Geostatistical inversion of geophysical data for near-surface modelling and characterization

A subsuperfície debaixo dos nossos pés é a parte da Terra que mais interage com actividades humanas e que armazena uma parte importante das águas subterrâneas e recursos minerais. É, portanto, fundamental caracterizar os primeiros metros da subsuperfície e quantificar com precisão as suas propriedades físicas, estruturais, químicas e biológicas. Para ultrapassar as limitações espaciais de medições directas por métodos invasivos, métodos geofísicos não invasivos têm sido aplicados na modelação e caraterização de ambientes subsuperficiais complexos e heterogéneos. Em particular, os métodos de indução electromagnética no domínio da frequência (FDEM) tornaram-se um dos métodos geofísicos mais utilizados nestes depósitos heterogéneos, devido à sensibilidade dos seus dados às alterações de duas propriedades físicas: a condutividade eléctrica e a susceptibilidade magnética. No entanto, transformar dados geofísicos em modelos espaciais da subsuperfície implica a resolução de um problema geofísico inverso, que é um problema não linear com múltiplas soluções. A resolução deste problema através de uma abordagem geoestatística permite combinar medições directas invasivas com dados geofísicos, para assim melhorar os modelos invertidos.
Combinando as vantagens dos dados FDEM com o potencial das metodologias de inversão geoestatística, esta tese apresenta um método de inversão geoestatística FDEM para modelar a distribuição espacial das propriedades na subsuperfície e avaliar a incerteza dos resultados previstos. A metodologia proposta é comparada com outro método probabilístico de inversão FDEM. Como os métodos de inversão geoestatísticos são computacionalmente exigentes quando se trata de resolver problemas inversos tridimensionais de grande escala, é apresentado um método de inversão probabilístico com um algoritmo de aprendizagem automática para melhorar a performance computacional. A partir de uma abordagem de inversão multi-geofísica, esta tese apresenta também um método de inversão conjunta de dados eléctricos e electromagnéticos que visa reduzir a incerteza dos modelos de subsuperfície previstos. Os métodos apresentados são aplicados em casos sintéticos e reais.

The main goal of this thesis was to develop and implement an iterative geostatistical geophysical inversion framework able to predict the subsurface spatial distribution of electrical conductivity and magnetic susceptibility at high spatial resolution from FDEM and ERT data. All the methodologies proposed herein were validated in a realistic synthetic data set and applied in real case examples. As main conclusion from these application examples, we can highlight that the geostatistical framework can handle the different spatial resolution from the geophysical and borehole data, that the proposed methodologies could cope with heterogenous subsurface environments, predicting local small-scale variability, while assessing simultaneously the uncertainty of the predicted models. The main conclusions of the four objectives of the thesis follow below.
Objective one: Realistic synthetic data set. We developed a realistic synthetic data set based on direct and laboratory measurements obtained from samples acquired in a mine tailing. These data can be used to benchmarking different geophysical inversion methods that have the potential to be applied in complex and heterogeneous near-surface environments. The work proposed in Bobe et al. (2019) (Chapter 3) is an illustrative example. This data set proved to be useful to test the sensibility of the proposed inversion methods to discontinuities in the physical properties and to capture their spatial continuity in highly heterogeneous environments. It also was useful to validate the proposed inversion methodologies throughout this thesis and to compare the corresponding predicted models. The data set is publicly available in http://doi.org/10.5281/zenodo.5116420
Objective two: Iterative geostatistical inversion of FDEM data. We developed and implemented an iterative geostatistical FDEM inversion methodology (Chapter 2) that allows to simultaneously predict EC and MS and can be applied to characterize complex and heterogeneous near-surface deposits of different types and nature. The proposed method was validated in the 3D synthetic data set developed under objective one, was tested in a real data set containing several archaeological features and strong local IP anomalies and was compared to a probabilistic KEG method and their predicted results. The results show the ability of the proposed method to reproduce the true EC and MS and the predicted FDEM measurements responses well enclosed the true FDEM. The uncertainty of the posterior distributions of EC and MS and the FDEM responses computed from the predicted models can also be assessed, presenting an advantage compared to deterministic FDEM inversion methods.
Objective three: Optimization of FDEM inversion. To improve the computational cost of the developed iterative geostatistical FDEM inversion method, we proposed a FDEM inversion method that performs the inversion in a reduced space without compromising the exploration of the model parameter space. We use a FDEM inversion scheme that combines ES-MDA with RTD and was able to predict the spatial distribution of EC and MS, in both synthetic and real case application examples. In both application examples, the predicted models reproduced the measured EC and MS data while allowing to assess the uncertainty of the predictions. The proposed methodology has the potential to solve large-scale three-dimensional problems in near-surface applications. The code of this method is available at: https://github.com/theanswer003/ES-RTD-FDEM
Objective four: Iterative geostatistical joint inversion of FDEM and ERT data. We developed and implemented an iterative geostatistical joint inversion method that couples data from different geophysical methods. The proposed method combines the benefits of the separate inversion methods of small-loop FDEM and direct current resistivity data in a joint inversion framework. Using a joint inversion approach, the perturbation of the joint parameter space represents improvements over the joint interpretation of the separate inversion. Though, most of the joint inversion methods that combine these two geophysical data use deterministic frameworks which require to explicitly weight the influence of the different data types. This work represents a milestone in the probabilistic joint inversion of FDEM and ERT data, as the proposed joint inversion method is, as far as our knowledge go, the first geostatistical joint inversion method of FDEM and ERT data, with the flexibility of application in a significant range of near-surface activities. From the application examples shown herein, we concluded that the proposed joint inversion method presents benefits over the separate inversion methods, increasing the accuracy of the predicted EC subsurface models with a better reproduction of the true EC models while reducing the uncertainty at the local small-scale, particularly at depth.