The roughness of Martian topography: A metre-scale fractal analysis of six selected areas

Available online 23 May 2022Studies of the roughness of natural surfaces (landscapes) provide useful information for planetary geology. This paper covers the mapping and analysis of the spatial variability of the surface roughness of Martian topography at a high spatial resolution (metre-scale). The methodology provides new images of the Martian surface texture at the metre-scale that can assist in the interpretation of geological events, processes and formations. It can also assist in geological mapping and in the evaluation of sites that merit further exploration. Digital elevation models, generated by stereo-pair HiRISE images, of six different terrains (aeolian, volcanic, hydrated, cratered, reticulate and sublimated) were used to characterize the metre-scale terrain roughness of representative test sites on Mars. Surface roughness was evaluated by using the local fractal dimension and the results show that the mean of the local fractal dimension ranges from 2.17 in reticulate terrain to 2.71 in sublimated terrain in the southern polar cap. The roughness of the sublimated terrain is significantly higher than the roughness of typical terrains on Earth. Basically, the roughness of the Martian terrain at the metre-scale depends on the rugosity of the landscape, which can be quantified as the number of metric-scale closed depressions and mounds present on the terrain. The information provided by the spatial variability patterns of metre-scale roughness maps provides a significant resource for local planetary geology research at high resolution scale.E. Pardo-Igúzquiza, P.A. Dow

The Many Forms of Co-kriging: A Diversity of Multivariate Spatial Estimators

OnlinePublIn this expository review paper, we show that co-kriging, a widely used geostatistical multivariate optimal linear estimator, has a diverse range of extensions that we have collected and illustrated to show the potential of this spatial interpolator. In the context of spatial stochastic processes, this paper covers scenarios including increasing the spatial resolution of a spatial variable (downscaling), solving inverse problems, estimating directional derivatives, and spatial interpolation taking boundary conditions into account. All these spatial interpolators are optimal linear estimators in the sense of being unbiased and minimising the variance of the estimation error.Peter A. Dowd, Eulogio Pardo-Igúzquiz

Geostatistics in the Presence of Multivariate Complexities: Comparison of Multi-Gaussian Transforms

Published 05 April 2023. OnlinePublOne of the most challenging aspects of multivariate geostatistics is dealing with complex relationships between variables. Geostatistical co-simulation and spatial decorrelation methods, commonly used for modelling multiple variables, are ineffective in the presence of multivariate complexities. On the other hand, multi-Gaussian transforms are designed to deal with complex multivariate relationships, such as non-linearity, heteroscedasticity and geological constraints. These methods transform the variables into independent multi-Gaussian factors that can be individually simulated. This study compares the performance of the following multi-Gaussian transforms: rotation based iterative Gaussianisation, projection pursuit multivariate transform and flow transformation. Case studies with bivariate complexities are used to evaluate and compare the realisations of the transformed values. For this purpose, commonly used geostatistical validation metrics are applied, including multivariate normality tests, reproduction of bivariate relationships, and histogram and variogram validation. Based on most of the metrics, all three methods produced results of similar quality. The most obvious difference is the execution speed for forward and back transformation, for which flow transformation is much slower.Sultan Abulkhair, Peter A. Dowd, Chaoshui X

Fuzzy clustering with spatial correction and its application to geometallurgical domaining

Published online: 25 July 2018This paper describes a proposed method for clustering attributes on the basis of their spatial variability and the uncertainty of cluster member- ship. The method is applied to geometallurgical domaining in mining ap- plications. The main objective of geometallurgical clustering is to ensure consistent feed to a processing plant by minimising transitions between di erent types of feed coming from di erent domains (clusters). For this purpose, clusters should contain not only similar geometallurgical char- acteristics but also be located in as few contiguous and compact spatial locations as possible so as to maximise the homogeneity of ore delivered to the plant. Most existing clustering methods applied to geometallurgy have two problems. Firstly, they are unable to di erentiate subsets of attributes at the cluster level and therefore cluster membership can only be assigned on the basis of exactly identical attributes, which may not be the case in practice. Secondly, as they do not take account of the spatial relationships they can produce clusters which may be spatially dispersed and/or overlapped. In the work described in this paper a new clustering method is introduced that integrates three distinct steps to ensure qual- ity clustering. In the rst step, fuzzy membership information is used to minimise compactness and maximise separation. In the second step, the best subsets of attributes are de ned and applied for domaining purposes. These two steps are iterated to convergence. In the nal step a graph- based labelling method, which takes spatial constraints into account, is used to produce the nal clusters. Three examples are presented to illus- trate the application of the proposed method. These examples demon- strate that the proposed method can reveal useful relationships among geometallurgical attributes within a clear and compact spatial structure. The resulting clusters can be used directly in mine planning to optimise the ore feed to be delivered to the processing plant.E. Sepúlveda, P. A. Dowd, C. X

Comparison of statistical methods for testing the hypothesis of constant global mean in spatial statistics

In spatial statistics in general, and in geostatistics in particular, the choice between a spatial model with drift and a model with constant global mean is often critical, especially when only a small number of samples are available. A statistical test provides an objective means of making this choice. Among the many available statistical tests, a variance-ratio test has been widely used for making this choice because of its good statistical properties but, in addition to a semi-variogram model, it also requires an alternative drift model hypothesis. Another test statistic is the global D-statistic, which is a complementary test in the sense that it does not require an alternative hypothesis model. In this paper, we use sparse data from simulated random fields to evaluate and compare the performances of these two methods for testing the hypothesis of constant global mean in spatial statistics. We do so by considering the influence of four factors: the amount of data, the type of random field, the amount of spatial or temporal correlation and parametric drifts. In addition, we evaluate their performances in time series analysis, in which testing the hypothesis of constant global mean is also of significant interest. The two test statistics are compared in terms of their achieved confidence level and achieved power. The better method is the one that achieves the nominal confidence level and has higher power. We discuss departures from the nominal values and the results are used to highlight the importance of this problem in spatial statistics.Hong Wang, Eulogio Pardo-Igúzquiza, Peter A. Dowd, Yongguo Yan

Stochastic simulation of the spatial heterogeneity of deltaic hydrofacies accounting for the uncertainty of facies proportions

The spatial geological heterogeneity of an aquifer significantly affects groundwater storage, flow and the transport of solutes. In the particular case of coastal aquifers, spatial geological heterogeneity is also a major determining factor of the spatio-temporal patterns of water quality (salinity) due to seawater intrusion. While the hydraulics of coastal hydrogeology can be modeled effectively by various density flow equations, the aquifer geology is highly uncertain. A stochastic solution to the problem is to generate numerical realisations of the geology using sequential stratigraphy, geophysical models or geostatistical approaches. The geostatistical methods (two-point geostatistics, Markov chain models and multiple-point geostatistics) have the advantage of minimal data requirements, e.g., when the only data available are from cores from a few sparsely located boreholes. We provide an extension of sequential indicator simulation by including the uncertainty of the hydrofacies proportions in the simulation approach. We also deal with the problem of variogram estimation from sparse boreholes and we discuss the implicit transition probabilities and the connectivity of simulated realisations of a number of categorical variables. The variogram model used in the simulation of hydrofacies significantly influences the degree of connectivity of the hydrofacies in the simulated model. The choice of model is critical as connectivity determines the amount and extent of seawater intrusion and hence the environmental risk. The methodology is illustrated with a case study of the Andarax river delta, a coastal aquifer in south-eastern Spain. This is a semi-arid Mediterranean region in which the increasing use of, and demand for, groundwater is exacerbated by a transient tourist population that reaches its peak in the summer when the demand for the permanent population is at its highest. The work reported here provides a sound basis for designing flow simulation models for the optimal management of groundwater resources. This paper is an extended version of a presentation given at the 2012 GeoENV Conference held in Valencia, Spain.S. Jorreto-Zaguirre, P.A. Dowd, E. Pardo-Igúzquiza, A. Pulido-Bosch and F. Sánchez-Marto

A global call for action to include gender in research impact assessment

Global investment in biomedical research has grown significantly over the last decades, reaching approximately a quarter of a trillion US dollars in 2010. However, not all of this investment is distributed evenly by gender. It follows, arguably, that scarce research resources may not be optimally invested (by either not supporting the best science or by failing to investigate topics that benefit women and men equitably). Women across the world tend to be significantly underrepresented in research both as researchers and research participants, receive less research funding, and appear less frequently than men as authors on research publications. There is also some evidence that women are relatively disadvantaged as the beneficiaries of research, in terms of its health, societal, and economic impacts. Historical gender biases may have created a path dependency that means that the research system and the impacts of research are biased towards male researchers and male beneficiaries, making it inherently difficult (though not impossible) to eliminate gender bias. In this commentary, we – a group of scholars and practitioners from Africa, America, Asia, and Europe– argue that gender-sensitive research impact assessment could become a force for good in moving science policy and practice towards gender equity. Research impact assessment is the multidisciplinary field of scientific inquiry that examines the research process to maximise scientific, societal, and economic returns on investment in research. It encompasses many theoretical and methodological approaches that can be used to investigate gender bias and recommend actions for change to maximise research impact. We offer a set of recommendations to research funders, research institutions, and research evaluators who conduct impact assessment on how to include and strengthen analysis of gender equity in research impact assessment and issue a global call for action

Variogram modelling and interpretation: two examples

P.A. Dow