Statistical Characterization of a Random Velocity Field Using Stacking Velocity Profiles

In petroleum exploration and production, it is important to have good estimations of the uncertainties on the reserves. Uncertainties in the velocity model used during the data processing are of major importance in this estimation. The use of geo-statistical tools can help in dealing with these uncertainties. Up to now, a strong limitation has been the inability to properly merge velocity functions measured in the wells with seismic velocity data. This was due to the different “supports” among the two, i.e. the well velocity may be regarded as a direct measurement of the instantaneous velocity field, while the seismic velocities correspond to an “average along the travelled paths” of this field. The problem is that, apart from the well positions, the instantaneous velocity field is out of reach. Luckily, for many practical applications, it is enough to know just its covariance model. However, no algorithmic method is available in the literature to yield the covariance model, and geologists are forced to use arbitrary distributions. The present paper proposes an original method to obtain a good estimate of this covariance model, using widely available information, mainly seismic stacking velocities. This method was first developed in a simple one-layer case with constant velocity, and then extended to more realistic situations. Finally, a real data application is performed, which highlights the robustness of the resulting estimation.     

An anemometry technique for turbulence measurements at low velocities

A method using symmetrically bent V-shaped hot-wires has been developed for the accurate measurement of low-speed turbulence. Directional characteristics of V-shaped hot-wires at low velocities are investigated, and a generalized expression is derived for the effective cooling velocity. The measurement with V-shaped hot-wires in a pseudo turbulent field, which is artificially produced by shaking the hot-wires with an accurately known motion in a steady flow, has confirmed that the expression for the effective cooling velocity is also valid for instantaneous velocity fluctuations. The accuracy of a practical technique comprising two V-shaped hot-wires in an X arrangement is investigated by an error analysis in simulated Gaussian velocity fields using a digital computer.     

A study of methods to estimate debris flow velocity

Debris flow velocities are commonly back-calculated from superelevation events which require subjective estimates of radii of curvature of bends in the debris flow channel or predicted using flow equations that require the selection of appropriate rheological models and material property inputs. This research investigated difficulties associated with the use of these conventional velocity estimation methods. Radii of curvature estimates were found to vary with the extent of the channel investigated and with the scale of the media used, and back-calculated velocities varied among different investigated locations along a channel. Distinct populations of Bingham properties were found to exist between those measured by laboratory tests and those back-calculated from field data; thus, laboratory-obtained values would not be representative of field-scale debris flow behavior. To avoid these difficulties with conventional methods, a new preliminary velocity estimation method is presented that statistically relates flow velocity to the channel slope and the flow depth. This method presents ranges of reasonable velocity predictions based on 30 previously measured velocities.     

薄层水流速度测量系统的研究

根据水流影响电解质扩散和其导电特性的分析,结合电解质脉冲在水流中迁移的数学模型,设计了薄层水流速度测试系统。用Visual Basic语言编写了操作系统,实现了数据采集、参数计算和分析自动化。实验和模拟结果表明,模拟水槽实验中用流量法测量的流速和电解质扩散法测量的水流速度误差很小,说明用此系统测量浅层水流的流速是可行的。     

Statistical properties of the atmospheric turbulent boundary layer over steep surface waves

A new method of digital optical anemometry (Particle Image Velocimetry, PIV) of turbulent flows is suggested and implemented in the laboratory; it is based on the use of continuous laser radiation and high-speed video photography, providing continuous statistical ensembles of flow velocity fields. Application of the method to the study of wind field over waves has allowed us to perform, for the first time, direct measurements of velocity fields, averaged over turbulent pulsations induced by waves in the air flow. The experiments demonstrated that the velocity fields, averaged over the turbulent pulsations, are nonseparated even in the case of steep and breaking waves, when separation of the flow from the wave crests in the instantaneous fields is observed. Based on comparison with the experimental data, it is shown that the average wind fields over waves are described well quantitatively in the framework of semiempirical closure models of turbulence.     

Modeling the influence of settling velocity on cohesive sediment transport in Tanshui River estuary

Settling velocities of suspended cohesive sediment in estuaries vary over a range of several orders in magnitude. Variations in the suspended sediment concentration are often considered as the principal cause. Turbulence and the suspended sediment concentration, as well as other factors such as salinity, dissolved organic substances, flocculation ability, and the rate of floc growth affect setting velocities. A laterally–averaged finite difference model for hydrodynamics and cohesive sediment transport is developed and applied in the Tanshui River estuary, Taiwan. The model has been calibrated and verified with water surface elevation, longitudinal velocity, salinity, and cohesive sediment measured. The overall performance of the model is in qualitative agreement with the available data. The model is used to investigate the influence of settling velocity on cohesive sediment transport dynamics. The simulation indicates that the turbidity maximum zone is near Kuan–Du. When settling velocities increase the surface cohesive sediment concentration at Kuan–Du station trends to decrease and bottom cohesive sediment concentration increases. Both surface and bottom cohesive sediment concentrations decrease at Taipei Bridge and Pa–Ling Bridge. This implies that suspended sediment advected seaward and deposited. There is consequently a net seaward flux of suspended sediment near surface, and a net landward flux near the bed.     

A comparative study for the estimation of geodetic point velocity by artificial neural networks

Space geodesy era provides velocity information which results in the positioning of geodetic points by considering the time evolution. The geodetic point positions on the Earth’s surface change over time due to plate tectonics, and these changes have to be accounted for geodetic purposes. The velocity field of geodetic network is determined from GPS sessions. Velocities of the new structured geodetic points within the geodetic network are estimated from this velocity field by the interpolation methods. In this study, the utility of Artificial Neural Networks (ANN) widely applied in diverse fields of science is investigated in order to estimate the geodetic point velocities. Back Propagation Artificial Neural Network (BPANN) and Radial Basis Function Neural Network (RBFNN) are used to estimate the geodetic point velocities. In order to evaluate the performance of ANNs, the velocities are also interpolated by Kriging (KRIG) method. The results are compared in terms of the root mean square error (RMSE) over five different geodetic networks. It was concluded that the estimation of geodetic point velocity by BPANN is more effective and accurate than by KRIG when the points to be estimated are more than the points known.     

Load-displacement uncertainty of vertically loaded shallow footings on sands and effects on probabilistic settlement estimation

This article focuses on the statistical characterisation and stochastic modelling of the load-displacement behaviour of shallow footings on cohesionless soils and on the probabilistic estimation of settlement for serviceability limit state design (LSD). The study relies on a field database of 30 full-scale footings subjected to vertical loading with cone penetration testing data available for each site. The performance of three load-displacement models in replicating field data is assessed comparatively through statistical analysis. Load-displacement uncertainty is subsequently modelled probabilistically to perform Monte Carlo Simulation (MCS)-based estimation of footing settlement using the best-performing power law model. The dependence among load-displacement model parameters is investigated and replicated using copula theory. Samples are generated to account for parametric uncertainties in model inputs. The simulation output samples of settlement are examined statistically in order to assess the relevance of parametric and load-displacement uncertainties in settlement estimation, as well as the importance of accounting for correlation between power law model parameters. A simple analytical model for the estimation of settlement at any target reliability level is obtained on the basis of the outputs of MCS. The model can be practically implemented in geotechnical LSD at serviceability limit states.     

黄土厚度变化较大地区煤田三维地震勘探时深转换方法的探讨

时深转换是煤田三维地震资料解释中非常关键的一步,时深转换方法的选取直接关系到地质成果的准确程度。针对山西某勘探区黄土覆盖厚度大且变化剧烈的实际情况,在比较大平均速度和分层速度两种时深转换方法的适应性和误差特点的基础上,优选分层速度计算方法作为本区时深转换方法。具体步骤为：根据地层沉积相和地质构造特点,结合由速度谱数据库和声波测井速度数据库确定的岩性分布规律,以单斜为基本单元进行区块划分;计算出各区块的新生界、煤系地层的厚度和速度后,从而求出较为准确的煤层埋深。实例表明,采用分区块、分层计算的煤层底板深度不仅准确程度高,而且还能克服由大平均速度时深转换方法造成的煤层假构造现象。     

Surface wave phase velocity maps from multiscale wave field interpolation

Availability of spatially dense broadband observations of seismic surface wave fields allows to derive phase velocity maps on regional scale by non-tomographic means. I present a multiscale interpolation scheme for surface wave fields where for each observed wave field, a multiscale phase velocity map and its standard deviation are calculated from subsets of the available data. Isotropic phase velocity (with an estimate on its standard deviation) is then found as the weighted mean of multiscale maps from different observations. Comparison of different interpolation schemes on synthetic wave fields shows that bivariate linear interpolation of phases in a triangulated region, in conjunction with multiscale stacking, is not inferior than methods involving higher-order polynomials. The recovered phase velocity maps are, in the presence of random uncertainties with realistic magnitude, largely free of artifacts and restore a synthetic input model reasonably well. The method is applied to a subset of Rayleigh wave observations at USArray which yields phase velocity maps well within the range of published results. Multiscale interpolation seems to be a practical alternative to tomographic inversion for regional broadband seismic networks (≥30 stations). It requires no choice of arbitrary parameters and is insensitive to number of earthquakes and their azimuthal distribution.     

基于岩石物理模型的页岩孔隙结构反演及横波速度预测

准确预测储层的等效孔隙纵横比对页岩储层岩石物理建模及横波速度预测具有重要意义。为分析页岩储层孔隙纵横比及预测横波速度,提出了基于岩石物理模型的页岩孔隙纵横比反演及横波速度预测方法。本文首先通过岩石物理模型建立岩石的纵、横波速度与孔隙纵横比、孔隙度和矿物组分等参数之间的定量关系,寻找最佳孔隙纵横比;然后通过使理论预测与实际测量的纵波速度之间误差达到最小的方式反演孔隙纵横比,并以此为约束预测横波速度。实际测井数据反演结果表明,龙马溪组页岩地层的孔隙纵横比稳定,而围岩的孔隙纵横比变化范围较大;说明与围岩相比,页岩的孔隙结构更为稳定。同时,预测得到的页岩横波速度与实测横波速度的误差较小,另外对于缺少矿物组分资料的页岩层段,用平均矿物组分预测得到的横波速度误差仍较小;说明与矿物组分相比,龙马溪组页岩的纵、横波速度对孔隙纵横比参数更敏感。综上所述,利用该方法可预测到较为准确的等效孔隙纵横比和横波速度。     

Contributions to the Deformation Analysis in Germany Based on Precise and Continuous GPS Measurements

Modern space geodetic techniques enable deformation monitoring of continental plate interiors with high spatial and temporal coverage. Resolving data and results are currently evaluated for their application for the integrated assessment of seismic hazard and risk in Germany. This goes especially for regions where earthquakes are generally rare but high magnitudes are still not unrealistic while vulnerability of today’s society is steadily growing. The present contribution deals with the continuous monitoring of tectonic fracture systems in Germany using the GPS. The estimation of the station velocities with GPS and the resulting geodetic strain is supposed to provide additional input to the earthquake hazard assessment. Unfortunately, the low expected and currently seen velocities (<1–2 mm/year) make it extremely difficult to distinguish between noise and a tectonic signal. Because of the short observation interval the velocity uncertainties are about 2 mm/year in the horizontal components. The essential goal of this program is to provide and model highly precise deformation data and to discuss its needs for a better assessment of geological hazard, especially for the most active tectonic regions in Germany, the Rhine-Graben, the Swabian Alb, the Alpine foreland, and the Vogtland. Here we present preliminary results from 2 years of measurements at currently 150 GPS stations throughout Germany. The time span of this program has proven to be too short and the density of the station network to be not dense enough yet for reliable significant horizontal station velocities and supporting the earthquake hazard assessment.     

Analytical modeling of glacier dynamics

Flow velocities and stresses within a glacier are determined by inverting known surface velocities with a specified glacier geometry. The surface velocities depend only weakly on the unknown velocities at the bed of a glacier, so the inversion is illposed and unstable. This instability causes both numerical computation errors and data errors to grow dramatically with depth, usually masking the actual velocity and stress solutions. To control the numerical errors, an analytical modeling scheme is presented which modifies the method of mean weighted residuals (used in finite element techniques). The resulting scheme impairs convergence by producing powerseries solutions, but in an advantageous tradeoff, the coefficients to the power series can be determined analytically rather than numerically. This leads to arbitrary order analytical powerseries solutions to the internal stress state of glaciers. The symbolic powerseries solutions can be evaluated at any point in the glacier with negligible roundoff and discretization errors. Analytical model accuracy is confirmed with known stress solutions for several widely used constitutive relations for ice.     

黏弹性和速度各向异性对薄层反射的影响

煤层具有强波阻抗差、低阻抗的特性,对地震勘探来说是一种典型的薄层。因为其黏弹性和速度各向异性导致薄层反射波场异常,为了定量分析黏弹性和速度各向异性对薄层地震反射的影响,针对强波阻抗差薄层模型,基于波动方程数值模拟方法,正演得到弹性速度各向同性、黏弹性速度各向同性及黏弹性速度各向异性的地震波场,并对比分析了3种模型的弹性波地震反射特征。研究结果表明:黏弹性对薄层的反射产生不可忽略的影响,会明显降低薄层弹性波的反射振幅,但黏弹性速度各向同性与各向异性对薄层的弹性波反射影响差异不大。相比于弹性各向同性情况,黏弹性会引起反射纵波（PP波）瞬时频率最大可达8%的改变量,而对转换横波（PS波）仅有3%的改变量,可以忽略不计。上述研究为利用构造煤品质因子极低的特征来预测构造煤提供了可能。      

Substantiation of debris flow velocity from super-elevation: a numerical approach

The use of super-elevations that a forced vortex flow leaves on the valley walls of a curved flume is a plausible approach toward estimating debris flow velocities in earthquake-induced geo-hazard studies. The centrifugal force of a speeding flow is responsible for a higher flow depth on the outer bend. However, in reality, a flow is not steady, and only the highest flow-marks are left at the outer and inner bends of the flow, which can lead to an inaccurate estimation of the actual velocity. Seeing the real scenario of the field, a series of numerical flume tests using smoothed particle hydrodynamics (SPH) is conducted to validate the estimation of debris flow velocities from flow-marks. Velocities estimated from flow-marks are lower than real velocities near the source region, but they converge to real velocities as the distance to the source increases. Based on several simulations, a best-fit line is proposed for adjusting debris flow velocity from mud-marks, and it is used to estimate flow velocities of the well-documented debris event called “Shiraito river debris flow,” which happened near the rim of the Hakone Crater, Kanagawa Prefecture, Japan, ensuing from the 1923 Great Kanto earthquake.     

Crustal Structure of the Crimean Mountains along the Sevastopol–Kerch Profile from the Results of DSS and Local Seismic Tomography

The paper discusses the velocity structure of the crust beneath the Crimean Mountains from the results of active and passive seismic experiments. Based on a new interpretation of seismic data from the old Sevastopol–Kerch DSS profile by modern full-wave seismic modeling methods, a velocity model of the crust beneath the Crimean Mountains has been constructed for the first time. This model shows the significant differences in the structure of two crustal blocks: (1) one characterized by higher velocities and located in the western and central Crimean Mountains, and (2) the other characterized by lower velocities and located in the east, in the Feodosiya–Kerch zone, which are subdivided by a basement uplift (Starokrymskoe Uplift). The former block is characterized by a more complex structure, with the Moho traced at depths of 43 and 55 km, forming two Moho discontinuities: the upper one corresponds to the platform stage, and the lower one, formed presumably at the Alpine stage of tectogenesis as a result of underthrusting of the East Black Sea microplate beneath the southern margin of the Scythian Plate in Crimea. At depths of 7–11 km, velocity inversion zone has been identified, indicating horizontal layering of the crust. Local seismic tomography using the data on weak earthquakes (m_b ≤ 3) recorded by the Crimean seismological network allowed us to obtain data on the crustal structure beneath the Crimean Mountains at depths of 10–30 km. The crustal structure at these depths is characterized by the presence of several high-velocity crustal bodies in the vicinity of cities Yalta, Alushta, and Sudak, with earthquake hypocenters clustered within these bodies. Comparison of this velocity model of the Crimean Mountains with the seismicity distribution and with the results from reconstruction of paleo- and present-day stress fields from field tectonophysical study and earthquake focal mechanisms allowed the conclusion that the Crimean Mountains were formed as a result of on mature crust at the southern margin of the East European Platform and Scythian Plate, resulting from processes during various phases of Cimmerian and Alpine tectogenesis in the compressional and transpressional geodynamic settings. The collisional process is ongoing at the present-day stage, as supported by high seismicity and uplift of the Crimean Mountains.     

The settling of consecutive spheres in viscoplastic fluids

One of the factors contributing to the uncertainties involved in the estimation of particle settling velocity in viscoplastic fluids is the time-dependent effect where the viscous parameters of the fluid change as a particle flows through and shears the medium. These changes, particularly at low shear Reynolds numbers, are reflected in the settling velocity of a following sphere that is released some time after an initial one, with the following sphere having a significantly greater velocity. This study found that changes in both fall velocity and equivalent viscosity can be correlated satisfactorily by a power law equation to the dimensionless form of the time interval between releases, and the rheogram shape factor for the fluid. A collision of particles occurs in cases where the time interval between releases is small, after which the particles combine and travel at a terminal velocity. A new variable, β, which takes into account the different surficial stress of the combined spheres, was introduced to the correlation of Wilson et al. [Wilson, K.C., Horsley, R.R., Kealy, T., Reizes, J.A., Horsley, M.R., 2003. Direct prediction of fall velocities in non-Newtonian materials. Int. J. Miner. Process. 71, 17–30] β was found to depend on the rheogram shape factor for the fluid and the shear Reynolds number for the particle. The validity of this approach was supported by experimental data.     

Estimating water volume discharge through salt-marsh tidal channels: An aspect of material exchange

Water volume discharge estimates were made at a sample cross-section of the Canary Creek salt marsh (Lewes, Delaware). To account for cross-sectional velocity variations, a dense spatial array of current meters was used. Simultaneous measurements were taken at hourly intervals over three complete tidal cycles. A practical method is presented whereby instantaneous average cross-sectional velocity, instantaneous cross-sectional discharge and tidal cycle discharge can be estimated from a dense current meter array, orideal data set. Based on theseideal estimates, it is shown that a simplified spatial array can be used to estimate water discharges within acceptable error limits. Instantaneous cross-sectional discharges and total tidal cycle discharges were estimated with uncertainties of ±11% and ±7%, respectively. To minimize errors when estimating material exchange between salt marshes and adjacent waters, it is suggested that a comprehensive assessment of cross-sectional lateral current velocity variations be conducted.     

考虑预报偏差的迭代式集合卡尔曼滤波在地下水水流数据同化中的应用

集合卡尔曼滤波（Ensemble Kalman Filter,EnKF）方法已广泛应用于地下水水流和污染物运移模拟相关问题的求解。但前人研究多建立在同化系统预报模型是准确的基础上,忽视了模型概化的不确定性。当模型概化不准确时,将导致预报偏差,可能带来错误的系统估计。因此,文章提出考虑模型预报偏差的迭代式集合卡尔曼滤波（Bias aware Ensemble Kalman Filter with Confirming Option,Bias-CEnKF）方法。以地下水水流数据同化为例,研究模型概化存在不确定条件下,边界条件、初始条件、源汇项概化不准确时新方法的有效性。结果表明,当预报模型概化不准确时,使用标准EnKF方法进行数据同化,可能会导致滤波发散,造成同化失败。Bias-CEnKF方法不仅保留了较好的同化性能,同时减小了参数、变量、偏差项非线性关系带来的不一致性。针对文章中4种情景,Bias-CEnKF同化获得的含水层渗透系数场以及水头场均接近真实场,且预报结果可靠。本研究进一步提升了模型概化不确定时EnKF方法的适用性,为实际野外复杂条件下地下水水流数据同化问题提供了可靠的方法。