用Velocity Verlet积分器改进HMC抽样方法

Hamilton Monte Carlo (HMC)方法是一种常用的快速抽样方法.在对哈密顿方程进行抽样时,HMC方法使用Leapfrog积分器,这可能造成方程的位置及动量的迭代值在时间上不同步,其产生的误差会降低抽样效率及抽样结果的稳定性.为此,本文提出了IHMC(Improved HMC)方法,该方法用Velocity Verlet积分器替代Leapfrog积分器,每次迭代时都计算两变量在同一时刻的值.为验证方法的效果,本文进行了两个实验,一个是将该方法应用于非对称随机波动率模型(RASV模型)的参数估计,另一个是将方法应用于方差伽马分布的抽样,结果显示:IHMC方法比HMC方法的效率更高、结果更稳定.

Electrical structure identification of deep shale gas reservoir in complex structural area using wide field electromagnetic method

To fully exploit the technical advantages of the large-depth and high-precision artificial source electromagnetic method in the complex structure area of southern Sichuan and compensate for the shortcomings of the conventional electromagnetic method in exploration depth,precision,and accuracy,the large-depth and high-precision wide field electromagnetic method is applied to the complex structure test area of the Luochang syncline and Yuhe nose anticline in the southern Sichuan.The advantages of the wide field electromagnetic method in detecting deep,low-resistivity thin layers are demonstrated.First,on the basis of the analysis of physical property data,a geological–geoelectric model is established in the test area,and the wide field electromagnetic method is numerically simulated to analyze and evaluate the response characteristics of deep thin shale gas layers on wide field electromagnetic curves.Second,a wide field electromagnetic test is conducted in the complex structure area of southern Sichuan.After data processing and inversion imaging,apparent resistivity logging data are used for calibration to develop an apparent resistivity interpretation model suitable for the test area.On the basis of the results,the characteristics of the electrical structure change in the shallow longitudinal formation of 6 km are implemented,and the transverse electrical distribution characteristics of the deep shale gas layer are delineated.In the prediction area near the well,the subsequent data verification shows that the apparent resistivity obtained using the inversion of the wide field electromagnetic method is consistent with the trend of apparent resistivity revealed by logging,which proves that this method can effectively identify the weak response characteristics of deep shale gas formations in complex structural areas.This experiment,it is shown shows that the wide field electromagnetic method with a large depth and high precision can effectively characterize the electrical characteristics of deep,low-resistivity thin layers in complex structural areas,and a new set of low-cost evaluation technologies for shale gas target layers based on the wide field electromagnetic method is explored.

Feasibility of the 2-point method to determine the load-velocity relationship variables during the countermovement jump exercise

Purpose:This study aimed to examine the reliability and validity of load-velocity(L-V)relationship variables obtained through the 2-point method using different load combinations and velocity variables.Methods:Twenty men performed 2 identical sessions consisting of 2 countermovement jumps against 4 external loads(20 kg,40 kg,60 kg,and80 kg)and a heavy squat against a load linked to a mean velocity(MV)of 0.55 m/s(load_(0.55)).The L-V relationship variables(load-axis intercept(L_(0)),velocity-axis intercept(v_(0)),and area under the L-V relationship line(A_(line)))were obtained using 3 velocity variables(MV,mean propulsive velocity(MPV),and peak velocity)by the multiple-point method including(20-40-60-80-load_(0.55))and excluding(20-40-60-80)the heavy squat,as well as from their respective 2-point methods(20-load_(0.55)and 20-80).Results:The L-V relationship variables were obtained with an acceptable reliability(coefncient of variation(CV)≤7.30%;intra-class correlation coefficient>0.63).The reliability of L_(0)and v_(0)was comparable for both methods(CV_(ratio)(calculated as higher value/lower value):1.11-1.12),but the multiple-point method provided Al_(ine)with a greater reliability(CV_(ratio)=1.26).The use of a heavy squat provided the L-V relationship variables with a comparable or higher reliability than the use of a heavy countermovement jump load(CV_(ratio):1.06-1.19).The peak velocity provided the load-velocity relationship variables with the greatest reliability(CV_(ratio):1.15-1.86)followed by the MV(CV_(ratio):1.07-1.18),and finally the MPV.The 2-point methods only revealed an acceptable validity for the MV and MPV(effect size≤0.19;Pearson s product-moment correlation coefficient≥0.96;Lin's concordance correlation coefficient≥0.94).Conclusion:The 2-point method obtained from a heavy squat load and MV or MPV is a quick,safe,and reliable procedure to evaluate the lower-body maximal neuromuscular capacities through the L-V relationship.

Energy-Saving and Punctuality Combined Velocity Planning for the Autonomous-Rail Rapid Tram with Enhanced Pseudospectral Method

Autonomous-rail rapid transit(ART)is a new medium-capacity rapid transportation system with punctuality,comfort and convenience,but low-cost construction.Combined velocity planning is a critical approach to meet the requirements of energy-saving and punctuality.An ART velocity pre-planning and re-planning strategy based on the combination of punctuality dynamic programming(PDP)and pseudospectral(PS)method is proposed in this paper.Firstly,the longitudinal dynamics model of ART is established by a multi-particle model.Secondly,the PDP algorithm with global optimal characteristics is adopted as the pre-planning strategy.A model for determining the number of collocation points of the real-time PS method is proposed to improve the energy-saving effect while ensuring computation efficiency.Then the enhanced PS method is utilized to design the velocity re-planning strategy.Finally,simulations are conducted in the typical scenario with sloping roads,traffic lights,and intrusion of the pedestrian.The simulation results indicate that the ART with the proposed velocity trajectory optimization strategy can meet the punctuality requirement,and obtain better economy efficiency compared with the punctuality green light optimal speed advisory(PGLOSA).

2-D Seismic Reflection Method Using Iso Velocity Method of Mianwali Area

A seismic reflection of Line 12-B belonging to Mianwali Re-entrant was acquired and processed for 2-D interpretation. The line orients itself NNE-SSW direction. The sections have the shot points from VP-199 to VP-1044. Eleven Reflectors R1, R2, R3, Base Miocene, Pinchout P1, P2, P3, P4, P5P6 (Pinchout) are marked and a basement has been marked and interpreted. All the reflectors above the basement show a downward bending at the center. The depth of each reflector was calculated by iso velocity contour map method. The depth section obtained by this method shows stratigraphic features like Pinchouts. The reflectors are then correlated with the subsurface structures and stratigraphy of the area.

Herrmann Method of Analyzing Structure Design Velocity Field

The shape optimization is studied by adopting the domain integrated method which is based on the calculus of variations during the shape design sensitivity analysis. A new method of improving the efficiency of the design velocity field analysis and the quality of the finite element method (FEM) mesh is put forward. The sensitivity analysis which is based on the calculus of variations is used in the shape optimization. The design velocity field is solved by Herrmann method. An example shows that both the quality of the FEM mesh and the efficiency of the computing of the design velocity field are improved by Herrmann method. So the effect and the efficiency of the shape optimization are guaranteed. If using sensitivity analysis which is based on the calculus of variations in the shape optimization, the sensitivity analysis can be a relatively independent module. The efficiency of computing the design velocity field and the quality of mesh will be improved by using Herrmann method.

Low-velocity Impact Damage Analysis of Composite Laminates Using Self-adapting Delamination Element Method

On the basis ofa 2D 4-node Mindlin shell element method, a novel self-adapting delamination finite element method is presented, which is developed to model the delamination damage of composite laminates. In the method, the sublaminate elements are generated automatically when the delamination damage occurs or extends. Thus, the complex process and state of delamination damage can be simulated practically with high efficiency for both analysis and modeling. Based on the self-adapting delamination method, linear dynamic finite element damage analysis is performed to simulate the low-velocity impact damage process of three types of mixed woven composite laminates. Taking the frictional force among sublaminations during delaminating and the transverse normal stress into account, the analytical results are consistent with those of the experimental data.

Local singularity and S–A methods for analyzing ore-producing anomalies in the Jianbiannongchang area of Heilongjiang,China

The Heilongjiang Jianbiannongchang area is located at the confluence of the Great and Lesser Xing’an Ranges.This area has a complex magmatic and tectonic evolutionary history that has resulted in a complex and diverse geological background for mineralization.In this study,isometric logarithmic ratio(ILR)transformations of Au,Cu,Pb,Zn,and Sb contents were performed in the1:50,000 soil geochemical data of the Jianbiannongchang area.Robust principal component analysis(RPCA)was conducted based on ILR transformation.The local singularity and spectrum-area(S-A)methods were used to extract information on mineralogic anomalies.The results showed that:(1)the transformed data eliminated the influence of the original data closure effect,and the PC1and PC2 information obtained by applying RPCA reflected ore-producing element anomalies dominated by Au and Cu.(2)The local singularity method can enhance the information of the local strong and weak slow anomalies.After performing local singularity analysis on PC1 and PC2,the obtained local anomalies reflected the local singularity spatial anomaly patterns related to Cu and Au mineralization in this area,which is an effective method for trapping ore-producing anomalies.(3)Furthermore,the composite anomaly decomposition of PC1 and PC2 was performed using the S-A method,and the screened anomalous and background fields reflect the ore-producing anomalies related to Cu and Au mineralization.This information is in agreement with known Cu and Au mineralization.(4)The geochemical anomalies with mineralization potential were obtained outside the known mineralization sites by integrating the information of oreproducing anomalies extracted by the local singularity and S-A methods,providing the theoretical basis and exploration direction for future exploration in the study area.

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part II:Numerical Methods and Test Experiments

Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary（around a data hole） inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes（grid-staggering,local-nesting and piecewise continuous integration） are designed to deal with the singularity of the Green＇s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential（or streamfunction） component to zero,the other component of the solution can be computed in two ways：（1） Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.（2） Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting（or piecewise continuous integration）,the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point（or along the entire boundary）.When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.

Effect of SACMA and QMW Test Methods on Compressive Properties of Composite Laminates after Low Velocity Impact

Experimental studies on the compressive behavior of composite laminates after low velocity impact was carried out with two test methods. One is SACMA Standard, and the other is a small dimensional specimen test method. Impact damage distributions, compressive failure process after impact, quasi static indentation and compression of laminates with a hole were brought into comparison between these two test methods. The results showed that there is a great difference between these two test methods. Compressive behavior of laminates after impact varies with different test methods. Residual compressive strength of laminates after low velocity impact measured with SACMA Standard can reflect stiffness properties of composite resins more wholely than that measured with the other method can do. Small dimensional specimen test method should be improved on as an experimental standard of compressive strength after impact. \{

Signal processing method for shear wave velocity measurement

Soil shear wave velocity （SWV） is an important parameter in geotechnical engineering. To measure the soil SWV, three methods are generally used in China, including the single-hole method, cross-hole method and the surface-wave technique. An optimized approach based on a correlation function for single-hole SWV measurement is presented in this paper. In this approach, inherent inconsistencies of the artificial methods such as negative velocities, and too-large and too-small velocities, are eliminated from the single-hole method, and the efficiency of data processing is improved. In addition, verification using the cross-hole method of upper measuring points shows that the proposed optimized approach yields high precision in signal processing.

A method to model the effect of pre-existing cracks on P-wave velocity in rocks

Crack closure is one of the reasons inducing changes of P-wave velocity of rocks under compression.In this context,a method is proposed to investigate the relationships among P-wave velocity,pre-existing cracks,and confining pressure based on the discrete element method(DEM).Pre-existing open cracks inside the rocks are generated by the initial gap of the flat-joint model.The validity of the method is evaluated by comparing the P-wave velocity tested on a sandstone specimen with numerical result.As the crack size is determined by the diameter of particles,the effects of three factors,i.e.number,aspect ratio,and orientation of cracks on the P-wave velocity are discussed.The results show that P-wave velocity is controlled by the(i.e.number) of open micro-cracks,while the closure pressure is determined by the aspect ratio of crack.The reason accounting for the anisotropy of P-wave velocity is the difference in crack number in measurement paths.Both of the number and aspect ratio of cracks can affect the responses of P-wave velocity to the applied confining pressure.Under confining pressure,the number of open cracks inside rocks will dominate the lowest P-wave velocity,and the P-wave velocity of the rock containing narrower cracks is more sensitive to the confining pressure.In this sense,crack density is difficult to be back-calculated merely by P-wave velocity.The proposed method offers a means to analyze the effect of pre-existing cracks on P-wave velocity.

Effect of particle shape on packing fraction and velocity profiles at outlet of a silo

Many studies on how the particle shape affects the discharge flow mainly focus on discharge rates and avalanche statistics. In this study, the effect of the particle shape on the packing fraction and velocities of particles in the silo discharge flow are investigated by using the discrete element method. The time-averaged packing fraction and velocity profiles through the aperture are systematically measured for superelliptical particles with different blockinesses. Increasing the particle blockiness is found to increase resistance to flow and reduce the flow rate. At an identical outlet size, larger particle blockiness leads to lower velocity and packing fraction at the outlet. The packing fraction profiles display evidently the self-similar feature that can be appropriately adjusted by fractional power law. The velocity profiles for particles with different shapes obey a uniform self-similar law that is in accord with previous experimental results, which is compatible with the hypothesis of free fall arch. To further investigate the origin of flow behaviors, the packing fraction and velocity field in the region above the orifice are computed. Based on these observations, the flow rate of superelliptical particles is calculated and in agreement with the simulated data.

Debris cloud structure and hazardous fragments distribution under hypervelocity yaw impact

This study investigates how the debris cloud structure and hazardous fragment distribution vary with attack angle by simulating a circular cylinder projectile hypervelocity impinging on a thin plate using the finite element-smoothed particle hydrodynamics(FE-SPH)adaptive method.Based on the comparison and analysis of the experimental and simulation results,the FE-SPH adaptive method was applied to address the hypervelocity yaw impact problem,and the variation law of the debris cloud structure with the attack angle was obtained.The screening criterion of the hazardous fragment at yaw impact is given by analyzing the debris formation obtained by the FE-SPH adaptive method,and the distribution characteristics of hazardous fragments and their relationship with the attack angle are given.Moreover,the velocity space was used to evaluate the distribution range and damage capability of asymmetric hazardous fragments.The maximum velocity angle was extended from fully symmetrical working conditions to asymmetrical cases to describe the asymmetrical debris cloud distribution range.In this range,the energy density was calculated to quantitatively analyze how much damage hazardous fragments inflict on the rear plate.The results showed that the number of hazardous fragments generated by the case near the 35°attack angle was the largest,the distribution range was the smallest,and the energy density was the largest.These results suggest that in this case,debris cloud generated by the impact had the strongest damage to the rear plate.

3-D velocity images of the crust and upper mantle of the Tianshan area

D velocity images of the crust and upper mantle in the Tianshan are established by means of seismic tomograghy. From the results, some understanding can be achieved as follows: (1) The northern and central parts of the Tianshan are the uplifted areas with high velocities. The low velocity areas in front of the northern and southern flanks of the Tianshan are formed by the southern margin of the Junggar Basin, Turpan Basin, Kuqa depression, Kalpin fault block and Kaxgar depression. The Ili Basin and the western Kunlun appear as intracrustal stable high velocity blocks, while the Bachu uplift extends down to the crustal bottom. Along the main peaks of the Tianshan and Mt. Kongur of the western Kunlun, the Moho depresses on a great scale to form five large low velocity areas. (2) In the northern Tianshan snd western Junggar Basin, the lithosphere is thicker and features a high velocity probably with an asthenolith layer existing on the top of the upper mantle. In the southern Tianshan, the feature of the lithosphere is not very clear, and the existence of a comic low velocity block between 120-280 km depth in the Kaxgar area is presumably related with the upwelling of astenolith from the upper mantle. (3) Some relation does exist between velocity structures and seismic activities, especially those gradient belts between the low velocity zone in the upper crust and the low velocity zone in the lower crust may be the tectonic positions for the preparation of moderate-strong earthquakes. (4) Seismically active areas on the northern and southern flanks of the Tianshan are locations with most inhomogeneous crustal media and welldeveloped deep faults. Fractures or interlayer-gliding are very likely to occur under the action of tectonic forces and thus to induce earthquakes in these areas.

S-wave velocity structure inferred from receiver function inversion in Tengchong volcanic area

Tengchong volcanic area is located near the impinging and underthrust margin of India and Eurasia plates. The volcanic activity is closely related to the tectonic environment. The deep structure characteristics are inferred from the receiver function inversion with the teleseismic records in the paper. The results show that the low velocity zone is influenced by the NE-trending Dayingjiang fault. The S-wave low velocity structure occurs obviously in the southern part of the fault, but unobviously in its northern part. There are low velocity zones in the shallow po-sition, which coincides with the seismicity. It also demonstrates that the low velocity zone is directly related to the thermal activity in the volcanic area. Therefore, we consider that the volcano may be alive again.

Revision of P-wave Velocity and Thickness of Hydrate Layer in Shenhu Area, South China Sea

To revise P-wave velocity and thickness of the hydrate layer in the Shenhu area of the South China Sea, acoustic and resistivity logging curves are reanalyzed. The waterlogging phenomenon is found in the shallow sediments of five drilling wells, which causes P-wave velocity to approximate the propagation velocity of sea water(about 1500 m s-1). This also affects the identification of the hydrate layer and results in the underestimate of its thickness. In addition, because there could be about a 5 m thick velocity ramp above or below the hydrate layer as interpreted by acoustic and resistivity logging curves, the recalibrated thickness of this layer is less than the original estimated thickness. The recalibrated P-wave velocity of the hydrate layer is also higher than the original estimated velocity. For the drilling well with a relatively thin hydrate layer, the velocity ramp plays a more important role in identifying and determining the thickness of the layer.

3D P-wave Velocity Structure and Active Tectonics in the Xinfengjiang Area of Guangdong

In this paper,we determined an earthquake sequence location in the Xingfengjiang area from June,2007 to July,2014 and the 3 D P-wave velocity structure by a simultaneous inversion method. On that basis,we studied the occurrence features of active tectonics and the earthquake source mechanism. The results show that the reservoir fracture system has a tendency to increase with gradual depth from southeast to northwest,consistent with gravitational field research results. There are 4 high velocity zones( HVZ) under the depth of the 7 km-12 km crust between the Xinfengjiang Reservoir dam and Xichang District,Dongyuan. The max velocity of the biggest HVZ which is under Xichang is 6. 3 km/s. Under the reservoir dam there is a strong tectonic deformation zone,as the center exit Renzishi fault( F_2),Nanshan-Aotou faults( F_4),Heyuan fault( F_1) and Shijiao-Xingang-Baitian fault( F_5),7 earthquakes with M_L≥ 5. 0( including M 6. 1 in March,1962) occurred at the high gradient zone of the HVZ Ⅲ and HVZ Ⅳ edge which has been under the reservoir dam since 1960, with relativity energy releasing more thoroughly. Moderate seismic activity occurred at the HVZ Ⅰ edge which has been under Xichang since 2012,and is a danger zone for M5. 0 earthquakes in the future.

Three-Dimensional Wind Field Retrieved from Dual-Doppler Radar Based on a Variational Method:Refinement of Vertical Velocity Estimates

In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method,avoiding a weighting parameter specification step.Compared with conventional dual-Doppler wind synthesis approaches,this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process,which is one of the main sources of errors.Then,through the accelerated Liebmann method,the vertical velocity is further reestimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause.The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation.Compared with the method proposed by O’Brien,this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability.Furthermore,the method proposed in this paper is applied to Doppler radar observation of a squall line process.It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display(VAD)method,and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations.There is a good correspondence between the divergence field of the derived wind field and the vertical velocity.And,the horizontal and vertical circulations within and around the squall line,as well as strong updrafts,the associated downdrafts,and associated rear inflow of the bow echo,are analyzed well.It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations.

A multi-scale 3-D crust velocity model in the Hefei-Chao Lake area around the southern segment of Tanlu Fault Zone

Regional high-precision velocity models of the crust are an important foundation for examining seismic activity,seismogenic environments,and disaster distribution characteristics.The Hefei-Chao Lake area contains the main geological units of Hefei Basin,with thick sediments and the Chao Lake depression.Several major concealed faults of the southern NNE-trending Tanlu Fault Zone cross this area.To further explore the underground distribution characteristics of the faults and their tectonic evolutionary relationship with adjacent tectonic units,this study used ambient noise data recorded by a seismic array deployed in Hefei City and Chao Lake,constructing a 3-D velocity model at the depth of 1–8 km.Then a multi-scale high-resolution 3-D velocity model of this area was constructed by this new upper crustal velocity model with the previous middle and lower crustal model.The new model reveals that a high-velocity belt is highly consistent with the strike of the Tanlu Fault Zone,and a low-velocity sedimentary characteristic is consistent with the Hefei Basin and Chao Lake depression.The distribution morphology of high and low velocity bodies shows that the sedimentary pattern of Hefei-Chao Lake area is closely related to the tectonic evolution of the Tanlu Fault Zone since the Mesozoic.This study also identifies multiple low-velocity anomalies in the southeastern Hefei City.We speculate that strong ground motion during the 2009 Feidong earthquake(magnitude of 3.5)was related to amplification by the thick sediments in the Hefei Basin.We also discuss further applications of multi-scale high-resolution models of the shallow layer to strong ground motion simulations in cities and for earthquake disaster assessments.