Randomized maximum likelihood based posterior sampling

Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples generated by minimization is not the desired target density, unless the observation operator is linear, but the distribution of samples is useful as a proposal density for importance sampling or for Markov chain Monte Carlo methods. In this paper, we focus on applications to sampling from multimodal posterior distributions in high dimensions. We first show that sampling from multimodal distributions is improved by computing all critical points instead of only minimizers of the objective function. For applications to high-dimensional geoscience inverse problems, we demonstrate an efficient approximate weighting that uses a low-rank Gauss-Newton approximation of the determinant of the Jacobian. The method is applied to two toy problems with known posterior distributions and a Darcy flow problem with multiple modes in the posterior.

     

Reconstruction and post-event analysis of a flash flood in a small ungauged basin: a case study in Slovak territory

Flash floods are one of the major natural hazards occurring in small streams with a negative effect on the country as well as on human lives. Heavy rainfall occurred on July 20, 2014 and July 21, 2014 and caused severe surface water flooding and a flash flood in the Malá Fatra National Park (Slovakia). The most affected was Vrátna Valley with the Varínka stream. This study presents a reconstruction and post-event analysis of a flash flood on small ungauged basin located in this protected area of Slovakia. The reconstruction included hydraulic terrain measurements on estimating the flood’s culmination and documenting the flood’s development. The measurements were taken at three cross sections of the Varínka stream. This paper is focused mainly on post-event analysis of the Varínka stream in two profiles: Strá?a (gauged profile) and Tiesňavy (ungauged cross section). Subsequently, the extremeness of the flash flood was preliminary evaluated. Results of the post-event analysis showed that the July 2014 flood was not the highest flood in this area despite its catastrophic consequences. By studying historical materials, we came to the conclusion that in the past (e.g. in 1848 or 1939) some devastating floods in this area had occurred, which had disastrous consequences for the population. The second part of the study is focused on comparing this flash flood with three major floods which have occurred in Slovak territory since 1998. The first flood occurred on the 20th of July, 1998 on the Malá Svinka stream, and the two others are floods which occurred on the 7th of June, 2011 in the Small Carpathian Mountains: on the Gidra stream in Píla village and on the Parná stream in Horné Ore?any village. Such comparison of flash floods from different geographical regions and different rainfall events can provide comprehensive information about their regimes, threats and disastrous effects.     

Tourmalines from the siderite-quartz-sulphide hydrothermal veins,Gemeric unit,western Carpathians,Slovakia: crystal chemistry and evolution

Mineralogy and Petrology - Tourmaline is an important gangue mineral in a large number of Cretaceous siderite-quartz-sulphide hydrothermal veins in the Gemeric Unit, Slovak Ore Mountains, Slovakia,...     

西藏拉萨岩体黑云母二长花岗岩：锆石U-Pb年龄、地球化学特征及其地质意义

拉萨岩体位于冈底斯铜、铁、铅锌多金属成矿带东段,是一个典型的复式岩体。通过对拉萨岩体开展详细的野外地质调查和岩相学观察,结合锆石LA-ICP-MS U-Pb定年、岩石地球化学分析等研究,认为拉萨岩体中代表性的黑云母二长花岗岩具有高SiO₂（含量为69.94%～76.62%,平均为72.18%）、高碱（Na₂O+K₂O=6.95%～8.44%,平均为7.44%）、较高CaO（含量为0.68%～2.53%,平均2.00%）的特点,相对富集Ba、Rb、Th,亏损Nb、Ta、P、Ti,LREE富集、HREE亏损,轻、重稀土元素分馏强烈,Eu负异常明显,是典型的钙碱性I型花岗岩。3件黑云母二长花岗岩成岩的锆石LA-ICP-MS U-Pb年龄为57±0.5Ma、58±1Ma、59±1Ma,表明其为古新世岩浆活动产物。综合研究认为,拉萨岩体黑云母二长花岗岩形成于印度与亚洲大陆主碰撞阶段（65～45Ma）,为底侵作用产生的大量壳源熔体与少量幔源熔体混合并发生一定程度分离结晶后的产物。陆内碰撞环境下的岩浆活动及元素的迁移和富集,为冈底斯成矿带内铜、金等矿产提供了良好的成矿条件。     

察右中旗马铃薯种植的气候条件分析与区划

通过对察右中旗马铃薯种植气候条件分析和生产现状的调查,利用相关分析方法得出影响马铃薯生产的关键气候因子,采用回归分析方法确定出区划因子,并建立了产量和产量平均相对变率与主要气象要素的关系模型,基于1:25万地理信息数据和气候因子空间分布模型,应用GIS分析技术实现了马铃薯气候资源区划,并进行了分区描述,提出了生产建议和减灾对策。为有效开发利用察右中旗农业气候资源,促进马铃薯种薯和商品薯生产基地建设,降低灾害风险提供科学依据。     

藏北高寒牧区NPP的时空变化特征及2 ℃全球变暖背景下的预估

利用多源气象要素数据估算了1998 - 2016年的藏北高寒牧区植被净初级生产力（Net Primary Productivity, NPP）的变化特征并预估了其在2 ℃全球变暖背景下的变化趋势, 结果表明： 研究区域71.9%的NPP呈上升趋势, 仅中部部分区域有下降趋势; 平均NPP以每年0.54%速率增加, 同期气温和降水均呈增加趋势, NPP和气温在2007前后有显著增加趋势; 总体来说降水是影响NPP的最主要气候因子, 且随着纬度升高其影响越来越大, 气温对于NPP的影响从东南向西北依次递减, 在西北地区出现弱的负相关; 在2 ℃全球变暖大背景下, 分析得出IPCC“典型浓度路径”（Representative Concentration Pathways, 简称RCPs）三种温室气体排放情景下（RCP2.6、 RCP4.5、 RCP8.5）的NPP平均状态几乎没有变化, 其影响仅限于对研究区东南部的较高NPP有较小的改善作用, 其作用依次为\mathrm{高}\mathrm{浓}\mathrm{度}\mathrm{排}\mathrm{放}\approx \mathrm{中}\mathrm{浓}\mathrm{度}\mathrm{排}\mathrm{放}>\mathrm{低}\mathrm{浓}\mathrm{度}\mathrm{排}\mathrm{放}, 表明气候变暖对研究区NPP影响有限, 预估结果对认清高原地区气候变化下NPP时空变化特征有重要意义。     

In-plane dynamic Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic(TI)half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf(1985),and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.     

Drained-to-undrained transition of bulk modulus in fluid-saturated porous rock induced by dead volume variation

We examine the effect of poroelastic boundary conditions when determining elastic properties of fluid-saturated porous rocks from forced-oscillation laboratory experiments. One undesired yet often unavoidable complication in the estimation of the undrained bulk modulus is due to the presence of the so-called dead volume. It implies that some fluid mass can escape the rock sample under applying a confining pressure perturbation. Thus, the dead volume compromises the undrained state required to unambiguously determine the undrained bulk modulus. In this paper, we model data of recently performed low-frequency (0.1 Hz) measurements. Therein, the dead volume has been systematically varied from 10% to 1000% of the pore volume. For the smallest dead volume, the inferred bulk modulus is close to the Biot–Gassmann undrained bulk modulus. With increasing dead volume, the experimentally inferred bulk modulus approaches the drained bulk modulus. We show that the transition from undrained to drained state as a function of dead volume can be modelled with a 1D poroelastic model for the rock sample-dead volume system with a boundary condition that honours the continuity of the fluid volume flux. We discuss the limitations of the 1D model when applied to data recorded at higher frequencies (up to 100 Hz).     

Seismic-impedance inversion with fuzzy clustering constraints: an example from the Carlin Gold District,Nevada, USA

The seismic reflection method provides high-resolution data that are especially useful for discovering mineral deposits under deep cover. A hindrance to the wider adoption of the seismic reflection method in mineral exploration is that the data are often interpreted differently and independently of other geophysical data unless common earth models are used to link the methods during geological interpretation. Model-based inversion of post-stack seismic data allows rock units with common petrophysical properties to be identified and permits increased bandwidth to enhance the spatial resolution of the acoustic-impedance model. However, as seismic reflection data are naturally bandlimited, any inversion scheme depends upon an initial model, and must deal with non-unique solutions for the inversion. Both issues can be largely overcome by using constraints and integrating prior information. We exploit the abilities of fuzzy c-means clustering to constrain and to include prior information in the inversion. The use of a clustering constraint for petrophysical values pushes the inversion process to select models that are primarily composed of several discrete rock units and the fuzzy c-means algorithm allows some properties to overlap by varying degrees. Imposing the fuzzy clustering techniques in the inversion process allows solutions that are similar to the natural geologic patterns that often have a few rock units represented by distinct combinations of petrophysical characteristics. Our tests on synthetic models, with clear and distinct boundaries, show that our methodology effectively recovers the true model. Accurate model recovery can be obtained even when the data are highly contaminated by random noise, where the initial model is homogeneous, or there is minimal prior petrophysical information available. We demonstrate the abilities of fuzzy c-means clustering to constrain and to include prior information in the acoustic-impedance inversion of a challenging magnetotelluric/seismic data set from the Carlin Gold District, USA. Using fuzzy c-means guided inversion of magnetotelluric data to create a starting model for acoustic-impedance proved important in obtaining the best result. Our inversion results correlate with borehole data and provided a better basis for geological interpretation than the seismic reflection images alone. Low values of the acoustic impedance in the basement rocks were shown to be prospective by geochemical analysis of rock cores, as would be predicted for later gold mineralization in weak, decalcified rocks.