magnetic data inversion: proof-of-concept and field application

We propose, test and apply a methodology integrating 1D magnetotelluric (MT) and magnetic data inversion, with a focus on the characterisation of the cover–basement interface. It consists of a cooperative inversion workflow relying on standalone inversion codes. Probabilistic information about the presence of rock units is derived from MT and passed on to magnetic inversion through constraints combining structural constraints with petrophysical prior information. First, we perform the 1D probabilistic inversion of MT data for all sites and recover the respective probabilities of observing the cover–basement interface, which we interpolate to the rest of the study area. We then calculate the probabilities of observing the different rock units and partition the model into domains defined by combinations of rock units with non-zero probabilities. Third, we combine these domains with petrophysical information to apply spatially varying, disjoint interval bound constraints (DIBC) to least-squares magnetic data inversion using the alternating direction method of multipliers (or ADMM). We demonstrate the proof-of-concept using a realistic synthetic model reproducing features from the Mansfield area (Victoria, Australia) using a series of uncertainty indicators. We then apply the workflow to field data from the prospective mining region of Cloncurry (Queensland, Australia). Results indicate that our integration methodology efficiently leverages the complementarity between separate MT and magnetic data modelling approaches and can improve our capability to image the cover–basement interface. In the field application case, our findings also suggest that the proposed workflow may be useful to refine existing geological interpretations and to infer lateral variations within the basement.</p

3D Bayesian Variational Full Waveform Inversion

Seismic full-waveform inversion (FWI) provides high resolution images of the subsurface by exploiting information in the recorded seismic waveforms. This is achieved by solving a highly nonnlinear and nonunique inverse problem. Bayesian inference is therefore used to quantify uncertainties in the solution. Variational inference is a method that provides probabilistic, Bayesian solutions efficiently using optimization. The method has been applied to 2D FWI problems to produce full Bayesian posterior distributions. However, due to higher dimensionality and more expensive computational cost, the performance of the method in 3D FWI problems remains unknown. We apply three variational inference methods to 3D FWI and analyse their performance. Specifically we apply automatic differential variational inference (ADVI), Stein variational gradient descent (SVGD) and stochastic SVGD (sSVGD), to a 3D FWI problem, and compare their results and computational cost. The results show that ADVI is the most computationally efficient method but systematically underestimates the uncertainty. The method can therefore be used to provide relatively rapid but approximate insights into the subsurface together with a lower bound estimate of the uncertainty. SVGD demands the highest computational cost, and still produces biased results. In contrast, by including a randomized term in the SVGD dynamics, sSVGD becomes a Markov chain Monte Carlo method and provides the most accurate results at intermediate computational cost. We thus conclude that 3D variational full-waveform inversion is practically applicable, at least in small problems, and can be used to image the Earth's interior and to provide reasonable uncertainty estimates on those images