Dynamic analysis of a cylindrical casing–cement structure in a poroelastic stratum

The transient response of a cylindrical casing–cement structure in a poroelastic stratum under dynamic radial tractions is one of the significant issues during the analysis of downhole operations and the selection of safe material. Based on the Biot theory and general elastic mechanics, this paper gives a set of exact solutions for radial displacement, stresses for the casing–cement system and the pore pressure of the infinite surrounding poroelastic stratum in the Laplace transform space. Solutions are presented for three different types of transient radial loadings acting on the surface of casing, i.e., suddenly applied constant load, gradually applied step load and triangular pulse load. Time domain solutions are obtained using a reliable numerical method of inverse Laplace transforms. A detailed parametric study about the transient response is presented both at the casing–cement interface and the cement–stratum interface, and the distributions of the pore pressure and the effective stresses in the stratum are also examined. Copyright © 2017 John Wiley & Sons, Ltd.     

Book review of ENCYCLOPEDIA OF NONLINEAR SCIENCE,edited by Alwyn Scott,Routledge, Taylor and Francis Group, 2005, VII +1053 pp., 135, $225 hardback (ISBN 1-57958-385-7).

We present three-dimensional (3D) solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make analytical progress we neglect outflows and specify a particular form for the current density. The magnetohydrostatic equations can then be reduced to a single linear partial differential equation for a pseudo-potential U, from which the magnetic field can be calculated by differentiation. The equation for U can be solved by standard methods. The solutions can also be used to determine the plasma pressure, density and temperature as functions of all three spatial coordinates. Despite the obvious limitations of this approach, it can, for example, be used as a simple tool to create 3D models for the closed field line regions of rotating magnetospheres without rotational symmetry.     

Physics of fracturing and seismic energy release: A review

This review was prepared as an opening lecture for the International Symposium on Physics of Fracturing and Seismic Energy Release, held at the Castle of Liblice near Prague from October 28 to November 1, 1985, and organized by the Geophysical Institute of the Czechoslovak Academy of Sciences. The review attempts to classify and synthesize results of recent studies in fracture mechanics and earthquake source physics. The following topics are discussed: recent developments in fracture mechanics, earthquake source modeling, heterogeneous fault planes, foreshocks and aftershocks, faults and fractals, and moment tensor solutions. This rather broad range of topics prevents presentation of a complete list of all relevant works, though over one hundred and seventy references are cited.     

花岗岩中铀性状的实验研究—铀的可溶性及含铀溶液的酸性演化

实验主要针对内生条件下花岗岩中铀的可溶性进行的。恒压(500bar)变温(200—400℃,个别达480℃)以及恒温(300℃)变压(100—1500bar)状态下的实验结果表明,花岗岩中铀的最大溶解度多发生在温度低于250℃、压力(P_(H_2O))低于500bar(个别小于1000bar)的范围内。铀最易溶解在碳酸溶液中。伴随压力的降低,碳酸盐和富含碳酸的溶液溶解铀的能力显著增强。含铀溶液随着温度的降低,呈碱性—酸性—碱性演化。     

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.     

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