Eigenrays in 3D heterogeneous anisotropic media,Part I: Kinematics

We present a new ray bending approach, referred to as the Eigenray method, for solving two‐point boundary‐value kinematic and dynamic ray tracing problems in 3D smooth heterogeneous general anisotropic elastic media. The proposed Eigenray method is aimed to provide reliable stationary ray path solutions and their dynamic characteristics, in cases where conventional initial‐value ray shooting methods, followed by numerical convergence techniques, become challenging. The kinematic ray bending solution corresponds to the vanishing first traveltime variation, leading to a stationary path between two fixed endpoints (Fermat's principle), and is governed by the nonlinear second‐order Euler–Lagrange equation. The solution is based on a finite‐element approach, applying the weak formulation that reduces the Euler–Lagrange second‐order ordinary differential equation to the first‐order weighted‐residual nonlinear algebraic equation set. For the kinematic finite‐element problem, the degrees of freedom are discretized nodal locations and directions along the ray trajectory, where the values between the nodes are accurately and naturally defined with the Hermite polynomial interpolation. The target function to be minimized includes two essential penalty (constraint) terms, related to the distribution of the nodes along the path and to the normalization of the ray direction. We distinguish between two target functions triggered by the two possible types of stationary rays: a minimum traveltime and a saddle‐point solution (due to caustics). The minimization process involves the computation of the global (all‐node) traveltime gradient vector and the traveltime Hessian matrix. The traveltime Hessian is used for the minimization process, analysing the type of the stationary ray, and for computing the geometric spreading of the entire resolved stationary ray path. The latter, however, is not a replacement for the dynamic ray tracing solution, since it does not deliver the geometric spreading for intermediate points along the ray, nor the analysis of caustics. Finally, we demonstrate the efficiency and accuracy of the proposed method along three canonical examples.     

Intraseasonal non-stationarity of the leading modes of atmospheric moisture over Europe during summer

A gridded monthly precipitable water (PW) data for 1979?C2007 from the NCEP/NCAR reanalysis are used to investigate summertime interannual PW variability over Europe and its relation to the key climate parameters in the region. During summer season the first EOF mode of PW, explaining 27?C41% of its total variance, demonstrates significant month-to-month changes in its structure, thus, implying its essential non-stationarity. The second EOF mode of PW is also non-stationary during the summer season. In contrast to precipitation, both leading modes of PW are not associated with the North Atlantic Oscillation (NAO), as well as with other regional teleconnections, suggesting relatively minor role of the atmospheric dynamics in atmospheric moisture variability over Europe during summer season. Analysis of links between leading EOF modes of regional PW and air temperature (AT) has revealed a strong link between PW and AT over Europe, persisting during entire summer season. Locally, these links imply that positive (negative) AT anomalies result in enhanced (decreased) PW over particular region. Revealed links between leading modes of PW and AT highlight important role of thermodynamics in summertime PW variability over Europe. Detected relatively weak and unstable links between leading modes of PW and precipitation over Europe were somewhat expected since in contrast to atmospheric moisture, regional precipitation variability is largely driven by the atmospheric dynamics (particularly, the NAO).     

Variations in tree ring stable isotope records from northern Finland and their possible connection to solar activity

Within a project on climate in Europe during the past few hundred years we have collected a record on stable isotope ratios ¹³C/¹²C and ¹⁸O/¹⁶O in tree ring cellulose from pine trees in northern Finland. The records cover the time interval 1600–2002 AD and have an annual time resolution. The carbon stable isotope record from northernmost Finland correlates quite strongly with local growth period temperature. Statistical analysis of the carbon and oxygen stable isotope records reveals variations in the periods around 100, 11 and 3 years. A century scale connection between the ¹³C/¹²C record and solar activity is most evident. These results based on stable isotope records support previous evidences of a centennial solar-climatic link obtained for northern Finland using tree ring data.     

Integrated geological risk mapping: a qualitative methodology applied in St. Petersburg, Russia

The current active development of the city of St. Petersburg in Russia has led to high growth rates in both industrial and housing areas, causing an increased load on geological media. Taking into account the rather unfavourable geological conditions of the city area, such a development can entail to an intensification of environmental risks. Sustainable and cost-effective land-use planning requires information on geological conditions. Stakeholders need general geological information on the area of St. Petersburg, hydrogeological information on groundwater and information on geological risks. Geological risk maps help to identify whether an area under consideration requires special measures for geological risk management. This paper describes a first attempt to analyze potential geological risks in the city of St. Petersburg, Russia. The approach is to introduce a methodology for multi-risk assessment to be used in land-use planning. The core of the methodology is a matrix that assigns a certain level of geological risk depending on the combination of land use stipulated by the master plan of St. Petersburg and geological characteristics. Based on the matrix, a map presenting potential integrated geological risk can be created. At the same time, the combination of the integrated geological risk map, single geological risk maps and the matrix allows the retracement of which geological characteristics and which land use types contribute to the resulting risk. Users of the methodology in St. Petersburg were trained and an end-user manual was prepared by the authors. The methodology was introduced to professionals who utilize geological information and assess potential risks related to geology.     

Determination of grid size for digital terrain modelling in landscape investigations—exemplified by soil moisture distribution at a micro-scale

The central problem of a combined analysis of digital terrain models (DTMs) and other landscape data is determination of a DTM grid size (w) providing a correct study of relationships between topographic variables and landscape properties. Generally, an adequate w is determined by an expert estimate, and solutions are largely subjective. We developed an experimental statistical method to determine an adequate w for DTMs applied to landscape studies. The method includes the following steps: (a) derivation of a DTM set using a series of w_i , (b) performance of a correlation analysis of data on a landscape property and a topographic variable estimated with various w_i , (c) plotting of correlation coefficients obtained versus w, and (d) determination of smoothed plot portions indicating intervals of an adequate w. We applied the method developed to study the ifluence of topography on the spatial distribution of soil moisture (M) at a micro-scale. We investigated the dependence of M on gradient (G), horizontal (k_h ), vertical (k_v ), and mean (H) landsurface curvatures. For DTM derivation, we used 13 values of w_i from 1 to 7m. An interval of adequate w_i for M falls between 2.25 and 3.25m in the given terrain conditions. In absolute magnitudes, correlation coefficients are largest within this interval; correlation coefficients of M with G, k_h , k_v and H are 0.28, 0.52, 0.50 and 0.60, respectively, for w = 3m. The results obtained demonstrate that the method actually works to identify an adequate w at a micro-scale. The method developed allows estimation of an adequate area of landform which realise a topographic control of landscape properties.     

Multi-hydro hydrological modelling of a complex peri-urban catchment with storage basins comparing C-band and X-band radar rainfall data

ABSTRACT

The spread of impervious surfaces in urban areas combined with the rise in the intensity of rainfall events as a result of climate change has led to dangerous increases in storm water flows. This paper discusses a new implementation of the fully distributed hydrological model Multi-Hydro (developed at École des Ponts ParisTech), when operating storage basins, and its ability to deal with high-resolution radar rainfall data. The peri-urban area of Massy (south of Paris, France) was selected as a case study for having six of these drainage facilities, used extensively in flood control. Two radar rainfall datasets with different spatiotemporal resolutions were used: Météo-France’s PANTHER rainfall product (C-band) and ENPC’s X-band DPSRI. The rainfall spatiotemporal variability was analysed statistically using Universal Multifractals (UM). Finally, to validate the application, the water level simulations were compared with local measurements in the Cora storage basin located next to the catchment’s single outlet.     

Short‐period static correction without Normal Move Out†

Static correction is a common step in a seismic data proccessing flowchart for land data. Here we propose a new algorithm for automatic short‐period static correction. The algorithm is based on the assumption that seismic events after short‐period static correction should be locally plane nearly everywhere. No other assumptions are made. Therefore the proposed method does not require a preliminary velocity analysis. The algorithm consists in two main parts: evaluation of second spatial differences of trajectories and subsequent regularized integration of these differences. The proposed method proves its robustness and shows results comparable with conventional residual static correction based on improving common‐midpoint stacking. In contrast to the conventional residual static, the proposed algorithm can estimate short‐period statics in complex cases where common‐midpoint stacking fails because of non‐hyperbolic events.     

Recent progress in the study of accessory minerals

Mineralogy and Petrology -     

Analysis of the impact of injection mode in transport through strongly heterogeneous aquifers

Large-scale advective transport through highly heterogeneous 3D formations is investigated using highly resolved numerical simulations and simple analytic models. Investigations are focused on impacts of two types of contaminant injection on transport through isotropic formations where flow conditions are uniform in the average. Transport is quantified by analyzing breakthrough curves for control planes at various distances from the injection zone. In flux-proportional injection mode local mass in injection zone is proportional to local groundwater flux; this setup models many practical cases such as contaminant injection through wells. In resident concentration mode local concentration in injection zone is constant. Results show that impacts of injection mode on breakthrough curves and their moments are strong and they persist for hundreds of correlation scales. The resident concentration mode leads to a fatter tails of the breakthrough curves, while the peaks are generally underpredicted. For a synthetic porous medium with logconductivity variance of 8, dispersivity computed using resident concentration mode at control plane 100 integral scales away from the injection zone was about 10 times larger than corresponding one for flux-proportional mode. Hence, injection mode impacts on transport through highly heterogeneous formations are strong and they persist for large distances from the injection zone.