High-order Statistics of Spatial Random Fields: Exploring Spatial Cumulants for Modeling Complex Non-Gaussian and Non-linear Phenomena

The spatial distributions of earth science and engineering phenomena under study are currently predicted from finite measurements and second-order geostatistical models. The latter models can be limiting, as geological systems are highly complex, non-Gaussian, and exhibit non-linear patterns of spatial connectivity. Non-linear and non-Gaussian high-order geostatistics based on spatial connectivity measures, namely spatial cumulants, are proposed as a new alternative modeling framework for spatial data. This framework has two parts. The first part is the definition, properties, and inference of spatial cumulants—including understanding the interrelation of cumulant characteristics with the in-situ behavior of geological entities or processes, as examined in this paper. The second part is the research on a random field model for simulation based on its high-order spatial cumulants. Mathematical definitions of non-Gaussian spatial random functions and their high-order spatial statistics are presented herein, stressing the notion of spatial cumulants. The calculation of spatial cumulants with spatial templates follows, including anisotropic experimental cumulants. Several examples of two- and three-dimensional images, including a diamond bearing kimberlite pipe from the Ekati Mine in Canada, are analyzed to assess the relations between cumulants and the spatial behavior of geological processes. Spatial cumulants of orders three to five are shown to capture directional multiple-point periodicity, connectivity including connectivity of extreme values, and spatial architecture. In addition, they provide substantial information on geometric characteristics and anisotropy of geological patterns. It is further shown that effects of complex spatial patterns are seen even if only subsets of all cumulant templates are computed. Compared to second-order statistics, cumulant maps are found to include a wealth of additional information from underlying geological patterns. Further work seeks to integrate this information in the predictive capabilities of a random field model.     

Nonplanar ion-acoustic Gardner solitons in a pair-ion plasma with nonextensive electrons and positrons

The properties of nonplanar (cylindrical and spherical) ion-acoustic solitary waves (IA SWs) in an unmagnetized, collisionless electron-positron-ion (e-p-i) plasma, whose constituents are q-distributed electrons and positrons and inertial ions, are investigated by deriving the modified Gardner (MG) equation. The well known reductive perturbation method is employed to derive the MG equation. The basic features of nonplanar IA Gardner solitons (GSs) are discussed. It is found that the properties of nonplanar IA GSs (rarefactive and compressive) are significantly affected by the particle nonextensivity.     

Observations of sea ice interannual variations and spring bloom occurrences at the Japanese scallop farming area in the Okhotsk Sea using satellite imageries

The dynamics of ice formation and phytoplankton bloom development in the coastal region of the Okhotsk Sea, Hokkaido, where the Japanese scallop, Mizuhopecten yessoensis, are cultured were investigated using seven years (1998–2004) satellite data from the Special Sensor Microwave/Imager (SSM/I) and Sea-viewing Wide Field-of-view Sensor (SeaWiFS). The interannual variability of sea ice cover and timing of spring bloom occurrences were analyzed. Longer ice cover in 1999, 2001 and 2003 with the presence of ice until early April and shortened ice cover in 1998, 2000, 2002 and 2004 with the occurrence of ice until early March were recognized at this area. Variability in the timing of sea ice retreat and development of spring blooms at the scallop areas were observed. Progression of a single ice edge bloom showed higher Chl-a concentration compared to development of an initial ice edge bloom followed by a later open water bloom. Higher concentration of phytoplankton biomass was observed in the initial bloom when sea ice melting is delayed compared to when the sea ice leaves earlier. Wind events were also observed to affect the occurrences of spring bloom.     

Surface-rupturing history of the Bree fault scarp, Roer Valley graben: Evidence for six events since the late Pleistocene

Since 1996 paleoseismological investigations have been used to develop the surface- rupturing history of the Bree fault scarp, the morphologically best-defined segment of the southwestern border fault of the Roer Valley graben in northeastern Belgium. The first studies determined that the escarpment is associated with a surface fault, and they exposed evidence for three surface displacements since about 40 ka BP. The most recent eventprobably occurred between 1000 and 1350 yr cal BP. Geophysical and trenching studies at a new site near the southeastern end of the fault scarp reconfirmed the coincidence of the frontal escarpment with a shallow normal fault, which displaces the Middle Pleistocene `Main Terrace' of the Maas River, as well as overlying coversands of Saalian to late Weichselian age. Different amounts of displacement shown by the two youngest coversand units indicate two discrete faulting events, but primary evidence for the coseismic nature of these events is sparse. Radiocarbon and optically stimulated luminescence dating constrainthe age of these events to the Holocene and between 14.0 ± 2.3 ka BP and 15.8 ± 2.9 ka BP, respectively. In addition, four older surface-rupturing events are inferred from the presence of four wedge-shaped units of reworked Main Terrace deposits that are interbedded with coversand units in the hanging wall of the trench and in shallow boreholes. These wedges are interpreted as colluvial wedges, produced by accelerated slope processes in response torejuvenation of the fault scarp, most probably in a periglacial environment. Luminescence dating indicates that five out of a total of six identified faulting events are younger than 136.6 ± 17.6 ka. The antepenultimate event was the largest faulting event, associated with a total fault displacement in excess of 1 m. Thus, the newly investigated trench site represents the longest and most complete record of surface rupturing recovered so far along the Bree fault scarp. This study also demonstrates the viability of the paleoseismological approach to identify past large earthquakes in areas of present-day moderate to low seismic activity.     

Simulating daily, monthly and annual water balances in a land surface model using alternative root water uptake schemes

Hydrological simulations at multi-temporal time scales by a widely used land surface model (LSM) are investigated under contrasting vegetation and meteorological conditions. Our investigation focuses particularly on the effects of two different representations of root water uptake and root profile on simulated evapotranspiration (ET) and soil moisture by the Integrated BIosphere Simulator (IBIS). For this purpose, multi-year eddy covariance measurements, collected at four flux-tower sites across North America, were used to gauge IBIS simulations with: (a) its standard version (IBIS2.1), in which static root water uptake (RWU) and root profile schemes are incorporated; and (b) a modified version in which dynamic RWU and root profile schemes replaces the static schemes used in the standard version. Overall, our results suggest that the modified version of the model performs more realistically than the standard version, particularly when high atmospheric demand for evaporation is combined with high atmospheric vapour pressure deficit and low soil water availability. The overall correlation between simulated and measured monthly ET rates at the simulated sites reached 0.87 and 0.91 for the standard and the modified versions, respectively. Our results also show that the incorporation of the dynamic RWU in IBIS yields improved simulations of ET under very dry conditions, when soil moisture falls down to very low levels. This suggests that adequate representations of vegetation responses to drought are needed in LSMs as many state of the art climate models projections of future climate indicate more frequent and/or more intense drought events occurring in some regions of the globe. Our analysis also highlighted the urgent need for adequate methodologies to correct field measurements that exhibit energy imbalances in order to provide rigorous assessments of land surface model simulations of heat and mass exchanges between the land surface and the atmosphere.     

Characteristics of the 1912 co-seismic rupture along the North Anatolian Fault Zone (Turkey): implications for the expected Marmara earthquake

Evidence of right‐lateral offsets associated with the 1912 earthquake (M_w 7.4) along the North Anatolian Fault (Gaziköy–Saros segment) allow us to survey (using DGPS) the co‐seismic and cumulative slip distribution. The damage distribution and surface breaks related with the earthquake show an elongated zone of maximum intensity (X MSK) parallel to the fault rupture on land but this may extend offshore to the north‐east and south‐west. Detailed mapping of the fault using topographic maps and aerial photographs indicates the existence of pull‐apart basins and pressure ridges. At several localities, the average 1912 offset along strike is 3.5–4 m and cumulative slip is 2–6 times that of individual movement. The fault rupture geometry and slip distribution suggest the existence of three subsegments with a combined total length of 110–120 km, a fault length and maximum slip similar to those of the 1999 Izmit earthquake. The amount of slip at the north‐easternmost section and in the coastal region of the Sea of Marmara reaches an average 4 m, thereby implying the offshore extension of the 1912 rupture. The results suggest that the 1912 event generated up to 150 km of surface faulting, which would imply a M_w 7.2–7.4 earthquake and which, added with rupture lengths of the 1999 earthquakes, help to constrain the remaining seismic gap in the Sea of Marmara.     

Analysis, in a free surface steady flow, of the interstitial velocity field inside a sedimentary bed

The objective of our study is to exploit ultrasonic Doppler velocimetry (UDV) to analyze the velocity field within a steady flow on a porous sedimentary bottom. Velocities are measured for several sedimentary beds, as well within the fluid vein as within the sediment. Our results highlight an exponential distribution of the velocities inside the sediment and a discontinuity of the velocity at the interface water–sediment, between the velocity in the free flow and the velocity within the sediment. These results highlight the need to base the analysis of sedimentary transport on the reality of the physical processes at the interface water–sediment.     

Mediterranean Sea and anthropogenic influences on ambient vibration amplitudes in the low-frequency and high-frequency domains in the Algiers region

Ambient vibrations have been continuously recorded at Dar El Beida, about 20 km from Algiers (Algeria). This data set allows determining that, in the low-frequency domain (<1 Hz), ambient vibration sources are mainly linked to Mediterranean Sea effects, while in the high-frequency domain, they are closely related to anthropogenic activity. Climatic conditions have an influence on the ambient vibration spectral amplitudes in the low-frequency domain, which is not the case in the high-frequency domain. The limit between the low-frequency and high-frequency domain, based on natural versus anthropogenic activity, is not clear cut and lies between 1.25 and 1.50 Hz. Variations of H/V peak amplitudes in the low-frequency domain are clearly linked to the climatic conditions. In the high-frequency domain, H/V peaks are not related to climatic conditions and cannot be clearly related to anthropogenic source changes.