Updating prior geologic uncertainty with GPR traveltime tomographic data

ENIGMA IT

Constraining gradient-based inversion with a variational autoencoder to reproduce geological patterns

Given the sparsity of geophysical data it is useful to rely on prior information on the expected geological patterns to constrain the inverse problem and obtain a realistic image of the subsurface. By using several examples of such patterns (e.g. those obtained from a training image), deep generative models learn a low-dimensional latent space that can be seen as a reparameterization of the original high-dimensional parameters and then inversion can be done in this latent space. Examples of such generative models are the variational autoencoder (VAE) and the generative adversarial network (GAN). Both usually include deep neural networks within their architecture and have shown good performance in reproducing high-dimensional structured subsurface models. However, they both use a highly nonlinear function to map from latent space to the original high-dimensional parameter space which hinders the optimization of the objective function during inversion. Particularly, such nonlinearity may give rise to local minima where gradient-based inversion gets trapped and therefore fails to reach the global minimum. GAN has been previously used with gradient-based inversion in a linear traveltime tomography synthetic test where it was shown to often fail in reaching a consistent RMSE (compared to the added noise) because optimization converges to local minima. On the other hand, inversion with MCMC and GAN was shown to reach acceptable RMSE values. When applicable, however, a gradient-based inversion is preferred because of its lower computational demand. We propose using VAE together with gradient-based inversion and show that optimization reaches lower RMSE values on average compared to GAN in a linear traveltime tomography synthetic case. We also compare the subsurface models that are generated during the iterations of the optimization to explore the effect of the different latent spaces used by GAN and VAE. We identify a trade-off between a strict following of the patterns and getting trapped in local minima during optimization, i.e. VAE seems to be able to break some continuous channels in order to not get trapped in local minima whereas GAN does not break channels. Finally, we perform some synthetic tests with nonlinear traveltime tomography and show that gradient-based inversion with VAE is able to recover a similar global structure to the true model but its final RMSE values are still far from the added noise level

Imaging the subsurface to inform hydrological models : a geophysicist's perspective

Heterogeneity plays a major role in subsurface processes from the local scale (preferential infiltration and flow paths, fractures) to the catchment scale (presence of lateral and vertical variability, multiple horizons, bedrock interface, etc.). If high-resolution direct observations are often available through drillholes, CPT or installing in-situ monitoring probes, those local measurements only provide punctual or 1D information. Within this context, geophysical techniques can provide relevant spatially-distributed information (2D, 3D or even 4D) with a much larger coverage than direct measurements. However, geophysical information remains indirect and must be translated into the sought parameter through petrophysical or transfer functions. Geophysicists are facing two important issues when imaging the subsurface: 1) Generating images of the subsurface that are consistent in terms of soil or geological structures; 2) Integrating the geophysical information into hydrological models. Both issues will be discussed in this contribution. Geophysical imaging is the result of an inversion process whose solution is non-unique. This problem is generally solved using a regularization approach introducing some a priori characteristics of the model. The dominant choice is still the smoothness constraint inversion, which often introduces a too simplistic representation of the subsurface, and decreases the potential of geophysics to discriminate between different facies. In the first part of this contribution, we will analyze what can be expected from geophysical methods in terms of characterization of the heterogeneity. We will illustrate how the inversion method affects the discrimination potential of geophysics, and how we can improve the geophysical image by accounting for prior information. We will see how the discrimination potential decreases with the loss of resolution. Finally, we will investigate how recent methodologies using machine learning can improve our ability to image the subsurface. Given the high spatial coverage of geophysical methods, they have a huge potential to inform hydrological models in terms of heterogeneity. However, the limitations related to geophysical inversion also make the geophysical model uncertain and the risk to propagate erroneous information exists. In the second part of this contribution, we will illustrate how to incorporate geophysical data into hydrological models to unravel their spatial complexity. At the early stage of a project, several scenarios regarding spatial heterogeneity are often possible (orientation of fractures, number of facies to consider, interconnection within one facies, etc.), and this can largely influence the outcomes of the hydrological models. In this context, geophysical data can be used to verify the consistency of some scenarios without requiring any inversion in a process called falsification. Once realistic scenarios have been identified, geophysical data can be used to spatially constrain hydrological models. However, this should ideally account for the uncertainty related to geophysical inversion. One possibility is to use a fully-coupled approach where geophysical data are integrated directly in the hydrological model inversion. This requires nevertheless a transfer function to relate hydrological and geophysical variables. As an alternative, a sequential approach using a probabilistic framework accounting for the imperfect geophysical data can be used. The latter requires co-located measurements

Estimation of spatially-structured subsurface parameters using variational autoencoders and gradient-based optimization

Environmental models of the subsurface usually require the estimation of high-dimensional spatially-distributed parameters. However, the sparsity of subsurface data hinders such estimation which may in turn affect predictions using these models. In order to mitigate this issue, parameter estimation can be constrained to prior information on the expected subsurface patterns (e.g. geological facies). By using several examples of such patterns (e.g. those obtained from a training image), a variational autoencoder (VAE) learns a low-dimensional latent space that can be seen as a reparameterization of the original high-dimensional parameters and then estimation by means of gradient-based optimization can be performed in this latent space. Spatial parameters estimated in this way display the enforced patterns. VAEs usually include deep neural networks within their architecture and have shown good performance in reproducing high-dimensional structured subsurface models. However, they use a highly nonlinear function to map from latent space to the original high-dimensional parameter space which may give rise to local minima where gradient-based optimization gets trapped and therefore fails to reach the global minimum. Global optimization strategies may be used to solve this issue, however, a gradient-based inversion is preferred because of its lower computational demand. We propose using VAE together with gradient-based optimization in a linear traveltime tomography synthetic case with added noise and show that it often reaches low data error values and produces visually similar spatial parameters when compared with different test subsurface realizations. We also add regularization to the objective function to improve the number of times it reaches an adequate minimum. Finally, we perform a synthetic test with nonlinear traveltime tomography and show that the proposed strategy is able to recover visually similar spatial parameters with an error close to the added noise level

Advancing measurements and representations of subsurface heterogeneity and dynamic processes: towards 4D hydrogeology

Essentially all hydrogeological processes are strongly influenced by the subsurface spatial heterogeneity and the temporal variation of environmental conditions, hydraulic properties, and solute concentrations. This spatial and temporal variability generally leads to effective behaviors and emerging phenomena that cannot be predicted from conventional approaches based on homogeneous assumptions and models. However, it is not always clear when, why, how, and at what scale the 4D (3D + time) nature of the subsurface needs to be considered in hydrogeological monitoring, modeling, and applications. In this paper, we discuss the interest and potential for the monitoring and characterization of spatial and temporal variability, including 4D imaging, in a series of hydrogeological processes: (1) groundwater fluxes, (2) solute transport and reaction, (3) vadose zone dynamics, and (4) surface–subsurface water interactions. We first identify the main challenges related to the coupling of spatial and temporal fluctuations for these processes. We then highlight recent innovations that have led to significant breakthroughs in high-resolution space–time imaging and modeling the characterization, monitoring, and modeling of these spatial and temporal fluctuations. We finally propose a classification of processes and applications at different scales according to their need and potential for high-resolution space–time imaging. We thus advocate a more systematic characterization of the dynamic and 3D nature of the subsurface for a series of critical processes and emerging applications. This calls for the validation of 4D imaging techniques at highly instrumented observatories and the harmonization of open databases to share hydrogeological data sets in their 4D components

Mapping geographical inequalities in access to drinking water and sanitation facilities in low-income and middle-income countries, 2000-17

Background: Universal access to safe drinking water and sanitation facilities is an essential human right, recognised in the Sustainable Development Goals as crucial for preventing disease and improving human wellbeing. Comprehensive, high-resolution estimates are important to inform progress towards achieving this goal. We aimed to produce high-resolution geospatial estimates of access to drinking water and sanitation facilities. Methods: We used a Bayesian geostatistical model and data from 600 sources across more than 88 low-income and middle-income countries (LMICs) to estimate access to drinking water and sanitation facilities on continuous continent-wide surfaces from 2000 to 2017, and aggregated results to policy-relevant administrative units. We estimated mutually exclusive and collectively exhaustive subcategories of facilities for drinking water (piped water on or off premises, other improved facilities, unimproved, and surface water) and sanitation facilities (septic or sewer sanitation, other improved, unimproved, and open defecation) with use of ordinal regression. We also estimated the number of diarrhoeal deaths in children younger than 5 years attributed to unsafe facilities and estimated deaths that were averted by increased access to safe facilities in 2017, and analysed geographical inequality in access within LMICs. Findings: Across LMICs, access to both piped water and improved water overall increased between 2000 and 2017, with progress varying spatially. For piped water, the safest water facility type, access increased from 40·0% (95% uncertainty interval [UI] 39·4–40·7) to 50·3% (50·0–50·5), but was lowest in sub-Saharan Africa, where access to piped water was mostly concentrated in urban centres. Access to both sewer or septic sanitation and improved sanitation overall also increased across all LMICs during the study period. For sewer or septic sanitation, access was 46·3% (95% UI 46·1–46·5) in 2017, compared with 28·7% (28·5–29·0) in 2000. Although some units improved access to the safest drinking water or sanitation facilities since 2000, a large absolute number of people continued to not have access in several units with high access to such facilities (>80%) in 2017. More than 253 000 people did not have access to sewer or septic sanitation facilities in the city of Harare, Zimbabwe, despite 88·6% (95% UI 87·2–89·7) access overall. Many units were able to transition from the least safe facilities in 2000 to safe facilities by 2017; for units in which populations primarily practised open defecation in 2000, 686 (95% UI 664–711) of the 1830 (1797–1863) units transitioned to the use of improved sanitation. Geographical disparities in access to improved water across units decreased in 76·1% (95% UI 71·6–80·7) of countries from 2000 to 2017, and in 53·9% (50·6–59·6) of countries for access to improved sanitation, but remained evident subnationally in most countries in 2017. Interpretation: Our estimates, combined with geospatial trends in diarrhoeal burden, identify where efforts to increase access to safe drinking water and sanitation facilities are most needed. By highlighting areas with successful approaches or in need of targeted interventions, our estimates can enable precision public health to effectively progress towards universal access to safe water and sanitation

Measuring universal health coverage based on an index of effective coverage of health services in 204 countries and territories, 1990–2019 : A systematic analysis for the Global Burden of Disease Study 2019

Background Achieving universal health coverage (UHC) involves all people receiving the health services they need, of high quality, without experiencing financial hardship. Making progress towards UHC is a policy priority for both countries and global institutions, as highlighted by the agenda of the UN Sustainable Development Goals (SDGs) and WHO's Thirteenth General Programme of Work (GPW13). Measuring effective coverage at the health-system level is important for understanding whether health services are aligned with countries' health profiles and are of sufficient quality to produce health gains for populations of all ages. Methods Based on the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, we assessed UHC effective coverage for 204 countries and territories from 1990 to 2019. Drawing from a measurement framework developed through WHO's GPW13 consultation, we mapped 23 effective coverage indicators to a matrix representing health service types (eg, promotion, prevention, and treatment) and five population-age groups spanning from reproductive and newborn to older adults (≥65 years). Effective coverage indicators were based on intervention coverage or outcome-based measures such as mortality-to-incidence ratios to approximate access to quality care; outcome-based measures were transformed to values on a scale of 0–100 based on the 2·5th and 97·5th percentile of location-year values. We constructed the UHC effective coverage index by weighting each effective coverage indicator relative to its associated potential health gains, as measured by disability-adjusted life-years for each location-year and population-age group. For three tests of validity (content, known-groups, and convergent), UHC effective coverage index performance was generally better than that of other UHC service coverage indices from WHO (ie, the current metric for SDG indicator 3.8.1 on UHC service coverage), the World Bank, and GBD 2017. We quantified frontiers of UHC effective coverage performance on the basis of pooled health spending per capita, representing UHC effective coverage index levels achieved in 2019 relative to country-level government health spending, prepaid private expenditures, and development assistance for health. To assess current trajectories towards the GPW13 UHC billion target—1 billion more people benefiting from UHC by 2023—we estimated additional population equivalents with UHC effective coverage from 2018 to 2023. Findings Globally, performance on the UHC effective coverage index improved from 45·8 (95% uncertainty interval 44·2–47·5) in 1990 to 60·3 (58·7–61·9) in 2019, yet country-level UHC effective coverage in 2019 still spanned from 95 or higher in Japan and Iceland to lower than 25 in Somalia and the Central African Republic. Since 2010, sub-Saharan Africa showed accelerated gains on the UHC effective coverage index (at an average increase of 2·6% [1·9–3·3] per year up to 2019); by contrast, most other GBD super-regions had slowed rates of progress in 2010–2019 relative to 1990–2010. Many countries showed lagging performance on effective coverage indicators for non-communicable diseases relative to those for communicable diseases and maternal and child health, despite non-communicable diseases accounting for a greater proportion of potential health gains in 2019, suggesting that many health systems are not keeping pace with the rising non-communicable disease burden and associated population health needs. In 2019, the UHC effective coverage index was associated with pooled health spending per capita (r=0·79), although countries across the development spectrum had much lower UHC effective coverage than is potentially achievable relative to their health spending. Under maximum efficiency of translating health spending into UHC effective coverage performance, countries would need to reach $1398 pooled health spending per capita (US$ adjusted for purchasing power parity) in order to achieve 80 on the UHC effective coverage index. From 2018 to 2023, an estimated 388·9 million (358·6–421·3) more population equivalents would have UHC effective coverage, falling well short of the GPW13 target of 1 billion more people benefiting from UHC during this time. Current projections point to an estimated 3·1 billion (3·0–3·2) population equivalents still lacking UHC effective coverage in 2023, with nearly a third (968·1 million [903·5–1040·3]) residing in south Asia. Interpretation The present study demonstrates the utility of measuring effective coverage and its role in supporting improved health outcomes for all people—the ultimate goal of UHC and its achievement. Global ambitions to accelerate progress on UHC service coverage are increasingly unlikely unless concerted action on non-communicable diseases occurs and countries can better translate health spending into improved performance. Focusing on effective coverage and accounting for the world's evolving health needs lays the groundwork for better understanding how close—or how far—all populations are in benefiting from UHC