Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenisation theory

Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic (APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed, for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches are exhibited numerically.     

Analysis of radial movement of an unconfined leaky aquifer due to well pumping and injection

Radial movement of an unconfined leaky aquifer was studied with respect to hydraulic forces that are induced by well recharge and discharge. New analytic solutions in the velocity and displacement fields were found and applied to describe transient movement in an unconfined leaky aquifer. Linear momentum and mass balance of saturated porous sediments, the Darcy-Gersevanov law, and the analytic solution of hydraulic drawdown for unsteady flow within the unconfined leaky aquifer were introduced to find the new solutions. Analytic results indicate that the nonlinear relation between the initial hydraulic head (h₀) and the well function has an insignificant effect on the aquifer transient movement when the drawdown s<0.02h ₀. When the well function is simplified with different assumptions and pumping conditions, the new solutions correspondingly reduce to cases that are similar to the Hantush-Jacob, Muskat, and Theis transient movement of a confined leaky aquifer. It was found that large leakance is important in slowing radial movement and reducing aquifer deformation. Flow velocity in the aquifer is more responsive to leakance than to cumulative displacement within the aquifer. The zones and boundary with tensile stress can be located using the same approach applied to a confined aquifer for risk assessment of earth fissuring.

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Résumé Le mouvement radial dans un aquifère semi-perméable libre a été étudié en considérant les forces hydrauliques induites par la recharge et le prélèvement au niveau d’un puits. De nouvelles solutions analytiques des champs de vitesse et de déplacement ont été trouvées et appliquées pour décrire le mouvement transitoire dans un aquifère semi-perméable libre. Pour trouver les nouvelles solutions, le moment linéaire et le bilan de masse dans les sédiments poreux saturés, la loi de Darcy-Gersevanov, et la solution analytique du rabattement hydraulique pour un écoulement transitoire dans un aquifère semi-perméable libre sont pris en compte. Les résultats analytiques montrent que la relation non-linéaire entre le potentiel hydraulique initial (h₀) et la fonction de puits a un effet insignifiant sur le mouvement transitoire de l’aquifère quand le rabattements s <0.02h₀. Si la fonction de puits est simplifiée en tenant compte de différentes hypothèses et conditions de pompage, les nouvelles solutions se réduisent en conséquence à des cas similaires au mouvement transitoire dans un aquifère semi-perméable captif selon Hantush-Jacob, Muskat, et Theis. Il s’est avéré qu’une drainance élevée est importante pour le ralentissement du mouvement radial et la réduction de la déformation de l’aquifère. La vitesse d’écoulement dans l’aquifère est plus sensible à la drainance qu’au déplacement cumulé dans l’aquifère. Les zones et la frontière présentant des contraintes de traction peuvent être localisées en utilisant la même approche appliquée à un aquifère captif pour l’évaluation des risques de fissuration du sol.

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Resumen Se ha estudiado el movimiento radial en un acuífero no confinado con fuga en relación a las fuerzas hidráulicas que son inducidas por la descarga y recarga del pozo. Se encontraron nuevas soluciones analíticas en los campos de desplazamiento y velocidad, las cuales se aplicaron para describir el movimiento transitorio en un acuífero no confinado con fuga. Se han introducido cálculos de balance de masa y momentum lineal de los sedimentos porosos saturados, la Ley Darcy-Gersevanov, y la solución analítica de descenso hidráulico para flujo sin régimen permanente dentro del acuífero no confinado con goteo para encontrar las nuevas soluciones. Los resultados analíticos indican que la relación no lineal entre la presión hidráulica inicial (h₀) y la función del pozo tiene efecto insignificante en el movimiento transitorio del acuífero cuando el descenso s < 0.02h₀. Cuando se simplifica la función del pozo en base a diferentes supuestos y condiciones de bombeo se reducen las nuevas soluciones a casos que son similares a el movimiento transitorio Hantush-Jacob, Muskat, y Theis de un acuífero confinado con goteo. Se encontró que las fugas grandes son importantes en la disminución del movimiento radial y en la reducción de la deformación del acuífero. La velocidad de flujo en el acuífero responde más a las fugas que al desplazamiento acumulativo dentro del acuífero. Pueden localizarse zonas y límites con esfuerzos tensionales usando el mismo enfoque aplicado a acuíferos confinados para evaluación de riesgo de generación de fracturas en el terreno.

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Source Parameters of the Deadly M<Subscript>w</Subscript> 7.6 Kashmir Earthquake of 8 October, 2005

During the last six years, National Geophysical Research Institute, Hyderabad has established a semi-permanent seismological network of 5–8 broadband seismographs and 10–20 accelerographs in the Kachchh seismic zone, Gujarat with a prime objective to monitor the continued aftershock activity of the 2001 M_w 7.7 Bhuj mainshock. The reliable and accurate broadband data for the 8 October M_w 7.6 2005 Kashmir earthquake and its aftershocks from this network as well as Hyderabad Geoscope station enabled us to estimate the group velocity dispersion characteristics and one-dimensional regional shear velocity structure of the Peninsular India. Firstly, we measure Rayleigh-and Love-wave group velocity dispersion curves in the period range of 8 to 35 sec and invert these curves to estimate the crustal and upper mantle structure below the western part of Peninsular India. Our best model suggests a two-layered crust: The upper crust is 13.8 km thick with a shear velocity (Vs) of 3.2 km/s; the corresponding values for the lower crust are 24.9 km and 3.7 km/sec. The shear velocity for the upper mantle is found to be 4.65 km/sec. Based on this structure, we perform a moment tensor (MT) inversion of the bandpass (0.05–0.02 Hz) filtered seismograms of the Kashmir earthquake. The best fit is obtained for a source located at a depth of 30 km, with a seismic moment, Mo, of 1.6 × 10²⁷ dyne-cm, and a focal mechanism with strike 19.5°, dip 42°, and rake 167°. The long-period magnitude (M_A ~ M_w) of this earthquake is estimated to be 7.31. An analysis of well-developed sPn and sSn regional crustal phases from the bandpassed (0.02–0.25 Hz) seismograms of this earthquake at four stations in Kachchh suggests a focal depth of 30.8 km.     

A Least-squares Window Curves Method for Interpretation of Magnetic Anomalies Caused by Dipping Dikes

We have developed a least-squares method to determine simultaneously the depth and the width of a buried thick dipping dike from residualized magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the half-width of the source and a combination of windowed observations. The relationship represents a family of curves (window curves). For a fixed window length, the depth is determined for each half-width value by solving one nonlinear equation of the form f (z) = 0 using the least-squares method. The computed depths are plotted against the width values representing a continuous curve. The solution for the depth and the width of the buried dike is read at the common intersection of the window curves. The method involves using a dike model convolved with the same moving average filter as applied to the observed data. As a result, this method can be applied to residuals as well as to measured magnetic data. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to theoretical data with and without random errors. The validity of the method is tested on airborne magnetic data from Canada and on a vertical component magnetic anomaly from Turkey. In all cases examined, the model parameters obtained are in good agreement with the actual ones and with those given in the published literature.     

重磁遗传算法三维反演中动态数组优化方法

将地下场源划分成很多规划小单元，并且反演这些单元的物性变化是重磁反演，特别是三维反演的重要方向。在应用遗传算法进行该类反演过程中，隐含着数据量大时高维动态数据内存管理问题。为此，作者在本文中提出了简单、有效的动态内存优化方法。     

Anomalous Enrichment of Silver in Organic Matter of the Songxi Shale-hosted Ag-Sb Deposit in Northeastern Guangdong

The silver contents of organic matter in the host rocks of the Songxi shale-hosted Ag-Sb deposit of northeastern Guangdong, South China, have been directly determined using the electron microprobe technique. The silver contents in two types of organic matter, marine vitrinite and solid bitumen, vary in the range from 100×10-6to 350×10-6, which are from tens of times to thousands of times higher than those of the host rocks in the ore deposit. The average silver content of the organic matter is also several times higher than the pay grade of silver for commercial mining of the ore deposit. It is quite obvious that the organic matter of the host rocks in the ore district is characterized by an anomalous enrichment of silver. The results of this study indicate that the silver anomalies in the organic matter have been derived from both the host rocks and the silver-bearing fluids of the Songxi black shale ore source. In the course of sedimentation and later hydrothermal reworking, organic matter was able     

关于地球磁场极性反转机制的思索

地球磁场极性在地质历史中发生过相当频繁的倒转。作者将地球内部划分为岩石圈－软流圈－中圈－液圈－固核等5个动力学圈层，认为中圈与固核间可异步旋转；地球偶极磁场由中圈与固核异步旋转时所驱动的液圈中的封闭涡流与系磁场作用产生；该偶极子场极性由地球所通过的银道面上侧或下侧磁场方向及液圈涡流的方向共同决定，二者之一反向，极性发生倒转。     

New analytical and numerical approaches for geopotential modeling

 The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential coefficients _n,m . In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal harmonic series is developed for the geopotential and then its coefficients _n,m ^e are transformed to the unknown _n,m . The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From two sets of _n,m (n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068) by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to apply the LS technique for evaluating geopotential coefficients. Received: 12 December 2000 / Accepted: 21 June 2001     

粘弹性介质中的地震波

给出了三元件的标准线性粘弹性固体在半平面内传播的地震波的解析解，它是由已知的弹性半平面内的解析解迭粘滞性解而得，从而克服了视地壳为二元件粘弹性体的Voigt模型或Maxell模型的缺点。