An Improved Perturbation Mechanism for Simulated Annealing Simulation

Simulated annealing (SA) is being increasingly used for the generation of stochastic models of spatial phenomena because of its flexibility to integrate data of diverse types and scales. The major shortcoming of SA is the extensive CPU requirements. We present a perturbation mechanism that significantly improves the CPU speed. Two conventional perturbation mechanisms are to (1) randomly select two locations and swap their attribute values, or (2) visit a randomly selected location and draw a new value from the global histogram. The proposed perturbation mechanism is a modification of option 2: each candidate value is drawn from a local conditional distribution built with a template of kriging weights rather than from the global distribution. This results in accepting more perturbations and in perturbations that improve the variogram reproduction for short scale lags. We document the new method, the increased convergence speed, and the improved variogram reproduction. Implementation details of the method such as the size of the local neighborhood are considered.     

Calculation of the Inverse of the Covariance

In reservoir characterization, the covariance is often used to describe the spatial correlation and variation in rock properties or the uncertainty in rock properties. The inverse of the covariance, on the other hand, is seldom discussed in geostatistics. In this paper, I show that the inverse is required for simulation and estimation of Gaussian random fields, and that it can be identified with the differential operator in regularized inverse theory. Unfortunately, because the covariance matrix for parameters in reservoir models can be extremely large, calculation of the inverse can be a problem. In this paper, I discuss four methods of calculating the inverse of the covariance, two of which are analytical, and two of which are purely numerical. By taking advantage of the assumed stationarity of the covariance, none of the methods require inversion of the full covariance matrix.     

Accounting for Estimation Optimality Criteria in Simulated Annealing

This paper presents both estimation and simulation as optimization problems that differ in the optimization criteria, minimization of a local expected loss for estimation and reproduction of global statistics (semivariogram, histogram) for simulation. An intermediate approach is proposed whereby an initial random image is gradually modified using simulated annealing so as to better match both local and global constraints. The relative weights of the different constraints in the objective function allow the user to strike a balance between smoothness of the estimated map and reproduction of spatial variability by simulated maps. The procedure is illustrated using a synthetic dataset. The proposed approach is shown to enhance the influence of observations on neighboring simulated values, hence the final realizations appear to be better conditioned to the sample information. It also produces maps that are more accurate (smaller prediction error) than stochastic simulation ignoring local constraints, but not as accurate as E-type estimation. Flow simulation results show that accounting for local constraints yields, on average, smaller errors in production forecast than a smooth estimated map or a simulated map that reproduces only the histogram and semivariogram. The approach thus reduces the risk associated with the use of a single realization for forecasting and planning.     

Numerical Method for Conditional Simulation of Levy Random Fields

Stochastic simulations of subsurface heterogeneity require accurate statistical models for spatial fluctuations. Incremental values in subsurface properties were shown previously to be approximated accurately by Levy distributions in the center and in the start of the tails of the distribution. New simulation methods utilizing these observations have been developed. Multivariate Levy distributions are used to model the multipoint joint probability density. Explicit bounds on the simulated variables prevent nonphysical extreme values and introduce a cutoff in the tails of the distribution of increments. Long-range spatial dependence is introduced through off-diagonal terms in the Levy association matrix, which is decomposed to yield a maximum likelihood type estimate at unobserved locations. This procedure reduces to a known interpolation formula developed for Gaussian fractal fields in the situation of two control points. The conditional density is not univariate Levy and is not available in closed form, but can be constructed numerically. Sequential simulation algorithms utilizing the numerically constructed conditional density successfully reproduce the desired statistical properties in simulations.     

Flow Simulations To Evaluate Upscaling of Permeability

We study upscaling of the permeability for porous media flow on a grid with one million blocks. The purpose is to illustrate how flow simulations can be used to evaluate upscaling methods.     

Closed Form Solutions of the Two-Dimensional Turning Bands Equation

The turning bands method generates realizations of isotropic Gaussian random fields by means of appropriately summed line processes. For two-dimensional simulations the relation between the isotropic correlation function of the random field and the correlation function to be simulated along the lines is given by an integral equation of Abel type. We present closed form solutions of this integral equation for almost all two-dimensional correlation models encountered in practice and discuss their numerical implementation. As an additional benefit, our tables and illustrations serve as a concise guide to correlation models useful in geostatistics.     

The main structure and tectonic features of the Chernorud-Mukhor site on the western shore of Lake Baikal from TEM and SP measurements

Transient electromagnetic (TEM), self-potential (SP) and geoelectrical mapping measurements were carried out at the Chernorud-Mukhor site in the Priolkhonje area on the western shore of the Lake Baikal. All measurements were made along several profiles across the main strike of the regional Primorsky fault. TEM measurements were carried out in a time range from a few tens of microseconds to several tens of milliseconds. The most important result of the 1D modelling of TEM soundings is the discovery of nearly horizontal boundaries that divide high resistive overlying and well conducting underlying rocks. The resistivity of the former is in the range from 100 Ωm to 1000 Ωm, while the resistivity of the latter varies from less than 1 Ωm to several tens of Ωm. This good conductive zone could also be verified by geoelectrical mapping using Schlumberger array (AB/2=100 m). Due to high conductivity of the underlying rocks only the upper boundary of the conductive layer could be determined by TEM soundings. A regional SP anomaly with amplitude of about −450 mV has also been observed above the low resistivity zone indicating the electron nature of its conductance. Geologically, the conductive zone is represented by a graphite-bearing layer within the region of archean rocks. Since that layer extends over a large area, it may be used as a key in studying structures and tectonics of the Priolkhonje area. A 1D TEM geoelectric section shows a wide, gently sloping syncline as a probable base structure of the Chernorud-Mukhor site. Neotectonic faults divide the syncline into vertically displaced blocks that form a wide complicated graben with a total amplitude of about 250 m.     

1994年9月16日台湾海峡7.3级地震震源过程的研究

采用数字化台网Ｐ波波形资料及台湾台网Ｐ波初动方向资料,研究了１９９４年９月１６日台湾海峡７３级地震及邻近地区（北纬２１～２６°,东经１１５～１２０°）ＭＬ≥５８级共５次地震的矩张量解及震源参数。结果表明,这次７３级地震的矩张量解以双力偶成分为主,是断层面接近ＮＷ走向的正断层。断层面的走向与大震前地震的条带分布走向及余震分布显示的破裂图象较相象,震源机制的张应力轴接近水平,近ＮＥ走向;压应力轴几乎垂直,近ＮＷＷ走向,似乎表明这次地震是受菲律海板块向欧亚板块北西向挤压的力源控制。从Ｐ轴接近竖直而Ｔ轴接近水平来看,发震断层为强烈拉张性正断层,可能还同时存在垂直向上的应力作用。其它４个强震的震源机制解与７３级大震的差别较大。这些地震震源机制解的复杂性,表明台湾海峡地震序列的发展过程比较复杂。     

Inversion of source process and related studies of the Taiwan Strait earthquake using genetic algorithm

Applying genetic algorithm to inversion of seismic moment tensor solution and using the data of P waveform from digital network and initial motion directions of P waves of Taiwan network stations, we studied the moment tensor solutions and focal parameters of the earthquake of M=7.3 on 16 September of 1994 in Taiwan Strait and other four quakes of M _L≥5.8 in the near region (21°–26°N, 115°–120°E). Among the five earthquakes, the quake of M=7.3 on September 16, 1994 in Taiwan Strait is the strongest one in the southeastern coast area since Nan’ao earthquake of M=7.3 in 1918. The results show that moment tensor solution of M=7.3 earthquake is mainly double-couple component, and is normal fault whose fault plane is near NW. The strike of the fault plane resembles that of the distributive bands of earthquakes before the main event and fracture pattern shown by aftershocks. The tension stress axis of focal mechanism is about horizontal, near in NE strike, the compressive stress axis is approximately vertical, near in NWW strike. It seems that this quake is controlled by the force of Philippine plate’s pressing Eurasian plate in NW direction. But from the viewpoint of P axis of near vertical and T axis of near horizontal, it is a normal fault of strong tensibility. There are relatively big difference between focal mechanism solution of this quake and those of the four other strong quakes. The complexity of source mechanism solution of these quakes represents the complexity of the process of the strait earthquake sequences. Contribution No. 98A01001, Institute of Geophysics, State Seismological Bureau, China. The subject is supported and helped by Academician Yun-Tai CHEN, Profs. Qing-Yao HONG, Zhen-Xing YAO, Tian-Yu ZHENG, Yao-Lin SHI, Ji-An XU, Bo-Shou HUANG and colleague Mei-Jian AN, Xue-Reng DING, Rui-Feng LIU. De-Chong ZHANG and Ming Li provided the digital data warm-heartedly. Lin-Ying WANG offered us the catalogue of earthquakes in southeastern coastal area in China. Xi-Li WANG and Tong-Xia BAI provided us the issued annual reports data. The authors would like to express their gratitude to all of these people. This paper is sponsored by the National Natural Science Foundation of China and Scientific and Technological Commission of Shantou, Guangdong Province.     

元代及其前历史强震目录增补与讨论（续）

在综合处理元代及其前地震震后救灾,减灾措施及社会影响的基础上,通过对比研究,对缺乏震害描述的地震进行了参数厘定,并对部分疑难地震进行了讨论,弥补了这一时期研究的不足。