Magnetic interpretation of two-dimensional dikes using integration-nomograms

The magnetic anomaly caused by a buried dike is separated into its even and odd components, which have a simple symmetry with respect to the origin. These values are integrated up to the half-maximum abscissa for the even component, and the maximum abscissa for the odd component. The integration nomograms are generated using various values to the half-width and depth in the theoretical anomaly equations. These nomograms are used to determine the half-width and depth to the top of the dike for the field anomaly. The method also includes the determination of the index parameter (Q) and the amplitude coefficient (P). An example using theoretical data shows the effectiveness of the present method.     

Mechanical models for correlation of ring-fracture eruptions at Pantelleria,Strait of Sicily,with glacial sea-level drawdown

Recent K-Ar dating of eruptions at Pantelleria, a peralkaline volcanic island in the Strait of Sicily, shows a correlation between eruption of pantellerite lavas from caldera ring fractures and low stands of sea level as determined from ¹⁸O stratigraphy. Post-caldera pantellerite lavas associated with an 114-ky-old caldera erupted along the ring-fracture zone during a major low stand of sea level at about 67 Ka. The most recent episode of lava-flow emplacement began about 20 ky ago during the last glacial maximum. Magma vented along the ring fault of a 45-ky-old caldera, from fractures radial to the caldera, and along faults formed by intracaldera trapdoor uplift. Two mechanical models based on elasticity theory are presented to explain the correlation of post-caldera ring-fracture eruptions at Pantelleria with lowering of sea level. A simple analysis of a bending circular plate of thickness,T _r, and radius,R, representing the magma-chamber roof block, shows that tensile stress is concentrated by a factor of 0.75R ²/T _r ² at the lower perimeter of the plate when sea level drops. Stress changes may be even greater ifT _r is effectively less than the stratigraphic thickness due to layering of rocks in the roof block. Calculated stress changes due to a 100-m drawdown of sea level are similar in magnitude to stresses associated with dike propagation. More realistic model geometries, including different chamber shapes, a conical volcanic edifice, and sea-level drawdown beyond the surface projection of the magma chamber, were tested using the boundary-element method. Lowering sea level generates a horizontal tensile stress above the chamber, even when sea water is removed outboard of the magma chamber. For some chamber geometries the magnitude of the tensile stress maximum is greater than the 1 MPa pressure of the 100 m of removed water and is of the right order of magnitude for dike propagation. Dikes initiated by the change of the stress field may originate and propagate along fractures inboard of the chamber margin. The magnitudes of tensile maxima along the top of the chamber decrease as original sea level is moved outboard of the chamber margin and as the chamber thickness decreases. When the depth to the top of the magma chamber reaches a critical value, dependent on chamber geometry, the propagation of dikes to the surface is inhibited.     

A METHOD OF WEATHERING CORRECTION *

In western Canada, the near surface weathered zone has variable velocity and is underlain by more uniform subweathering material. The uphole time is often used to compensate for the weathered zone, but there are limitations to its use. A method is proposed using the refraction delay time which is exactly proportional to the weathering correction time for several commonly assumed weathering velocity functions. The method does not require accurate determination of velocities or weathering depth nor even the depth of shot, yet is theoretically exact. A strip off time t_r is used to replace the weathered zone mathematically with high velocity material where t_r= zD/F, where D is the delay time and F the Blondeau factor. An algorithm using first break times is proposed that is amenable to computer use for determining D for each geophone point. F might be constant in some areas but is more likely a variable to be solved in an automatic static program. Thus, structure and residual statics can be handled at once.     

Radial expansion of the magnetohydrodynamic equations for axially symmetric configurations

Abstract

We introduce a general expansion approach to obtain a fully consistent closed set of magnetohydrodynamic equations in two independent variables, which is particularly useful to describe axially symmetric, time-dependent problems with weak variation of all quantities in the radial direction. This is done by considering the hierarchy of expanded magnetofluid equations in cylindrical coordinates and equating terms with equal powers in the radial coordinate r. From geometrical considerations it is shown that the radial expansions of the pertaining physical quantities are either even series or odd series in r; this introduces a significant reduction in the number of variables and equations. The closure of the system is provided by appropriate boundary conditions. Among other possible applications, the method is relevant for the analysis of structure and dynamics of magnetic field concentrations in stellar atmospheres.     

On the growth of disturbances to forced and dissipated barotropic flows

Abstract

We consider the growth of disturbances to large-scale zonally-asymmetric steady states in a truncated spectral model for forced and dissipated barotropic flow. A variant of the energy method is developed to optimize the instantaneous disturbance energy growth rate. The method involves solving a matrix eigenvalue problem amenable to standard numerical techniques. Two applications are discussed. (1) The global stability of a family of steady states is assessed in terms of the Ekman damping coefficient r. It is shown that monotonic global stability (i.e., every disturbances energy monotonically decays to zero) prevails when r≥r_c . (2) Initially fastest-growing disturbances are constructed in the r<r_c regime. Particular attention is paid to a subregion of the r<r_c regime where initially-growing disturbances exist despite stability with respect to normal modes. Nonlinear time-dependent simulations are performed in order to appraise the time evolution of various disturbances.     

On the free oscillations of a laterally heterogeneous earth model

Summary The equations of motion for the free oscillations of a heterogeneous spherical earth model are derived. It is found that the lateral variations of density and elastic moduli couple the odd(even) harmonics of the spheroidal oscillations with themselves as well as with the even (odd) harmonics of the torsional oscillations.List of symbols r, , Spherical coordinates;r is the radial distance from earth's center, is the co-latitude, and is the east longitude - r Space vector denoting a point with coordinatesr, , and - Gradient operator - ² Laplacian operator - _ij Kronecker's delta function - I Identity matrix - i      

Improved Vertical Streambed Flux Estimation Using Multiple Diurnal Temperature Methods in Series

Analytical solutions that use diurnal temperature signals to estimate vertical fluxes between groundwater and surface water based on either amplitude ratios (A_r) or phase shifts (Δ?) produce results that rarely agree. Analytical solutions that simultaneously utilize A_r and Δ? within a single solution have more recently been derived, decreasing uncertainty in flux estimates in some applications. Benefits of combined (A_rΔ?) methods also include that thermal diffusivity and sensor spacing can be calculated. However, poor identification of either A_r or Δ? from raw temperature signals can lead to erratic parameter estimates from A_rΔ? methods. An add‐on program for VFLUX 2 is presented to address this issue. Using thermal diffusivity selected from an A_rΔ? method during a reliable time period, fluxes are recalculated using an A_r method. This approach maximizes the benefits of the A_r and A_rΔ? methods. Additionally, sensor spacing calculations can be used to identify periods with unreliable flux estimates, or to assess streambed scour. Using synthetic and field examples, the use of these solutions in series was particularly useful for gaining conditions where fluxes exceeded 1 m/d.     

Generating ground motion by two new techniques of adding harmonic wave in the time domain and approximating to response spectrum as a whole

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A simple parameterization of bulk canopy resistance from climatic variables for estimating hourly evapotranspiration

This paper examines a model for estimating canopy resistance r_c and reference evapotranspiration ET_o on an hourly basis. The experimental data refer to grass at two sites in Spain with semiarid and windy conditions in a typical Mediterranean climate. Measured hourly ET_o values were obtained over grass during a 4 year period between 1997 and 2000 using a weighing lysimeter (Zaragoza, northeastern Spain) and an eddy covariance system (Córdoba, southern Spain). The present model is based on the Penman–Monteith (PM) approach, but incorporates a variable canopy resistance r_c as an empirical function of the square root of a climatic resistance r* that depends on climatic variables. Values for the variable r_c were also computed according to two other approaches: with the r_c variable as a straight‐line function of r* (Katerji and Perrier, 1983, Agronomie 3 (6): 513–521) and as a mechanistic function of weather variables as proposed by Todorovic (1999, Journal of Irrigation and Drainage Engineering, ASCE 125 (5): 235–245). In the proposed model, the results show that r_c/r_a (where r_a is the aerodynamic resistance) presents a dependence on the square root of r*/r_a, as the best approach with empirically derived global parameters. When estimating hourly ET_o values, we compared the performance of the PM equation using those estimated variable r_c values with the PM equation as proposed by the Food and Agriculture Organization, with a constant r_c = 70 s m^?1. The results confirmed the relative robustness of the PM method with constant r_c, but also revealed a tendency to underestimate the measured values when ET_o is high. Under the semiarid conditions of the two experimental sites, slightly better estimates of ET_o were obtained when an estimated variable r_c was used. Although the improvement was limited, the best estimates were provided by the Todorovic and the proposed methods. The proposed approach for r_c as a function of the square root of r* may be considered as an alternative for modelling r_c, since the results suggest that the global coefficients of this locally calibrated relationship might be generalized to other climatic regions. It may also be useful to incorporate the effects of variable canopy resistances into other climatic and hydrological models. Copyright © 2005 John Wiley & Sons, Ltd.     

Research on the time changes of transfer functions at Heze observatory before and after Heze earthquake of magnitude 5.9 A discussion with Qi Wang

In this paper, the coefficients of Parkinson vectora, b and the in-phase partA _r, B_r and quadrature-phase partA _i, B_i of transter functions are calculated by using two kinds of data processing methods, respectively. The results of both methods are close to each other. All these six parameters above are low in value, showing that the electric structure in Heze area is rather uniform. It seems that the anomalous changes appeared in both results, and the values of parameters decrease before and after Heze earthquake. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 113–120, 1991.     

Estimating magnetic dike parameters using a non‐linear constrained inversion technique: an example from the Särna area,west central Sweden

In this paper, we describe a non‐linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low‐pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non‐linear least squares inversion of the high resolution magnetic field data along the flight lines. We use the Levenberg‐Marquardt algorithm together with the trust‐region‐reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated g_zz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of g_zz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one. Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Särna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.     

Relationships between correlation lengths and integral scales for covariance models with more than two parameters

In geostatistical applications, the terms correlation length and range are often used interchangeably and refer to a characteristic covariance length ξ that normalizes the lag distance in the variogram or the covariance model. We present equations that strictly define the correlation length (r _c ) and integral range (ℓ _c ). We derive analytical expressions for r _c and ℓ _c of the Whittle–Matérn, fluctuation gradient curvature and rational quadratic covariances. For these covariances, we show that the correlation length and integral range for a given model are not fully determined by ξ. We define non-trivial covariance functions, and we formulate an ergodicity index based on ℓ _c . We propose using the ergodicity index to compare coarse-grained measures corresponding to non-trivial covariance functions with different parameters. Finally, we discuss potential applications of the proposed covariance models in stochastic subsurface hydrology.     

Multifractal measures of earthquakes in west Taiwan

The generalized fractal dimension for epicentral distribution of earthquakes in west Taiwan is measured. The entire area is first divided into two zones, i.e., north and south zones, after which the two zones are further separated into three subzones for the former and two for the latter. The logC _q (r) versus logr function, whereC _q (r) is the generalized correlation integral andr is the distance between two epicenters, shows that a linear relation between logC _q and logr exists in the range ofr smaller thanr _c . The value ofr _c is 25 km for the north zone, 40 km for the south and 12 km for the three north subzones. The valuesr _c =25 and 40 km are almost the smallest ones of the width of epicentral distributions of the north and south zones, respectively. The value ofr _c =12 km for the three north subzones is approximately the smallest size of the cluster of epicenters. For the plots of two south subzones, the pattern of data points does not bend in the range ofr in consideration, and, thus, there is not such a critical radius. TheD _q –q relations forq=0, 1, 2,..., 15 are constructed for the two zones and five subzones. Results show significant multifractality and a spatial variation in multifractality for epicentral distributions of earthquakes in west Taiwan.     

Evaluation of combination rules for peak response calculation in three‐component seismic analysis

The responses, r_e, given by several multicomponent combination rules used in seismic codes for determining peak responses to three ground motion components are evaluated for elastic systems and compared with the critical response r_cr; this is defined as the largest response for all possible incident angles of the seismic components and obtained by means of the CQC3‐rule when a principal seismic component is vertical, or the GCQC3‐rule when it departs from the vertical direction. The combination rules examined are the SRSS‐, 30%‐, 40%‐ and IBC‐rules, considering different alternatives for the design horizontal spectrum. Assuming that a principal seismic component is along the vertical direction, the upper and lower bounds of the ratio r_e/r_cr for each combination rule are determined as a function of the spectral intensity ratio of the horizontal seismic components and of the responses to one seismic component acting alternately along each structural axis. Underestimations and overestimations of the critical response are identified for each combination rule and each design spectrum. When a component departs from the vertical direction, the envelopes of the bounds of the ratio r_e/r_cr for each combination rule are calculated, considering all possible values of the spectral intensity ratios. It is shown that the inclination of a principal component with respect to the vertical axis can significantly reduce the values of r_e/r_cr with respect to the case when the component is vertical. Copyright © 2003 John Wiley & Sons, Ltd.     

The structure of the natural stratosphere and the impact of chlorofluoromethanes on the ozone layer investigated in a 2-D time dependent model

two-dimensional time dependent model of the stratosphere incorporating the major interactions between radiative-photochemical and dynamical processes is described. The main prognostic equations considered are the thermodynamic equation and the general conservation equation for the minor chemical constituents representing the odd oxygen (O _x =O+('D)+O₃), odd hydrogen (HO _x =HO+HO₂), N₂O, odd nitrogen (NO _x =NO+NO₂+HNO₃), CF₂Cl₂, CFCl₃ and odd chlorine (Cl _x =Cl+ClO+HCl). The zonal wind and mean meridional circulations are determined diagnostically by the integration of the thermal wind equation and the stream function equation in the meridional plane espectively. The large scale eddy processes are parameterized in terms of zonal mean quantities using the generalized diffusion formulation on a sloping surface. The radiative heating and cooling and the hotochemical sources and sinks are incorporated in a form which allows for the major interactions among the minor trace constituents, temperature and mean circulation.Two integrations consisting of natural stratosphere and a stratosphere contaminated by the chlorofluoromethanes through lower boundary fluxes are carried out for 23 model years by changing the declination of the sun every day and using 6-hour time step. The model simulations of temperature, mean circulation, ozone, HO _x , N₂O and NO _x in the meridional plane for the normal stratosphere, show satisfactory agreement with the available observations. Based on the results of second integration it is found that the injection of chlorofluoromethanes in the atmosphere at the estimated current production rates can lead to significant changes in the meridional distribution of ozone, temperature and NO _x in the middle and upper stratosphere. The results also indicate that the percentage total ozone depletion increases from tropics to high latitudes and from summer to winter high latitudes. Also discussed are the results of additional experiments incorporating the reaction of HO₂ with NO and the reactions involving ClNO₃.     

Evaluation of combination rules for maximum response calculation in multicomponent seismic analysis

The existing rules for combining peak response to individual components of ground motion are evaluated. The response values r_e to two horizontal components of ground motion estimated by four multicomponent combination rules—SRSS‐, 30%‐, 40%‐ and simplified‐SRSS‐rules—are compared with the critical response, r_cr, obtained by the CQC3‐rule, which takes into account the direction of the principal ground components with respect to the structural axes and provides the largest response over all possible seismic incident angles. The following results are obtained in the first part of the paper and are valid for any elastic structure and any earthquake design response spectrum: For realistic values of the ratio γ of the design spectra for the two principal components of ground motion the SRSS‐rule estimate lies between 0.79r_cr and 1.00r_cr, the Simplified‐SRSS‐rule estimate lies between 1.00r_cr and 1.26r_cr, the 40%‐rule estimate lies between 0.99r_cr and 1.25r_cr, and the 30%‐rule estimate lies between 0.92r_cr and 1.16r_cr. None of the multicomponent combination rules account for the increase in response of systems if the vibration periods of the two modes that contribute most to the response to the x‐ and y‐components of ground motion are close to each other. Evaluated in the second part of the paper is the accuracy of the multicomponent combination rules in estimating the response of a range of one‐storey systems with (a) symmetrical plan and (b) unsymmetrical plan, and of two multistorey buildings. The SRSS‐rule underestimates the response by up to 16% and the other three rules overestimate it by up to 18%. Although these errors appear to be smaller than the many approximations inherent in structural design, they can be eliminated with very little additional computation by using an explicit formula for the critical response based on the CQC3 rule. Copyright © 2001 John Wiley & Sons, Ltd.     

DIELECTRIC PROPERTIES OF WET SOILS IN THE FREQUENCY RANGE 1–3000 MHz1

The effective relative dielectric constant ?_{e, r} and the effective conductivity σ_e have each been determined as a function of frequency in the range 1–3000 MHz at volumetric water contents of up to approximately 0.74 for clays, 0.83 for a peat and 0.56 for a silt. At frequencies above about 25 MHz (depending on soil type), ?_{e, r}increases with water content for all samples. However, at lower frequencies, ?_{e, r}only increases with water content as long as the wet density also increases, which is the case for water contents up to a critical value lying between 0.35 and 0.48. At higher water contents, ?_{e, r}and the wet density decrease with increasing water content. Consequently, curves of ?_{e, r}versus frequency for two wet samples with different water contents, at least one of them higher than the critical value, are seen to cross at about 25 MHz. Below the critical value the curve of the sample with the lower water content is below the other curve at all freqencies applied. At a given frequency, σ_e has a maximum as a function of water content. This is tentatively explained by assuming that σ_e is the sum of pore water conductivity (increasing with water content until all salts in the soil are dissolved into the water and then decreasing) and surface water conductivity (increasing with wet density and therefore increasing with water content up to the critical value and then decreasing). At frequencies higher than 1000 MHz, ?_{e, r}depends only weakly on salinity (which is represented by the measured conductivity). It shows an increasing dependence if the frequency is decreased towards 1 MHz. The highest values of ?_{e, r}and σ_e, measured in this work, occur for a sample of wet, nearly saturated silt originating from a location below sea-level near to the Dead Sea, Israel: ?_{e, r}decreases continuously from a value of about 10⁴ at 3 MHz to about 10² at 200 MHz, while σ_e rises from about 4 S/m to 5 S/m at these respective frequencies. The dependence of the wavelength on the loss-tangent is strong and the wavelength is considerably smaller than it would be in a dielectric. This is the only sample for which σ_e increases with water content, even if the latter is above its critical value. Therefore it is assumed that the pore water conductivity is greater than the surface water conductivity if the volumetric water content is lower than 0.564, the maximum value applied. The measurements give evidence for the presence of a relaxation at about 3 MHz for all samples examined.     

Short-period rayleigh waves recorded in the western carpathians during dss

Summary The periods, the maximum absolute displacement amplitudes and the maximum particle velocities of the surface waves, propagating in the weathered layer are investigated. Dependences of the parameters under discussion on the distance r (km) between sites and shot points are expressed for distances from 3.6 to 38.6 km by the functions: T(s)=0.40r ^0.30 , A _max (m)==502.73r ^–1.93 and v _max (mm s –1)=7.95 r –2.22.     

Seismic vulnerability evaluation of axially loaded steel built-up laced members Ⅱ： evaluations

The test results described in Part 1 of this paper （Lee and Bruneau, 2008） on twelve steel built-up laced members （BLMs） subjected to quasi-static loading are analyzed to provide better knowledge on their seismic behavior. Strength capacity of the BLM specimens is correlated with the strength predicted by the AISC LRFD Specifications. Assessments of hysteretic properties such as ductility capacity, energy dissipation capacity, and strength degradation after buckling of the specimen are performed. The compressive strength of BLMs is found to be relatively well predicted by the AISC LRFD Specifications. BLMs with smaller kl/r were ductile but failed to reach the target ductility of 3.0 before starting to fracture, while those with larger kl/r could meet the ductility demand in most cases. The normalized energy dissipation ratio, EC/ET and the normalized compressive strength degradation, Cr″/Cr of BLMs typically decrease as normalized displacements δ/δb,exp increase, and the ratios for specimens with larger kl/r dropped more rapidly than for specimens with smaller kl/r; similar trends were observed for the monolithic braces. The BLMs with a smaller slenderness ratio, kl/r, and width-to-thickness ratio, b/t, experienced a larger number of inelastic cycles than those with larger ratios.     

Performance of the White method for estimating groundwater evapotranspiration under conditions of deep and fluctuating groundwater

The White method is a simple but the most frequently applied approach to estimate groundwater evapotranspiration (ET_g) from groundwater level diurnal signals. Because of a lack of direct measurements of ET_g, it is difficult to evaluate the performance of the White method, particularly in field environments with variable groundwater fluctuations. A 2‐year field observation in a hyper‐arid riparian tamarisk (Tamarix spp.) stand with deep groundwater depth in the lower Tarim River basin of China was conducted to measure the surface evapotranspiration (ET_s) and groundwater table. The performance of the White method and the influences of the variable groundwater fluctuations on the determinations of the specific yield (S_y) and recharge rate of groundwater (r) in the White method were investigated. The results showed that the readily available S_y determined by Loheide's method was feasible but must be finely determined based on the soil textures in the layers in which the groundwater level fluctuated. A constant S_y value for a defined porous medium could be assumed regardless of the discharge or recharge processes of groundwater. The time span of 0000 h to 0600 h for r estimation for the White method worked best than other time spans. A 2‐day moving average of r values further enhance ET_g estimation. Slight effects of environmental or anthropogenic disturbances on the diurnal fluctuations of groundwater level did not influence the ET_g estimations by the White method. Our results provide valuable references to the application of the White method for estimating daily ET_g in desert riparian forests with deep groundwater depth. Copyright © 2015 John Wiley & Sons, Ltd.