Grid Refinement in Cartesian Coordinates for Groundwater Flow Models Using the Divergence Theorem and Taylor's Series

Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non‐reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes.     

The Impact of Geology of Recharge Areas on Groundwater Quality: A Case Study of Zhob River Basin,Pakistan

Groundwater is a major source of water supply for domestic and irrigation uses in semiarid, remote but rapidly developing Kilasaifullah district part of Zhob River Basin, located at Pakistan–Afghanistan Border. Zhob River is among few major rivers of perennial nature in Balochistan, which flows from WSW to ENE and falls in Gomal River, a tributary of Indus River. Keeping in view the important geopolitical position and rapid development of the region, this study is primarily focused on groundwater chemistry for contamination sources as well as agriculture development. Water samples from open and tube wells are analyzed and calculated for electrical conductivity (EC), total dissolved solids (TDS), turbidity, pH, K⁺, Na⁺, Ca²⁺, Mg²⁺, HCO, Cl^?, NO, SO, PO, sodium percent (Na%), sodium adsorption ratio (SAR), Kelly's index (KI), and heavy metals (Fe, Cu, Cr, Zn, Pb, and Mn). On the basis of the chemical constituents two zones within the study area are identified and possible causes of the contaminants are pointed out. Two recharge areas were responsible for the different chemical results in groundwater, e.g., zone A was recharged from NNW saline geological formations (Nisai, Khojak, Multana, Bostan formations, and Muslim Bagh ophiolites), which are concentrated with high sodium and chloride. On the other hand Zone B was sourced from SSW from carbonate rich rocks (Alozai, Loralai, Parh formations, and Muslim Bagh ophiolites). The groundwater is classified as C2–S1, C3–S1, C3–S2, C4–S2 on the basis of EC and SAR values which indicate that most of the water of both zones can be used for irrigation safely except the samples plotted in C3–S2 and C4–S2 categories which could be dangerous for soil and crops. Groundwater samples are plotted in good to permissible limits with some samples excellent to good and few samples belong to doubtful category based on sodium percent. Groundwater of zone A is unsuitable for irrigation use due to higher values of KI (more than one) but water of zone B are good for irrigation based on KI. In general, water of both zones is suitable for irrigation but care should be taken during the selection of crops which are sensitive to alkalinity or sodium hazards particularly in zone A.     

Earthquake Stability Analysis of Rock Slopes: a Case Study

Stability analysis of Surabhi landslide in the Dehradun and Tehri districts of Uttaranchal located in Mussoorie, India, has been simulated numerically using the distinct element method focusing on the weak zones (fracture). This is an active landslide on the main road toward the town centre, which was triggered after rainfall in July–August 1998. Understanding the behaviour of this landslide will be helpful for planning and implementing mitigation measures. The first stage of the study includes the total area of the landslide. The area identified as the zone of detachment is considered the most vulnerable part of the landslide. Ingress of water and increased pore pressures result in reduced mobilized effective frictional resistance, causing the top layer of the zone of detachment to start moving. The corresponding total volume of rock mass that is potentially unstable is estimated to 11.58 million m³. The second stage of this study includes a 2D model focussing only on the zone of detachment. The result of the analyses including both static and dynamic loading indicates that most of the total displacement observed in the slide model is due to the zone of detachment. The discontinuum modelling in the present study gives reasonable agreement with actual observations and has improved understanding of the stability of the slide slope.     

Geochemistry and zircon U-Pb geochronology of Aligoodarz granitoid complex, Sanandaj-Sirjan Zone, Iran

The Aligoodarz granitoid complex (AGC) is located in the Sanandaj-Sirjan Zone (SSZ), western Iran and consists of quartz-diorites, granodiorites and subordinate granites. Whole rock major and trace element data mostly define linear trends on Harker diagrams suggesting a cogenetic origin of the different rock types. (⁸⁷Sr/⁸⁶Sr)_i and εNd_t ratios are in the ranges 0.7074-0.7110 and −3.56 to −5.50, respectively. The trace elements and Sr-Nd isotopic composition suggest that the granitoids from the AGC are similar to crustal derived I-type granitoids of continental arcs. The whole rock suite was produced by assimilation and fractional crystallization starting from a melt with intermediate composition likely possessing a mantle component. In situ zircon U-Pb data on the granites with LA-ICP-MS yield a crystallization age of ∼165 Ma. Inherited grains spanning in age from ∼180 Ma up to 2027 Ma were also found and confirm that assimilation of country rock has occurred.Chemical and chronological data on the AGC were compared with those available for other granitoid complexes of the central SSZ (e.g., Dehno, Boroujerd and Alvand). The comparison reveals that in spite of the different origins that have been proposed, all these granitoid complexes are likely genetically related. They share many chemical features and are derived from crustal melts with minor differences. Alvand granites have the most peculiar compositions most likely related to the presence of abundant pelitic component. All these intrusions are coeval and reveal the presence of an extensive magmatic activity in the central sector of the SSZ during middle Jurassic.     

Estimation of viscoelastic attenuation of real seismic data by use of ray tracing software: Application to the detection of gas hydrates and free gas

Analysis of P wave velocity profiles and seismic data recorded over the 2002 Hydratech cruise conducted in the Storegga region, North of Norway, has shown the existence of anomalies (a velocity decrease) in some layers of the medium. An elastic propagation model is not sufficient to explain clearly these anomalies, since the viscoelastic attenuation, represented by the quality factor Q_P, is sensitive to physical phenomena of geological media. The combination of the quality factor profile with the velocity profile leads to realistic explanations of these anomalies. In this article, we explain the procedure which we developed for determining the Q_P profile from the P wave velocity profile and the seismic data recorded during Hydratech cruise. Both the Q_P and velocity profiles indicate anomalies in the same layers. Based on previous studies, we interpret that these anomalies are being due to existence of gas hydrates and free gas within these layers.     

On the rise of strongly tilted mantle plume tails

The rise of an initially horizontal, buoyant cylinder of fluid through a denser fluid at low Reynolds number is used to look at the ascent of strongly tilted mantle plumes through the mantle. Such ascents are characterized by (1) the growth of instabilities and (2) the development of a thermal wake downstream. Three-dimensional numerical experiments were carried out to examine these features. An hybrid particle-in-cell finite element method was used to look at the rise of non-diffusing cylinders and, a standard finite element method was used to look at the diffusing case. First the experiments show that the timescale of the fastest growing instability vary with the Rayleigh number and the viscosity ratio. In particular the growth rate decreases as the Rayleigh number decreases, in agreement with our analysis of the laboratory experiments of Kerr et al. (2008). Second the experiments show that the length of the thermal wake increases with the Rayleigh number but the change in viscosity has almost no influence on the wake length. Applied to strongly tilted mantle plumes we conclude that such plumes cannot be unstable given the plume timescales. We also discuss the application of this conclusion to weakly tilted plumes. Besides, this study allows to predict that mantle plumes are unlikely to have developed a significant thermal wake by the time they reach the surface. Finally, the resolution that is required to allow for the growth of mantle plume tails by combined diffusion and thermal entrainment is shown to represent a challenge for the large scale mantle convection simulations.     

Empirical modeling of plate load test moduli of soil via gene expression programming

New empirical models were developed to predict the soil deformation moduli using gene expression programming (GEP). The principal soil deformation parameters formulated were secant (E_s) and reloading (E_r) moduli. The proposed models relate E_s and E_r obtained from plate load-settlement curves to the basic soil physical properties. The best GEP models were selected after developing and controlling several models with different combinations of the influencing parameters. The experimental database used for developing the models was established upon a series of plate load tests conducted on different soil types at depths of 1–24 m. To verify the applicability of the derived models, they were employed to estimate the soil moduli of a part of test results that were not included in the analysis. The external validation of the models was further verified using several statistical criteria recommended by researchers. A sensitivity analysis was carried out to determine the contributions of the parameters affecting E_s and E_r. The proposed models give precise estimates of the soil deformation moduli. The E_s prediction model provides considerably better results in comparison with the model developed for E_r. The simplified formulation for E_s significantly outperforms the empirical equations found in the literature. The derived models can reliably be employed for pre-design purposes.     

A hybrid computational approach to formulate soil deformation moduli obtained from PLT

In this study, new empirical equations were developed to predict the soil deformation moduli utilizing a hybrid method coupling genetic programming and simulated annealing, called GP/SA. The proposed models relate secant (E_s), unloading (E_u) and reloading (E_r) moduli obtained from plate load–settlement curves to the basic soil physical properties. Several models with different combinations of the influencing parameters were developed and checked to select the best GP/SA models. The database used for developing the models was established upon a series of plate load tests (PLT) conducted on different soil types at various depths. The validity of the models was tested using parts of the test results that were not included in the analysis. The validation of the models was further verified using several statistical criteria. A traditional GP analysis was performed to benchmark the GP/SA models. The contributions of the parameters affecting E_s, E_u and E_r were analyzed through a sensitivity analysis. The proposed models are able to estimate the soil deformation moduli with an acceptable degree of accuracy. The E_s prediction model has a remarkably better performance than the models developed for predicting E_u and E_r. The simplified formulations for E_s, E_u and E_r provide significantly better results than the GP-based models and empirical models found in the literature.     

Magnetic and DC resistivity investigation for groundwater in a complex subsurface terrain

Subsurface structures associated with hard rocks are very important for groundwater. Wadi Fatima runs through the volcanic and metamorphic rocks of the Arabian Shield which are characterized by higher magnetization than the overlaying alluvium sediments. Magnetic and direct current (DC) resistivity methods have been used for groundwater exploration in the northern part of Wadi Fatima. The magnetic survey was used mainly to map the subsurface structures, using analytic signal algorithm, of the study area. The DC resistivity method was applied to describe the lithologic domain as a function of depth, depending on their electrical property contrasts where it provided a good indication for water bearing formations. The magnetic and DC resistivity interpretations were confirmed by drilling which have provided a clear idea about the hydrogeological regime of the study area. The selected drilled well is successfully productive and it produces 30 m³/h.     

Application of spectrum–area fractal model to identify of geochemical anomalies based on soil data in Kahang porphyry-type Cu deposit,Iran

The aim of this study is to identify geochemical anomalies using power spectrum–area (S–A) method based on the grade values of Cu, Mo and Au in 2709 soil samples collected from Kahang porphyry-type Cu deposit, Central Iran. S–A log–log plots indicated that there are three stages of Cu, Mo and Au enrichment. The third enrichment was considered as the main stage for the presence of Cu, Mo and Au at the concentrations above 416 ppm, 23 ppm and 71 ppb, respectively. Elemental anomalies are positively associated with monzo–granite–diorite and breccias units which are in the central and western parts of the deposit. The anomalies are located within the potassic, phyllic and argillic alteration types and also there is the positive correlation between the anomalies and nearing faults in the studied area. The results obtained via fractal model were interpreted accordingly to incorporate the information for the mineralized areas including detailed geological map, structural analysis and alterations. The results show that S–A multifractal modeling is applicable for anomalies delineation based on soil data.