Background velocity estimation using non-linear optimization for reflection tomography and migration misfit

We show that it is possible to estimate the background velocity for prestack depth migration in 2D laterally varying media using a non-linear optimization technique called very fast simulated annealing (VFSA). We use cubic splines in the velocity model parametrization and make use of either successive pairs of shot gathers or several constant-offset sections as input data for the inversion. A Kirchhoff summation scheme based on first-arrival traveltimes is used to migrate/model the input data during the velocity analysis. We evaluate and compare two different measures of error. The first is defined in the recorded data or (x,t) domain and is based on a reflection-tomography criterion. The second is defined in the migrated data or (x,z) domain and is based on a migration-misfit criterion. Depth relaxation is used to improve the convergence and quality of the velocity analysis while simultaneously reducing the computational cost. Further, we show that by coarse sampling in the offset domain the method is still robust. Our non-linear optimization approach to migration velocity analysis is evaluated for both synthetic and real seismic data. For the velocity-analysis method based on the reflection-tomography criterion, traveltimes do not have to be picked. Similarly, the migration-misfit criterion does not require that depth images be manually compared. Interpreter intervention is required only to restrict the search space used in the velocity-analysis problem. Extension of the proposed schemes to 3D models is straightforward but practical only for the fastest available computers.     

Seismic zoning for initial‐ and total‐cost minimization

We consider two design criteria to study seismic zoning. In the first, codes require that structures be designed for some specified values. Zoning is then optimal when it minimizes the expected present value of the initial costs of all structures to be built in the region being zoned. In the second criterion, it is designed so that the present value of the total cost is minimized, including initial and maintenance costs as well as losses due to damage and failure. We will call these criteria zoning for the initial‐ and total‐cost minimization, respectively. It is shown that under certain conditions, the boundaries coincide with isoparametric curves and the problem may be solved in one dimension. We also deal with problems not reducible to a single dimension. Different methods are proposed to solve the various kinds of problems. The work ends with some illustrative examples. Copyright © 2000 John Wiley & Sons, Ltd.     

Validity and extension of the SCS‐CN method for computing infiltration and rainfall‐excess rates

A criterion is developed for determining the validity of the Soil Conservation Service curve number (SCS‐CN) method. According to this criterion, the existing SCS‐CN method is found to be applicable when the potential maximum retention, S, is less than or equal to twice the total rainfall amount. The criterion is tested using published data of two watersheds. Separating the steady infiltration from capillary infiltration, the method is extended for predicting infiltration and rainfall‐excess rates. The extended SCS‐CN method is tested using 55 sets of laboratory infiltration data on soils varying from Plainfield sand to Yolo light clay, and the computed and observed infiltration and rainfall‐excess rates are found to be in good agreement. Copyright © 2004 John Wiley & Sons, Ltd.     

Proportioning earthquake‐resistant RC frames in central/eastern U.S.

A maximum allowable period criterion is used to determine reasonable stiffness requirements for reinforced concrete frames with the seismicity associated with central and eastern U.S. A general relationship is developed to describe the displacement demand expected for central and eastern U.S. based on a survey of available ground motions, opinions of seismologists, and code‐based provisions. A series of hypothetical reinforced concrete frames is proportioned using a maximum allowable period criterion and evaluated for expected maximum displacement response using non‐linear dynamic analyses and a suite of ground motions. Results indicate that for the reinforced concrete structural systems considered in the study, proportioning for gravity loads will provide sufficient stiffness in central and eastern U.S. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of gravity source moment inversion. Part II: Usinga priori information about the source

The method of moment inversion, based on the approximation of the gravity anomaly by thetruncated series obtained from its multipole expansion, uses, implicitly,a priori information about the anomalous body. The series truncation imposes a regularizing condition on the equipotential surfaces (produced by the anomalous body), allowing the unique determination of some moments and linear combinations of moments that are the coefficients of the basis functions in the multipole expansion series. These moments define a class of equivalent distributions of mass. The equivalence criterion is based on the misfit between the observations and the field produced by the series truncated at a prefixed maximum order for the moments. The estimates of the moments of the equivalent distribution are shown to compose the stationary solution of a system of first-order linear differential equations for which uniqueness and asymptotic stability are guaranteed. Specifically for the series retaining moments up to second order, the implicita priori information introduced requires that the source have finite volume, be sufficiently distant from the measurement plane and that its spatial distribution of mass present three orthogonal planes of symmetry intersecting at the center of mass. Subject to these hypotheses, it is possible to estimate uniquely and simultaneously the total excess of mass, the position of the center of mass and the directions of the three principal axes of the anomalous body.     

基于Comsol的饱和多孔介质动力方程的数值模拟及应用

两相饱和多孔介质的动力响应问题在地震工程领域具有重要的研究意义,由于涉及到固相和液相的动力耦合,使得该问题的求解尤为复杂。本文利用Comsol在求解多场耦合问题上的优点,针对Biot饱和多孔介质u-U耦合形式下的波动方程特征,经过一系列微分算子运算和矩阵变换得到导数形式下的波动方程,基于Comsol Multiphysics提供的广义偏微分方程模式对变形后的波动方程进行求解,并把改进后的无限元边界应用到无限域动力问题的模拟中。通过与饱和多孔介质动力响应的解析解进行对比,验证模型求解技术的可行性和正确性,并在此基础上讨论饱和土地基中空沟隔振效果与饱和土体参数孔隙率、泊松比的关系。通过研究分析,可以为饱和土地基中空沟隔振设计提供一些有价值的参考。     

Damage evaluation models of reinforced concrete buildings based on the damage statistics and simulated strong motions during the 1995 Hyogo‐ken Nanbu earthquake

We have tried to estimate the yield shear strengths of reinforced concrete (RC) buildings based on the damage statistics in Kobe surveyed after the Hyogo‐ken Nanbu, Japan, earthquake of 1995 and the non‐linear response analyses for synthetic waveforms calculated from a complex seismic source and a three‐dimensional basin structure. First, a set of building models that represented the RC building stock in Kobe was constructed and plausible non‐linear multi‐degree‐of‐freedom models with four different numbers of stories were created based on the current seismic code and construction practice. For response analysis the damage criterion and the strength distribution should be assumed a priori. When the damage ratios for these standard models were calculated it was found that the damage ratios were so high that we had to increase the average yield strengths in order to match the calculated damage ratios to those observed. After searching the best models it was found that the estimated average yield strengths should be much higher than those based on the code, especially for low‐rise buildings. Using this set of building models we succeeded in reproducing the belt‐shaped area with high damage ratios in Kobe. One can apply the proposed methodology to different countries if there is enough damage data, strong motion records, and building statistics. If there is sparse damage data at several locations only, then our models can be adjusted to reproduce observed damage data and used for damage prediction as a first‐order approximation. Copyright © 2004 John Wiley & Sons, Ltd.     

Merging energy‐based design criteria and reliability‐based methods: exploring a new concept

This paper examines the potential development of a probabilistic design methodology, considering hysteretic energy demand, within the framework of performance‐based seismic design of buildings. This article does not propose specific energy‐based criteria for design guidelines, but explores how such criteria can be treated from a probabilistic design perspective. Uniform hazard spectra for normalized hysteretic energy are constructed to characterize seismic demand at a specific site. These spectra, in combination with an equivalent systems methodology, are used to estimate hysteretic energy demand on real building structures. A design checking equation for a (hypothetical) probabilistic energy‐based performance criterion is developed by accounting for the randomness of the earthquake phenomenon, the uncertainties associated with the equivalent system analysis technique, and with the site soil factor. The developed design checking equation itself is deterministic, and requires no probabilistic analysis for use. The application of the proposed equation is demonstrated by applying it to a trial design of a three‐storey steel moment frame. The design checking equation represents a first step toward the development of a performance‐based seismic design procedure based on energy criterion, and additional works needed to fully implement this are discussed in brief at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

On the hyperbolic nature of the equations of alluvial river hydraulics and the equivalence of stable and energy dissipating shocks

Abstract

The depth-averaged hydraulic equations augmented with a suitable bed-load sediment transport function form a closed system which governs the one-dimensional flow in an alluvial river or channel. In this paper, it is shown that this system is hyperbolic and yields three families of shock-wave solutions. These are determined to be temporally stable in restricted regions of the (H, F ₀)-plane, via the Lax shock inequalities. Further, it is demonstrated that this criterion is equivalent to the energy dissipation criterion developed by Needham and Hey (1991).     

The Effect of Porous Medium Storage on Unstable Density‐Driven Solute Transport

Unstable density‐driven groundwater flow and solute transport (i.e., free convection) leads to spatiotemporal variations in pressure. Specific storage (S_o) indicates the capability of a confined aquifer to release or store groundwater associated with a pressure change. Although S_o is known to dampen pressure propagation, S_o has been implicitly assumed to have a negligible impact on the unstable free convective process in prior studies. This work explores the effect of S_o on both the classic onset criterion and the fingering process using numerical models. Results show that the classic onset criterion is applicable when S_o is smaller than 10^–1 m^–1. Results also demonstrate that S_o does not play a significant role in the free convective fingering process unless it is greater than 10^–3 m^–1. For most practical purposes in hydrogeology (large Rayleigh number and small S_o), the implicit assumption of small or zero S_o is appropriate.     

H-adaptivity applied to liquefiable soil in nonlinear analysis of soil–pile interaction

This paper is concerned with application of the h-adaptive finite element method to dynamic analysis of a pile in liquefiable soil considering large deformation. In finite element analysis of pile behavior in liquefiable soil during an earthquake, especially considering large deformation of liquefied ground, error due to discretization in the zone near the pile becomes very large. Our purpose was to refine the approximation of the finite element method. The updated Lagrangian formulation and a cyclic elasto-plastic model based on the kinematic hardening rule were adopted to deal with the nonlinearity of the soil. The mixed finite element and finite difference methods together with the u-p formulation and Biot's two-phase mixture theory were used. To improve the accuracy and increase the efficiency of finite element analysis, an h-adaptive scheme that included a posteriori error estimation and h-version mesh refinement was applied to the analysis. The calculated results of effective stress were smoothed locally by the extrapolation method and smoothed stress was used to calculate the L₂ norm of the effective stress error in the last step of the calculation of each time increment. The mesh was refined by a fission procedure based on the indication of the error estimate As a numerical example, a soil–pile interaction system loaded cyclically was analyzed by our method.     

Diagnostics of solar wind streams and their sources in the solar corona

The studies are based on the experimental mass sounding of the interplanetary plasma near the Sun at radial distances of R = 4−70 R _S, performed at Pushchino RAO, Russian Academy of Sciences, and on the calculated magnetic fields in the solar corona based on the magnetic field strength and structure measured on the Sun’s surface at J. Wilcox Solar Observatory, United States. The experimental data make it possible to localize the position of the boundary closest to the Sun of the transition transonic region of the solar wind in the near-solar space (R ≈ 10−20 R _S) and to perform an interrelated study of the solar wind structure and its sources, namely, the magnetic field components in the solar corona based on these data. An analysis of the evolution of the flow types in 2000–2007 makes it possible to formulate the physically justified criterion responsible for the time boundaries of different epochs in the solar activity cycle.     

饱和土体-地下综合管廊结构地震响应分析

将土体视为固-液两相介质,基于饱和土体有效应力原理,建立饱和土体-地下综合管廊结构体系相互作用动力模型:在地应力平衡的静力状态下采用Duncan-Chang非线性弹性本构模型,在地震波作用的动力状态下采用Davidenkov非线性黏弹性本构模型;考虑饱和土体黏弹性动力人工边界条件,将地震动作用转化为作用在人工边界节点上的动力荷载。模型考察不同地震波时程、地震波加速度峰值、入射角度、孔隙率以及地应力场的影响,得出如下结论:(1)地震波的卓越周期与场地卓越周期相近时引起结构上的变形最大;随着地震波加速度峰值的增大结构变形增大;随着地震波入射角度的增加结构变形增大,地震波斜入射情况下产生的行波效应使得结构变形最大。(2)土体材料的孔隙水压力是影响地震中结构变形的主要因素之一。(3)将土体材料考虑为单相介质时结构上的变形要比考虑为固-液两相介质时大得多,直接将饱和土体场地中得到的地震波等效荷载施加到单相土介质-结构动力相互作用模型上,能够得到与完全基于有效应力法一致的结果。     

Comments on “Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady-state” by O.A. Cirpka and A.J. Valocchi

In this comment we present a re-analysis of the analytical solution presented by Cirpka and Valocchi for steady-state concentrations of dissolved bioreactive compounds and bacterial biomass in porous media. We discuss the validity range of the analytical solution. In particular, the criterion used to determine the sustainability of biomass is revisited. This re-analysis shows that the ω$\omega$ criterion used by Cirpka and Valocchi is only a necessary but not a sufficient criterion to determine the bioreactive zones. As a consequence, the analytical solution does not provide the exact distribution of compounds throughout the domain, but can serve as upper or lower boundaries for species concentrations at a given location. These conclusions are supported by the simulation results obtained from an established reactive transport model.     

Bayesian inference of the Cole–Cole parameters from time- and frequency-domain induced polarization

The inversion of induced‐polarization parameters is important in the characterization of the frequency electrical response of porous rocks. A Bayesian approach is developed to invert these parameters assuming the electrical response is described by a Cole–Cole model in the time or frequency domain. We show that the Bayesian approach provides a better analysis of the uncertainty associated with the parameters of the Cole–Cole model compared with more conventional methods based on the minimization of a cost function using the least‐squares criterion. This is due to the strong non‐linearity of the inverse problem and non‐uniqueness of the solution in the time domain. The Bayesian approach consists of propagating the information provided by the measurements through the model and combining this information with a priori knowledge of the data. Our analysis demonstrates that the uncertainty in estimating the Cole–Cole model parameters from induced‐polarization data is much higher for measurements performed in the time domain than in the frequency domain. Our conclusion is that it is very difficult, if not impossible, to retrieve the correct value of the Cole–Cole parameters from time‐domain induced‐polarization data using standard least‐squares methods. In contrast, the Cole–Cole parameters can be more correctly inverted in the frequency domain. These results are also valid for other models describing the induced‐polarization spectral response, such as the Cole–Davidson or power law models.     

Modified state–space procedures for pseudodynamic testing

The existing on‐line numerical integration algorithms are derived from the Newmark method, which is based on an approximation of derivatives in the differential equation. The state–space procedure (SSP), based on an interpolation of the discrete excitation signals for piecewise convolution integral, has been confirmed as more reliable than the Newmark method in terms of numerical accuracy and stability. In an attempt to enhance the pseudodynamic test, this study presents an on‐line integration algorithm (referred to as the OS–SSP method) via an integration of the state–space procedure with Nakashima's operator‐splitting concept. Numerical stability and accuracy assessment of the proposed algorithm in addition to the explicit Newmark method and the OS method were investigated via an eigenvalue, frequency‐domain and time‐domain analysis. Of the on‐line integration algorithms investigated, the OS–SSP method is demonstrated as the most accurate method with an acceptable stability (although not unconditionally stable) characteristic. Therefore, the OS–SSP method is the most desirable method for pseudodynamic testing if the numerical stability criterion (Δt/T⩽0.5) is ensured for every vibration mode involved. Copyright © 2001 John Wiley & Sons, Ltd.     

平面应变条件下基于弹性理论的土压力计算及适用性研究

针对工程中大量存在的平面应变问题,依据平面应变条件和广义胡克定律,基于SMP、Lade-Duncan、AC-SMP和广义Mises强度准则,推导出考虑中主应力及泊松比影响的无黏性土主、被动土压力计算公式,并将其扩展至黏性土,讨论基于各强度准则土压力计算公式的适用范围。结果表明：考虑中主应力对土强度的贡献后,基于各强度准则所计算的主动土压力均小于朗肯主动土压力,被动土压力均大于朗肯被动土压力;主动土压力P_a随着泊松比的增大而减小,被动土压力P_P随着泊松比的增大而增大,且泊松比越大,与实测数据更为接近;基于同一强度准则下得到的主、被动土压力适用的内摩擦角范围随着泊松比的增大而增大;基于各强度准则的土压力计算公式均能较好的描述挡土结构上土压力的大小,其中广义Mises强度准则计算结果与实际工程更为吻合,研究成果可为挡土结构上土压力的计算提供一定理论参考。     

AUTOMATIC PICKING OF FIRST ARRIVALS AND PARAMETERIZATION OF TRAVELTIME CURVES*

One of the methods for studying the near-surface low-velocity zone and for subsequent determination of static corrections is the technique of employing first arrivals. During the past few years several computer algorithms, based on some simplifying assumptions, have been suggested for automatic determination of first arrivals. This paper suggests a new method for automatic picking of first arrivals, which works under quite general assumptions concerning the character of the data. The method is based on the use of correlation properties of signals and the application of a statistical criterion for the estimation of first arrivals time. A number of dimensionless parameters is used in the algorithm making it possible to regulate the level of reliability and the resolution of the picking procedure. The second stage of the algorithm is the parameterization of the traveltime curve, that is a division of the previously obtained t—x curve into separate rectilinear segments. The suggested algorithm of parameterization is based on an heuristic use of some properties of maximum likelihood estimates. This permits location of the breakpoints of the t—x curve and the estimation of the parameters of each rectilinear segment. A computer program has been written based on the picking and parameterization algorithm. This program has been tested on a large amount of field data and the results show that it works at least as well as the hand procedure.     

Lateral load pattern in pushover analysis

The seismic capacity curves of three types of buildings including frame, frame-shear wall and shear wall obtained by pushover analysis under different lateral load patterns are compared with those from nonlinear time history analysis. Based on the numerical results obtained a two-phase load pattern; an inverted triangle (first mode) load pattern until the base shear force reachesβ times its maximum value, V_max, followed by a (x/H)^α form, hereβ and α being some coefficients depending on the type of the structures considered, is proposed in the paper, which can provide excellent approximation of the seismic capacity curve for low-to-mid-rise shear type buildings. Furthermore, it is shown both the two-phase load pattern proposed and the invariant uniform pattern can be used for low-to-mid-rise shear-bending type and low-rise bending type of buildings. No suitable load patterns have been found for high-rise buildings.     

IM‐based and EDP‐based decision models for the verification of the seismic collapse safety of buildings

Decision models for the verification of seismic collapse safety of buildings are introduced. The derivations are based on the concept of the acceptable (target) annual probability of collapse, whereas the decision making involves comparisons between seismic demand and capacity, which is familiar to engineering practitioners. Seismic demand, which corresponds to the design seismic action associated with a selected return period, can be expressed either in terms of an intensity measure (IM) or an engineering demand parameter (EDP). Seismic capacity, on the other hand, is defined by dividing the near‐collapse limit‐state IM or EDP by an appropriate risk‐targeted safety factor (γ _im or γ _edp ), which is the only safety factor used in the proposed decision model. Consequently, the seismic performance assessment of a building should be based on the best possible estimate. For a case study, it is shown that if the target collapse risk is set to 10^?4 (0.5% over a period of 50 years), and if the seismic demand corresponds to a return period of 475 years (10% over a period of 50 years), then it can be demonstrated that γ _im is approximately equal to 2.5 for very stiff buildings, whereas for buildings with long periods the value of γ _im can increase up to a value of approximately 5. The model using γ _edp is equal to that using γ _im only if it can be assumed that displacements, with consideration of nonlinear behavior, are equal to displacements from linear elastic analysis.