PML solution of longitudinal wave propagation in heterogeneous media

This paper describes the development of a model for unbounded heterogeneous domains with radiation damping produced by an unphysical wave absorbing layer. The Perfectly Matched Layer (PML) approach is used along with a displacement-based finite element. The heterogeneous model is validated using the closed-form solution of a benchmark problem: a free rod with two-part modulus subjected to a specified time history. Both elastically supported and unsupported semi-infinite rods with different degrees of inhomogeneity and loading are considered. Numerical results illustrate the effects of inhomogeneity on the response and are compared with those for equivalent homogeneous domains. The effects of characteristic features of the inhomogeneous problem, presence of local maxima and cut-off frequency are determined. A degenerate case of a homogeneous semi-infinite rod on elastic foundations is produced by tending the magnitude of the foundation stiffness to zero. The response of the latter is compared with that of a free rod. The importance of proper selection of the PML parameters to highly accurate and efficient results is demonstrated by example problems.     

Delineation of Rajmahal basaltic flows,inter-trappeans and associated coal layers using Audio-magneto-telluric method

The extensive volcanic activity of Rajmahal occurred during early Cretaceous (~117 Ma). Potentially perspective Gondawana sediments containing coal seam is partially covered by these basalts. Basalts as well as coal are already known to be of immense economic importance over Rajmahal traps. The present study mainly deals with delineation of basaltic lava flows and associated coal layers using the Audio-magneto-telluric (AMT) study in the south central region of Rajmahal traps near Suri, West Bengal, India. Initially, the field situations have been simulated using forward model with top alluvium cover followed by basaltic lava flows, a wedge shaped inter-trappean sedimentary formation with second basaltic lava flows and basement at the bottom. The model was constrained using available litholog. The model study reveals the presence of moderately resistive basalts, relatively conductive inter-trappeans and the basement, except the top alluvium layer and thin inter-trappeans. Subsequently, threeAMT sounding have been carried out over Cholaguria, Hatgacha and Pachami, Suri, West Bengal. The field AMT study reveals three basaltic lava flows with varying thickness from ~40m to ~350m and composite thickness of ~620m to ~640m, which match well with the published borehole litholog. The inter-trappeans have been identified at 500m to 620m, 310m to 400m and 500m to 640m depths over Cholaguria, Hatgacha and Pachami, respectively. It is interesting to mention that the identified inter-trappeans are inferred to be coal/shaly-coal which are matching very well with the published borehole lithologs.     

On Data Interpolation at Three Croatian Repeat Stations by Using the Spherical Elementary Currents Systems Method

A general mathematical tool for expanding vector systems on a sphere into basis functions, spherical elementary current system (SECS) method, was applied for separation of the geomagnetic field variations into external and internal parts, over a limited region of central and southeastern Europe. The registered variations at three Croatian repeat stations were compared to the variations estimated by the SECS method using the variations from the different sets of observatories. The results of the SECS method were also compared to a simple assumption that the variations at repeat station are equal to those at particular observatory. The relevance of this comparison was to get an insight about the possibility of using the SECS method for estimating the geomagnetic field variations over Croatia. The guidelines for the application of the SECS method for the purpose of reducing repeat station data were also given.     

Regional variations in electricity demand elasticities: The situation in the Central United States

Within the sizable literature on electricity demand relatively little attention is given to regional variations in electricity demand elasticities. This paper investigates 39 electric utility companies having a total of 93 separate operating regions in order to assess the nature of regional electricity demand elasticity variations. Residential, commercial, and industrial demand functions are estimated for each operating region using a flow adjustment model of demand. The resulting electricity price, measure of economic activity, and natural gas price elasticities vary regionally, but not in a systematic manner. The demand elasticities found in each sector range from highly inelastic to highly elastic with the pattern of elasticity variations exhibiting few spatial trends or relationships. Comparisons between operating region results and more aggregated statewide results indicate that statewide and national analysis of electricity demand masks much regional detail — a result which has important implications for energy policy making.     

Rapid report of the 8 January 2022 ​MS 6.9 Menyuan earthquake,Qinghai, China

The M_S 6.9 Menyuan earthquake in Qinghai Province, west China is the largest earthquake by far in 2022. The earthquake occurs in a tectonically active region, with a background b-value of 0.87 within 100 ?km of the epicenter that we derived from the unified catalog produced by China Earthquake Networks Center since late 2008. Field surveys have revealed surface ruptures extending 22 ?km along strike, with a maximum ground displacement of 2.1 ?m. We construct a finite fault model with constraints from InSAR observations, which showed multiple fault segments during the Menyuan earthquake. The major slip asperity is confined within 10 ?km at depth, with the maximum slip of 3.5 ?m. Near real-time back-projection results of coseismic radiation indicate a northwest propagating rupture that lasted for ～10 ?s. Intensity estimates from the back-projection results show up to a Mercalli scale of IX near the ruptured area, consistent with instrumental measurements and the observations from the field surveys. Aftershock locations (up to January 21, 2022) exhibit two segments, extending to ～20 ?km in depth. The largest one reaches M_S 5.3, locating near the eastern end of the aftershock zone. Although the location and the approximate magnitude of the mainshock had been indicated by previous studies based on paleoearthquake records and seismic gap, as well as estimated stressing rate on faults, significant surface-breaching rupture leads to severe damage of the high-speed railway system, which poses a challenge in accurately assessing earthquake hazards and risks, and thus demands further investigations of the rupture behaviors for crustal earthquakes.     

Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling

The perfectly matched layer (PML) absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme, thus resulting in an irregular-grid PML method. We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations. The irregular-grid PML method is implemented under a discretization of triangular grid cells, which has the ability to absorb incident waves in arbitrary directions. This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries. As a result, the computational domain can be constructed with smaller nodes, for instance, to represent the 2-D half-space by a semi-circle rather than a rectangle. By using a smooth artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media. The numerical simulations of a VTI lamb's problem, wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method.     

Carbon dioxide emission reduction quota allocation study on Chinese provinces based on two-stage Shapley information entropy model

Chinese central government made a commitment to achieve a 40–45% reduction in carbon dioxide (CO₂) per unit of GDP by 2020 compared with 2005. This targeted reduction was allocated averagely among all the provinces rather than individually according to different situations of each province. Though some research has been done regarding this rough allocation, two shortcomings in previous studies exist: Firstly, CO₂ marginal abatement cost (MAC) has been ignored as one of the CO₂ emission reduction allocation indexes. Secondly, either subjective or objective method has been used rather than comprehensively of both subjective and objective method to calculate the weight of each index in the previous studies. In order to fill the gaps, this paper builds a two-stage Shapley information entropy model to allocate CO₂ emission reduction quota among the Chinese provinces based on the equity and efficiency principles. Afterward, three CO₂ emission reduction quota allocation scenarios have been proposed. The results show that the CO₂ MAC is an indispensable index in CO₂ emission reduction quota allocation, because its value of CO₂ Shapley information entropy is the highest among five indexes. CO₂ emission reduction quota of lower-MAC provinces should be allocated larger, while the quota of higher-MAC provinces should be allocated smaller. Therefore, two suggested policies have been proposed: First, differential CO₂ emission reduction quota allocation should be proposed. Second, synergetic development should be promoted.     

Influence of food web structure on the biochemical composition of seston,zooplankton and recently deposited sediment in experimental freshwater mesocosms

The effects of food web structure on the quantity and biochemical composition of seston, zooplankton and recently deposited sediment in experimental freshwater mesocosms were examined. Food web structure was manipulated by addition of zooplanktivorous fish. Biochemical characterisations were carried out using lipid biomarkers (sterols, fatty acids, chlorophyll-derived compounds and long-chain alkanediols). Fish addition decreased zooplankton biomass and increased seston biomass and deposited sediment through a trophic cascade. Fish presence strongly influenced the biochemical characteristics of seston and sediment. In contrast, food web structure had a minor impact on the lipid biomarker composition of zooplankton. Although the relative abundance of sterols in the different compartments did not differ strongly between treatments, sterol profiles in seston and sediment depended on food web structure. The predominance of Δ⁷-sterols in seston and sediment in the fish treatment indicated a major contribution of Chlorophyceae. In contrast, the distribution of sterols in seston and sediment in the fishless treatment, dominated by cholesterol, indicated a major zooplanktonic input. The distribution of fatty acids and the relative abundance of chlorophyll-derived compounds and long-chain alkanediols agreed with the predominant contribution of phytoplankton or zooplankton to seston and sediment in the two treatments. The relative abundance of bacterial biomarkers suggested that the contribution of bacteria was rather low. The high relative abundance of polyunsaturated fatty acids (PUFAs) and the absence of stanols in sediments suggested low microbial reworking of organic matter in the recently accumulated sediments. The trophic cascade, generated by the addition of fish, increased the relative abundance of PUFAs in deposited organic matter, thus enhancing sediment quality and potential degradability.