Earthquake modelling at the country level using aggregated spatio-temporal point processes

The goal of this paper is to derive a hazard map for earthquake occurrences in Pakistan from a catalogue that contains spatial coordinates of shallow earthquakes of magnitude 4.5 or larger aggregated over calendar years. We test relative temporal stationarity by the KPSS statistic and use the inhomogeneous J-function to test for inter-point interactions. We then formulate a cluster model, and de-convolve in order to calculate the hazard map, and verify that no particular year has an undue influence on the map. Within the borders of the single country, the KPSS test did not show any deviation from homogeneity in the spatial intensities. The inhomogeneous J-function indicated clustering that could not be attributed to inhomogeneity, and the analysis of aftershocks showed some evidence of two major shocks instead of one during the 2005 Kashmir earthquake disaster. Thus, the spatial point pattern analysis carried out for these data was insightful in various aspects and the hazard map that was obtained may lead to improved measures to protect the population against the disastrous effects of earthquakes

Mark correlations: relating physical properties to spatial distributions

Mark correlations provide a systematic approach to look at objects both distributed in space and bearing intrinsic information, for instance on physical properties. The interplay of the objects' properties (marks) with the spatial clustering is of vivid interest for many applications; are, e.g., galaxies with high luminosities more strongly clustered than dim ones? Do neighbored pores in a sandstone have similar sizes? How does the shape of impact craters on a planet depend on the geological surface properties? In this article, we give an introduction into the appropriate mathematical framework to deal with such questions, i.e. the theory of marked point processes. After having clarified the notion of segregation effects, we define universal test quantities applicable to realizations of a marked point processes. We show their power using concrete data sets in analyzing the luminosity-dependence of the galaxy clustering, the alignment of dark matter halos in gravitational $N$-body simulations, the morphology- and diameter-dependence of the Martian crater distribution and the size correlations of pores in sandstone. In order to understand our data in more detail, we discuss the Boolean depletion model, the random field model and the Cox random field model. The first model describes depletion effects in the distribution of Martian craters and pores in sandstone, whereas the last one accounts at least qualitatively for the observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics, second Wuppertal conference "Spatial statistics and statistical physics

Knowledge-based systems and geological survey

This personal and pragmatic review of the philosophy underpinning methods of geological surveying suggests that important influences of information technology have yet to make their impact. Early approaches took existing systems as metaphors, retaining the separation of maps, map explanations and information archives, organised around map sheets of fixed boundaries, scale and content. But system design should look ahead: a computer-based knowledge system for the same purpose can be built around hierarchies of spatial objects and their relationships, with maps as one means of visualisation, and information types linked as hypermedia and integrated in mark-up languages. The system framework and ontology, derived from the general geoscience model, could support consistent representation of the underlying concepts and maintain reference information on object classes and their behaviour. Models of processes and historical configurations could clarify the reasoning at any level of object detail and introduce new concepts such as complex systems. The up-to-date interpretation might centre on spatial models, constructed with explicit geological reasoning and evaluation of uncertainties. Assuming (at a future time) full computer support, the field survey results could be collected in real time as a multimedia stream, hyperlinked to and interacting with the other parts of the system as appropriate. Throughout, the knowledge is seen as human knowledge, with interactive computer support for recording and storing the information and processing it by such means as interpolating, correlating, browsing, selecting, retrieving, manipulating, calculating, analysing, generalising, filtering, visualising and delivering the results. Responsibilities may have to be reconsidered for various aspects of the system, such as: field surveying; spatial models and interpretation; geological processes, past configurations and reasoning; standard setting, system framework and ontology maintenance; training; storage, preservation, and dissemination of digital records

Near-stasis in the long-term diversification of Mesozoic tetrapods

How did evolution generate the extraordinary diversity of vertebrates on land? Zero species are known prior to ~380 million years ago, and more than 30,000 are present today. An expansionist model suggests this was achieved by large and unbounded increases, leading to substantially greater diversity in the present than at any time in the geological past. This model contrasts starkly with empirical support for constrained diversification in marine animals, suggesting different macroevolutionary processes on land and in the sea. We quantify patterns of vertebrate standing diversity on land during the Mesozoic–early Paleogene interval, applying sample-standardization to a global fossil dataset containing 27,260 occurrences of 4,898 non-marine tetrapod species. Our results show a highly stable pattern of Mesozoic tetrapod diversity at regional and local levels, underpinned by a weakly positive, but near-zero, long-term net diversification rate over 190 million years. Species diversity of non-flying terrestrial tetrapods less than doubled over this interval, despite the origins of exceptionally diverse extant groups within mammals, squamates, amphibians, and dinosaurs. Therefore, although speciose groups of modern tetrapods have Mesozoic origins, rates of Mesozoic diversification inferred from the fossil record are slow compared to those inferred from molecular phylogenies. If high speciation rates did occur in the Mesozoic, then they seem to have been balanced by extinctions among older clades. An apparent 4-fold expansion of species richness after the Cretaceous/Paleogene (K/Pg) boundary deserves further examination in light of potential taxonomic biases, but is consistent with the hypothesis that global environmental disturbances such as mass extinction events can rapidly adjust limits to diversity by restructuring ecosystems, and suggests that the gradualistic evolutionary diversification of tetrapods was punctuated by brief but dramatic episodes of radiation.27 page(s

Geostatistical analysis of an experimental stratigraphy

[1] A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary basin dimensions where a natural log hydraulic conductivity (ln( K)) was assigned to each pixel on the basis of gray scale and conductivity end-members. The synthetic ln( K) map has mean, variance, and frequency distributions that are comparable to a natural alluvial fan deposit. A geostatistical analysis was conducted on selected regions of this map containing fluvial, fluvial/ floodplain, shoreline, turbidite, and deepwater sedimentary facies. Experimental ln(K) variograms were computed along the major and minor statistical axes and horizontal and vertical coordinate axes. Exponential and power law variogram models were fit to obtain an integral scale and Hausdorff measure, respectively. We conclude that the shape of the experimental variogram depends on the problem size in relation to the size of the local-scale heterogeneity. At a given problem scale, multilevel correlation structure is a result of constructing variogram with data pairs of mixed facies types. In multiscale sedimentary systems, stationary correlation structure may occur at separate scales, each corresponding to a particular hierarchy; the integral scale fitted thus becomes dependent on the problem size. The Hausdorff measure obtained has a range comparable to natural geological deposits. It increases from nonstratified to stratified deposits with an approximate cutoff of 0.15. It also increases as the number of facies incorporated in a problem increases. This implies that fractal characteristic of sedimentary rocks is both depositional process - dependent and problem-scale-dependent

Flood magnitude-frequency and lithologic control on bedrock river incision in post-orogenic terrain

Mixed bedrock-alluvial rivers - bedrock channels lined with a discontinuous alluvial cover - are key agents in the shaping of mountain belt topography by bedrock fluvial incision. Whereas much research focuses upon the erosional dynamics of such rivers in the context of rapidly uplifting orogenic landscapes, the present study investigates river incision processes in a post-orogenic (cratonic) landscape undergoing extremely low rates of incision (> 5 m/Ma). River incision processes are examined as a function of substrate lithology and the magnitude and frequency of formative flows along Sandy Creek gorge, a mixed bedrock-alluvial stream in arid SE-central Australia. Incision is focused along a bedrock channel with a partial alluvial cover arranged into riffle-pool macrobedforms that reflect interactions between rock structure and large-flood hydraulics. Variations in channel width and gradient determine longitudinal trends in mean shear stress (τb) and therefore also patterns of sediment transport and deposition. A steep and narrow, non-propagating knickzone (with 5% alluvial cover) coincides with a resistant quartzite unit that subdivides the gorge into three reaches according to different rock erodibility and channel morphology. The three reaches also separate distinct erosional styles: bedrock plucking (i.e. detachment-limited erosion) prevails along the knickzone, whereas along the upper and lower gorge rock incision is dependent upon large formative floods exceeding critical erosion thresholds (τc) for coarse boulder deposits that line 70% of the channel thalweg (i.e. transport-limited erosion). The mobility of coarse bed materials (up to 2 m diameter) during late Holocene palaeofloods of known magnitude and age is evaluated using step-backwater flow modelling in conjunction with two selective entrainment equations. A new approach for quantifying the formative flood magnitude in mixed bedrock-alluvial rivers is described here based on the mobility of a key coarse fraction of the bed materials; in this case the d84 size fraction. A 350 m3/s formative flood fully mobilises the coarse alluvial cover with τb200-300 N/m2 across the upper and lower gorge riffles, peaking over 500 N/m2 in the knickzone. Such floods have an annual exceedance probability much less than 10- 2 and possibly as low as 10- 3. The role of coarse alluvial cover in the gorge is discussed at two scales: (1) modulation of bedrock exposure at the reach-scale, coupled with adjustment to channel width and gradient, accommodates uniform incision across rocks of different erodibility in steady-state fashion; and (2) at the sub-reach scale where coarse boulder deposits (corresponding to <i>τ</i><sub>b</sub> minima) cap topographic convexities in the rock floor, thereby restricting bedrock incision to rare large floods. While recent studies postulate that decreasing uplift rates during post-orogenic topographic decay might drive a shift to transport-limited conditions in river networks, observations here and elsewhere in post-orogenic settings suggest, to the contrary, that extremely low erosion rates are maintained with substantial bedrock channel exposure. Although bed material mobility is known to be rate-limiting for bedrock river incision under low sediment flux conditions, exactly how a partial alluvial cover might be spatially distributed to either optimise or impede the rate of bedrock incision is open to speculation. Observations here suggest that the small volume of very stable bed materials lining Sandy Creek gorge is distributed so as to minimise the rate of bedrock fluvial incision over time