ALBERT

Description: 〈span〉〈div〉Summary〈/div〉Deterministic geophysical inversion approaches yield tomographic images with strong imprints of the regularization terms required to solve otherwise ill-posed inverse problems. While such tomograms enable an adequate assessment of the larger-scale features of the probed subsurface, the finer-scale details tend to be unresolved. Yet, representing these fine-scale structural details is generally desirable and for some applications even mandatory. To address this problem, we have developed a two-step methodology based on area-to-point kriging to generate fine-scale multi-Gaussian realizations from smooth tomographic images. Specifically, we use a co-kriging system, in which the smooth, low-resolution tomogram is related to the fine-scale heterogeneity through a linear mapping operation. This mapping is based on the model resolution and the posterior covariance matrices computed using a linearization around the final tomographic model. This, in turn, allows for analytical computations of covariance and cross-covariance models. The methodology is tested on a heterogeneous synthetic 2D distribution of electrical conductivity that is probed with a surface-based electrical resistivity tomography (ERT) survey. The results demonstrate the ability of this technique to reproduce a known geostatistical model characterizing the fine-scale structure, while simultaneously preserving the large-scale structures identified by the smoothness-constrained tomographic inversion. Small discrepancies between the geophysical forward responses of the realizations and the reference synthetic data are attributed to the underlying linearization. Overall, the method provides an effective and fast alternative to more comprehensive, but computationally more expensive approaches, such as, for example, Markov chain Monte Carlo techniques. Moreover, the proposed method can be used to generate fine-scale multivariate Gaussian realizations from virtually any smoothness-constrained inversion results given the corresponding resolution and posterior covariance matrices.〈/span〉

Description: A comprehensive worldwide permeability dataset has been compiled consisting of 29000 in-situ permeabilities from 221 publications and reports and delineating the permeability distribution in crystalline rocks into depths of 2000 mbgs. We analyze the influence of technical factors (measurement method, scale effects, preferential sampling, hydraulic anisotropy) and geological factors (lithology, current stress regime, current seismotectonic activity, long-term tectono-geological history) on the permeability distribution with depth, by using regression analysis and K-means clustering. The influence of preferential sampling and hydraulic anisotropy are negligible. A scale dependency is observed based on calculated rock test volumes equaling 0.6 orders of magnitude of permeability change per order of magnitude of rock volume tested. Based on the entire dataset, permeability decreases as log(k) = -1.5*log(z)-16.3 with permeability k [m2] and positively increasing depth z [km], and depth is the main factor driving the permeability distribution. The permeability variance is about two orders of magnitude at all depths, presumably representing permeability variations around brittle fault zones. Permeability and specific yield/storage exhibit similar depth trends. While in the upper 200 mbgs fracture flow varies between confined and unconfined, we observe confined fracture and matrix flow below about 600 mbgs depth. The most important geological factors are current seismotectonic activity (determined by peak ground acceleration) and long-term tectono-geological history (determined by geological province). The impact of lithology is less important. Based on the regression coefficients derived for all the geological key factors, permeability ranges of crystalline rocks at site scale can be predicted. First tests with independent datasets are promising.

Description: Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with site-specific data, but also display the same type of patterns as those found in a training image. The training image can be seen as a conceptual model of the subsurface and is used as a non-parametric model of spatial variability. Inversion based on multiple-point statistics is challenging due to high nonlinearity and time-consuming geostatistical resimulation steps that are needed to create new model proposals. We propose an entirely new model proposal mechanism for geophysical inversion that is inspired by texture synthesis in computer vision. Instead of resimulating pixels based on higher-order patterns in the training image, we identify a suitable patch of the training image that replace a corresponding patch in the current model without breaking the patterns found in the training image, that is, remaining consistent with the given prior. We consider three cross-hole ground-penetrating radar examples in which the new model proposal mechanism is employed within an extended Metropolis Markov chain Monte Carlo (MCMC) inversion. The model proposal step is about 40 times faster than state-of-the-art multiple-point statistics resimulation techniques, the number of necessary MCMC steps is lower and the quality of the final model realizations is of similar quality. The model proposal mechanism is presently limited to 2-D fields, but the method is general and can be applied to a wide range of subsurface settings and geophysical data types.

Description: The direct sampling technique, belonging to the family of multiple-point statistics, is proposed as a nonparametric alternative to the classical autoregressive and Markov-chain-based models for daily rainfall time-series simulation. The algorithm makes use of the patterns contained inside the training image (the past rainfall record) to reproduce the complexity of the signal without inferring its prior statistical model: the time series is simulated by sampling the training data set where a sufficiently similar neighborhood exists. The advantage of this approach is the capability of simulating complex statistical relations by respecting the similarity of the patterns at different scales. The technique is applied to daily rainfall records from different climate settings, using a standard setup and without performing any optimization of the parameters. The results show that the overall statistics as well as the dry/wet spells patterns are simulated accurately. Also the extremes at the higher temporal scale are reproduced adequately, reducing the well known problem of overdispersion.

Description: Limestone aeolianites constitute karstic aquifers covering much of the western and southern Australian coastal fringe. They are a key groundwater resource for a range of industries such as winery and tourism, and provide important ecosystem services such as habitat for stygofauna. Moreover, recharge estimation is important for understanding the water cycle, for contaminant transport, for water management and for stalagmite-based paleoclimate reconstructions. Caves offer a natural inception point to observe both the long-term groundwater recharge and the preferential movement of water through the unsaturated zone of such limestone. With the availability of automated drip rate logging systems and remote sensing techniques, it is now possible to deploy the combination of these methods for larger scale studies of infiltration processes within a cave. In this study, we utilize a spatial survey of automated cave drip monitoring in two large chambers of the Golgotha Cave, South-West Western Australia (SWWA), with the aim of better understanding infiltration water movement and the relationship between infiltration, stalactite morphology and unsaturated zone recharge. By applying morphological analysis of ceiling features from Terrestrial LiDAR (T-LiDAR) data, coupled with drip time series and climate data from 2012–2014, we demonstrate the nature of the relationships between infiltration through fractures in the limestone and unsaturated zone recharge. Similarities between drip-rate time series are interpreted in terms of flow patterns, cave chamber morphology and lithology. Moreover, we develop a new technique to estimate recharge in large scale caves, engaging flow classification to determine the cave ceiling area covered by each flow category and drip data for the entire observation period, to calculate the total volume of cave discharge. This new technique can be applied to other cave sites to identify highly focused areas of recharge and can help to better estimate the total recharge volume.

Description: The Direct Sampling technique, belonging to the family of multiple-point statistics, is proposed as a non-parametric alternative to the classical autoregressive and Markov-chain based models for daily rainfall time-series simulation. The algorithm makes use of the patterns contained inside the training image (the past rainfall record) to reproduce the complexity of the signal without inferring its prior statistical model: the time-series is simulated by sampling the training dataset where a sufficiently similar neighborhood exists. The advantage of this approach is the capability of simulating complex statistical relations by respecting the similarity of the patterns at different scales. The technique is applied to daily rainfall records from different climate settings, using a standard setup and without performing any optimization of the parameters. The results show that the overall statistics as well as the dry/wet spells patterns are simulated accurately. Also the extremes at the higher temporal scale are reproduced exhaustively, reducing the well known problem of over-dispersion.

Description: Limestone aeolianites constitute karstic aquifers covering much of the western and southern Australian coastal fringe. They are a key groundwater resource for a range of industries such as winery and tourism, and provide important ecosystem services such as habitat for stygofauna. Moreover, recharge estimation is important for understanding the water cycle, for contaminant transport, for water management, and for stalagmite-based paleoclimate reconstructions. Caves offer a natural inception point to observe both the long-term groundwater recharge and the preferential movement of water through the unsaturated zone of such limestone. With the availability of automated drip rate logging systems and remote sensing techniques, it is now possible to deploy the combination of these methods for larger-scale studies of infiltration processes within a cave. In this study, we utilize a spatial survey of automated cave drip monitoring in two large chambers of Golgotha Cave, south-western Western Australia (SWWA), with the aim of better understanding infiltration water movement and the relationship between infiltration, stalactite morphology, and unsaturated zone recharge. By applying morphological analysis of ceiling features from Terrestrial LiDAR (T-LiDAR) data, coupled with drip time series and climate data from 2012 to 2014, we demonstrate the nature of the relationships between infiltration through fractures in the limestone and unsaturated zone recharge. Similarities between drip rate time series are interpreted in terms of flow patterns, cave chamber morphology, and lithology. Moreover, we develop a new technique to estimate recharge in large-scale caves, engaging flow classification to determine the cave ceiling area covered by each flow category and drip data for the entire observation period, to calculate the total volume of cave discharge. This new technique can be applied to other cave sites to identify highly focussed areas of recharge and can help to better estimate the total recharge volume.