Structural complexity in space–time seismic event data

Different approaches and tools have been adopted for the analysis and characterization of regional seismicity based on spatio–temporal series of event occurrences. Two main aspects of interest in this context concern scaling properties and dimensional interaction. This paper is focused on the statistical use of information-theoretic concepts and measures in the analysis of structural complexity of seismic distributional patterns. First, contextual significance is motivated, and preliminary elements related to informational entropy, complexity and multifractal analysis are introduced. Next, several technical and methodological extensions are proposed. Specifically, limiting behaviour of some complexity measures in connection with generalized dimensions is established, justifying a concept of multifractal complexity. Under scaling behaviour, a mutual-information-related dependence coefficient for assessing spatio–temporal interaction is defined in terms of generalized dimensions. Also, an alternative form of generalized dimensions based on Tsallis entropy convergence rates is formulated. Further, possible incorporation of effects, such as earthquake magnitude, is achieved in terms of weighted box-counting distributions. Different aspects in relation to the above elements are analyzed and illustrated using two well-known series of seismic event data of an underlying different nature, occurred in the areas of Agrón (Granada, Spain) and El Hierro (Canary Islands, Spain). Finally, various related directions for continuing research are indicated.     

Effect of galvanic distortions on the series and parallel magnetotelluric impedances and comparison with other responses

The series and parallel impedances of the magnetotelluric tensor are appraised in relation to their relative immunity to galvanic electric distortions. The distorted responses are modeled using the Groom-Bailey decomposition of the tensor in terms of twist, shear, statics and strike direction. These four parameters and the undistorted responses are normally considered as unknowns, and are obtained from field data through the solution of an inverse problem. In the present work we use the decomposition as a forward model to simulate distorted sounding curves. Starting with undistorted 2-d te and tm responses, the tensor is distorted by assuming arbitrary values of twist, shear, static and strike direction. By default, both series and parallel responses are immune to the strike direction because they are invariants under rotation. In addition, series responses are immune to twist and shear and parallel responses only to twist. The dependence of the latter on shear is in the form of a real factor that shifts downwards the amplitude curves. On the other hand, the effect of statics on both series and parallel responses is more complicated than that on the impedance tensor because it cannot be accounted for by a simple shift of the curves. On the whole, there is a positive balance on the part of the series and parallel impedances over the te and tm responses because some of the distortions are filtered out by the invariants. It is shown that invariance is not sufficient to be immune to any of the distortions. The example chosen is Eggers’ eigenvalues, which are immune only to the by-the-fault strike direction. Invariance is not necessary either, as evidenced by the phase tensor, whose elements depend on strike but are immune to all distortions. The derivations are illustrated using soundings from the synthetic coprod2s1 and field-recorded coprod2 and bc87 data sets.     

The Precambrian of the Anti-Atlas (Morocco): A geochronological synthesis

Twenty total rock Rb/Sr isochrons ($\text{λ}{}^{87}\text{Rb}\text{= 1.47 · 10}{}^{\mathrm{?11}}\text{yr}{}^{\mathrm{?1}}$) and many individual data, mainly obtained by the K/Ar and Rb/Sr methods, on total rocks and minerals show that the orogenic story of the Precambrian of the Anti-Atlas, which was studied in its western and central parts, began with the Eburnean orogeny (1900-1650 m.y.). Up to now there is no good evidence of an older basement, even if the rather high initial ratio (0.707–0.709) of some Eburnean granites might suggest that such a basement exists at depth. There is also no geochronological evidence of plutonism until in early Panafrican time (680 m.y.) there started a period of intense magmatic and thermal activity which was ended by the emplacement of late post-tectonic granites at 530-520 m.y.The late Panafrican acid volcanism does not generally give suitable material for Rb/Sr dating, because of the great mobility of the radiogenic strontium in such a material even under very weak thermal conditions.     

Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution

We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

Discovery of High Proper-Motion Ancient White Dwarfs: Nearby Massive Compact Halo Objects?

We present the discovery and spectroscopic identification of two very high proper-motion ancient white dwarf stars, found in a systematic proper-motion survey. Their kinematics and apparent magnitude clearly indicate that they are halo members, while their optical spectra are almost identical to the recently identified cool halo white dwarf WD 0346+246. Canonical stellar halo models predict a white dwarf volume density that is 2 orders of magnitude less than the rho approximately 7x10-4 M middle dot in circle pc-3 inferred from this survey. With the caveat that the sample size is very small, it appears that a significant fraction, approximately 10%, of the local dark matter halo is in the form of very old, cool, white dwarfs.     

Mega-monsoon variability during the late Triassic: Re-assessing the role of orbital forcing in the deposition of playa sediments in the Germanic Basin

The formation of the supercontinent Pangaea during the Permo–Triassic gave rise to an extreme monsoonal climate (often termed ‘mega-monsoon’) that has been documented by numerous palaeo-records. However, considerable debate exists about the role of orbital forcing in causing humid intervals in an otherwise arid climate. To shed new light on the forcing of monsoonal variability in subtropical Pangaea, this study focuses on sediment facies and colour variability of playa and alluvial fan deposits in an outcrop from the late Carnian (ca 225 Ma) in the southern Germanic Basin, south-western Germany. The sediments were deposited against a background of increasingly arid conditions following the humid Carnian Pluvial Event (ca 234 to 232 Ma). The ca 2·4 Myr long sedimentary succession studied shows a tripartite long-term evolution, starting with a distal mud-flat facies deposited under arid conditions. This phase was followed by a highly variable playa-lake environment that documents more humid conditions and finally a regression of the playa-lake due to a return of arid conditions. The red–green (a*) and lightness (L*) records show that this long-term variability was overprinted by alternating wet/dry cycles driven by orbital precession and ca 405 kyr eccentricity, without significant influence of obliquity. The absence of obliquity in this record indicates that high-latitude forcing played only a minor role in the southern Germanic Basin during the late Carnian. This is different from the subsequent Norian when high-latitude signals became more pronounced, potentially related to the northward drift of the Germanic Basin. The recurring pattern of pluvial events during the late Triassic demonstrates that orbital forcing, in particular eccentricity, stimulated the occurrence and intensity of wet phases. It also highlights the possibility that the Carnian Pluvial Event, although most likely triggered by enhanced volcanic activity, may also have been modified by an orbital stimulus.     

A 36Cl age determination for Mystery Creek rock avalanche and its implications in the context of hazard assessment, British Columbia, Canada

The Sea to Sky Corridor has experienced hundreds of historic and prehistoric landslides. The most common types of historical landslides are rock falls and debris flows, which are relatively small in volume but can be damaging. These types of failures are more common in the southern part of the corridor, between Horseshoe Bay and Porteau, where infrastructure has been built in close proximity to steep slopes. Farther north, fewer landslides have been reported historically, but those that have been recorded are usually large and date to prehistoric time (e.g., Cheekye fan and Mystery Creek rock avalanche). As part of a Geological Survey of Canada surficial geology and landslide inventory mapping study, Mystery Creek rock avalanche, near Whistler, British Columbia, was sampled for ³⁶Cl dating. Samples were collected from three large flat boulders of quartz diorite in the rock avalanche deposit to test a correlation with the previously reported radiocarbon age of 800 ± 100 years BP on charcoal. One sample revealed a mean age of 2,400 years and the other two, 4,300 and 4,800 years, respectively. These new results point to four possible interpretations: (1) Mystery Creek landslide is about 800 years old; (2) Based on the overlapping 2σ uncertainties, the rock avalanche took place between 2,200 and 3,600 years ago; (3) The rock avalanche deposit is 2,400 years old and the other two blocks are too old; and (4) The rock avalanche is between 4,300 and 4,800 years old. Although there is strength in numbers and it is likely that the age varies between 4,300 and 4,800 years, we favor the second interpretation where the age range is broader and statistically significant for all three samples. Moreover, at this time, we favor discounting the radiocarbon age based on a greater number of samples analyzed for ³⁶Cl analysis and lack of detailed information on the charcoal sampling. The causes and triggers of the Mystery Creek rock avalanche remain unknown, but direct glacial debuttressing can be ruled out. Some of the causes are likely a combination of the regional tectonic setting which produced preferential planes of weakness reflected in the trend of major faults, headscarp, and reverse scarps. Yearly cycles of freezing and thawing are considered a plausible cause based on present-day climate records. Finally, a large earthquake still remains a possible trigger because of the active tectonic setting and the presence of potentially contemporaneous landslides in the same area. Mystery Creek rock avalanche and other historic and pre-historic landslides contributed to validation of a heuristic rock fall/rock slide/rock avalanche susceptibility mapping study, in which their headscarps correlated well with medium-high to high susceptibility zones. In terms of hazard assessment, Mystery Creek rock avalanche, although pre-historic in age, occurred in present-day climatic and geological conditions. This poses a threat to infrastructure such as the Sea to Sky Highway, railway, and power line.     

Comparison of Different Techniques of Tilt Testing and Basic Friction Angle Variability Assessment

A relevant parameter for estimating discontinuity shear strength is the basic friction angle, usually derived from different types of tilt tests. However, the tilt tests described in the literature produce varying basic friction angle values. From a large number of different types of tilt tests on different kinds of rocks, it was possible to conclude that the mechanisms of sliding along cylinder generatrixes and planar surfaces are quite different, and that tests based on sliding along generatrixes are not appropriate for determining reliable basic friction angle values for discontinuity planes. Tests on small specimens are also not recommended, for geometry reasons and because ensuring reliable stress conditions is difficult. To quantify the natural variability in tilt testing, large specimens of the same granite were tested. The results revealed coefficients of variation for the basic friction angle in the range of 5–10?%, a variability which is no greater than that found for other rock mechanics parameters. This observation enables to forward some recommendations concerning the appropriate number of tests needed to obtain reliable results.     

Post‐Variscan exhumation of the Central Anti‐Atlas (Morocco) constrained by zircon and apatite fission‐track thermochronology

The origin of the Anti‐Atlas relief is one of the currently debated issues of Moroccan geology. To constrain the post‐Variscan evolution of the Central Anti‐Atlas, we collected nine samples from the Precambrian basement of the Bou Azzer‐El Graara inlier for zircon and apatite fission‐track thermochronology. Zircon ages cluster between 340 ± 20 and 306 ± 20 Ma, whereas apatite ages range from 171 ± 7 Ma to 133 ± 5 Ma. Zircon ages reflect the thermal effect of the Variscan orogeny (tectonic thickening of the ca. 7 km‐thick Paleozoic series), likely enhanced by fluid advection. Apatite ages record a complex Mesozoic–Cenozoic exhumation history. Track length modelling yields evidence that, (i) the Precambrian basement was still buried at ca. 5 km depth by Permian times, (ii) the Central Anti‐Atlas was subjected to (erosional) exhumation during the Triassic‐Early Cretaceous, then buried beneath ca. 1.5 km‐thick Cretaceous‐Paleogene deposits, (iii) final exhumation took place during the Neogene, contemporaneously with that of the High Atlas.