断层图象层厚减薄的图象处理方法

本文全面讨论了断层图象层厚减薄的数字图象处理方法－断层间插值技术，详细介绍了现有的灰度插值和形状插值的思路、功能、实现步骤和优缺点。提出了深入研究的目标。     

福建定点和流动跨断层对台湾强震的反映及特征研究

借助Madab平台,应用能给出不同尺度下信号分解的近似部分和细节部分的小波变换方法．分析了福建省定点和流动跨断层场地的短水准形变观测资料。福建天马定点跨断层2003-2007年短水准观测资料的小波分析结果显示。分解到第七层的近似信号在极值和拐点出现前后往往有中强地震发生。由于福建省流动跨断层短水准测量为不定期观测,为取得等时间间隔的时序数据,我们采用三阶样条插值．在此基础上进行小波分析,发现分解到第三层的细节信号在台湾1999年“9．21”南投Ms7．6级地震前有明显的年变规律被破坏的现象．     

复杂构造条件下不同插值方法对MT二维有限元正演模拟的影响

以有限元法为基础,通过建立复杂的背斜模型、逆断层模型,比较了双线性插值和双二次插值方法对于复杂构造条件下的二维大地电磁正演模拟效果。结果显示,对于构造平缓的模型,2种插值方法均能较好地反映出模型的形态;对于构造起伏较大的模型,双二次插值法的效果要明显优于双线性插值法。     

分形插值对共炮集记录叠前逆时偏移的影响

利用分形插值方法对稀疏采样的地震记录进行了插值加密处理,并对原始记录和分形插值重建记录进行了叠前逆时偏移处理．数值实验表明,分形插值重建的地震图是原始地震图的良好近似,而分形插值叠前偏移剖面是原始记录偏移剖面的良好近似,二者的分辨率几乎一样．利用分形插值重建技术可以在节约经济成本的情况下,得到地下结构的高精度成像结果．      

1976年唐山地震震源动力过程的数值模拟

用新LDDA(Lagrangian DiscontinuousDeformation Analysis)方法模拟了唐山地震断层的破裂、错动和应力释放的整个动力过程．模拟结果表明,唐山地震的震源滑动过程在发震断层上各处不一样．近场位移受断层的曲率影响,断层凹侧的位移大于断层凸侧的位移．滑动过冲现象在震中处最大,并向断层两端衰减．我们发现,唐山地震断层的破裂速度和应力降与断层上的初始剪应力大小有关．唐山发震断层的最大动态、准静态位错量和剪应力降均发生在中间部位,分别是7.1 m、6.2 m和8.1 MPa、5.4 MPa,发震断层的平均准静态位错量和剪应力降分别为4.5 m和3.3 MPa,断层破裂的传播速度从震中向东南和西北方向分别为3.08 km/s和1.18 km/s．      

基于尺度分析的断层热信息遥感图像增强方法——以江山—绍兴断裂金衢段为例

根据热红外遥感影像上断层热信息具有特征几何尺寸的特点,以断层系统热信息分析为目标,提出了一种基于尺度分析的断层热信息遥感图像增强方法.在江山—绍兴断裂金衢段的实际工作中,通过断层两侧地表高温区域尺度分析、特征尺度网格抽样和样本插值成图等步骤,有效地降低了背景干扰,客观地描述了研究区与断层相关的热信息的空间分布形态及特征.多种尺度分析结果表明,在9 km2特征尺度上,断层热信息特征规律明显：地表高温区域沿北东走向的江山—绍兴断裂带和常山—漓渚断裂带两侧分布,呈线性特征;在淳安—温州断裂带与衢州—天台断裂带交叉位置地表温度较高.研究结果经实测资料验证,基本特征与实测资料相符.     

乌鲁木齐西山断层系的新构造变形特征与机制

通过对西山断层系详细地追踪考察和系列探槽的开挖,并结合深部探测资料进行了综合分析,认为晚第四纪以来,在近NS向的挤压应力作用下,西山块体不断向南侧天山山体方向发展,总体表现为向南的逆冲滑移和地壳缩短．其南侧的主控边界断裂——西山断层的新活动性主要表现为向南的逆冲．西山断层北侧的王家沟断层组和九家湾断层组是与西山断层具有成因联系的次级断层,均为伴随西山隆起形成的顺层滑动断层．但九家湾断层组明显受到博格达推覆体系的影响,是局部拉张应力下产生的正断层．这两组断层吸收转换了西山断层上盘的褶皱变形量,因而西山断隆表现为明显的单斜特征．西山断层系的各条次级断层属于同一发震构造体系,其大震的地震危险性应该合并考虑．      

具有分形结构强度分布的二维地震断层模拟

提出一种二维地震断层破裂模式，这是在一维弹簧-滑块模式的基础上建立的．利用这种断层的二维向量模型，研究了地震断层的动力学平面-应变的破裂问题．形象、直观地模拟了具有均匀或不均匀破裂强度分布的二维地震断层的破裂成核、扩展、传播直至停止的动力学全过程．阐明了在均匀预应力条件下，断层将获得足够的动量以克服破裂传播路径上的高强度障碍体．破裂锋面亦可绕过孤立的障碍体继续向前传播．整个模拟过程表明:断层破裂过程的停止条件对模拟地震破裂的全过程起着重要作用；我们还研究了断层面上破裂强度分布不均匀条件下断层的动态破裂过程，模拟了具有分形结构强度分布的二维地震断层产生的地震序列．它具有类似自然界地震现象的某些特征．这些特征主要取决于断层面上破裂强度的分布及初始应力降的大小．建立在实验和观测基础上的断层破裂过程模拟研究，为解释地震活动性统计规律的某些特征提供了物理基础.      

基于InSAR与GPS观测的汶川同震垂直形变场的获取

发震断层的形变是断层活动的重要参数之一,对认识断层性质、震源机理有重要作用。文中以逆冲性质为主的汶川地震为例,采用符合地表水平形变特征的Biharmonic样条插值对GPS水平形变矢量插值,然后再分解为EW和SN向分量。利用可靠的GPS观测值对InSAR参考点进行校正,统一两者的坐标系。通过对汶川地震视线向形变场剖面与GPS对比分析发现,断层上盘GPS与InSAR观测参考点相差9.93cm,而下盘则为-11.49cm。在此研究基础上,通过GPS水平形变场与InSAR视线向形变场联合解算,获取了汶川地震垂直连续形变场。结果表明,断层两侧垂直形变衰减较快,横跨断裂带形变量30cm的宽度不超过50km;沿发震断层附近垂直形变高值区分布不均匀,主要集中分布在发震断裂的汶川县城至都江堰段、茶坪—北川—南坝段和青川段。这3段各有特色,南段断层两侧垂直形变极不对称,主要以上盘剧烈抬升为主,最大抬升区域在映秀镇至连山坪一带,抬升量达到5.5m。中段表现为较强的反对称性,断层一侧抬升另一侧沉降。该段上盘最大抬升区域在茶坪东侧,抬升量为255cm,下盘最大沉降量在永庆,沉降量为-215cm。北端垂直形变相对较小,主要分布在青川北侧,呈对称分布,在发震断层最北端,最大抬升量为120cm。     

断层活动性定量评定之现状与展望

随着活断层理论研究的深入和工程评价要求的提高，对断层活动性仅作定性评价，已不能满足重大工程选址和设计的要求，而必须走量化评定的道路。作者分析了断层活动性定量评定之现状，科学京、工程师们虽已做了一些有益的尝试和实践，但当前仍处在探索研究阶段，至今尚未找到一个能被普遍接受的断层活动性量化评定标准。作者对断层活动性量化评定之前景亦做了展望，并着重指出几个今后应特别予以注意的问题：１．明确断层活动性的概念含义；２．找到影响断层活动性大小的主要因素；３．加强断层活动年代测定研究；４．重视活断层的地震活动和地表破裂研究；５．用概率论方法定量评定断层活动性。     

岩石圈磁场数据网格化方法研究

选取最小曲率、克里格、改进Shepard、反距离加权和径向基函数等5种网格化数学模型,对小江断裂地磁总强度加密区岩石圈磁场数据进行数据网格化,采用均方根预测误差和插值数据残差均方根等评价指标对网格化结果进行评价,结果表明,克里格插值与反距离加权插值法的精度最高。进一步比较克里格插值与反距离加权插值法的网格化图形质量,结果显示克里格插值网格化过程中兼顾了数据的平滑性和各实测点与待估点之间的空间位置关系,避免了系统误差,得出克里格插值更适用于岩石圈磁场数据网格化的结论。     

An improved interpolation scheme at receiver positions for 2.5D frequency-domain marine controlled-source electromagnetic forward modelling

An improved interpolation scheme is presented for 2.5-dimensional marine controlled-source electromagnetic forward modelling. For the marine controlled-source electromagnetic method, due to the resistivity contrast between the seawater and seafloor sedimentary layers, it is difficult to compute the electromagnetic fields accurately at receivers, which are usually located at the seafloor. In this study, the 2.5-dimensional controlled-source electromagnetic responses are simulated by the staggered finite-difference method. The secondary-field approach is used to avoid the source singularities, and the one-dimensional layered background model is used for calculating the primary fields excited by the source quasi-analytically. The interpolation of electromagnetic fields at the cell nodes for the whole computational domain to the receiver locations is discussed in detail. Numerical tests indicate that the improved interpolation developed is more accurate for simulating the electromagnetic responses at receivers located at the seafloor, compared with the linear or rigorous interpolation.     

Bedeutung von Transformationen in der Photogrammetrie

Summary Interpolation and projective methods are compared referring to corrections and or transformations of photogrammetric fields of points. Too many fixed points are needed for a reliable interpolation and, therefore, the interpolation methods are not economical. It is suggested to correct the image coordinates by means of the affine transformation, and the author states that four fiducial marks are sufficient for the transformation if they are placed in the image corners. The relations between the photogrammetric model on one side and the projection of the earth surface and the elevations above sea level on the other side are discussed.     

A vertical interpolation experiment

Summary Vertical interpolation of the data from the constant-pressure to the constant-density surfaces is discussed, and the results of an experiment given, wherein the data are interpolated to a constant-density surface using two different sets of the constant-pressure data. Comparison of the two results gives an estimate of the order of magnitude of the errors inherent in the interpolation.Hydrometeorological Institute of SR Serbia, Belgrade, Yugoslavia. The experiment reported here has been made while the author was visiting the National Center for Atmospheric Research, Boulder, Colorado.     

Bilinear surface smoothing for spatial interpolation with optional incorporation of an explanatory variable. Part 2: Application to synthesized and rainfall data

ABSTRACT

The non-parametric mathematical framework of bilinear surface smoothing (BSS) methodology provides flexible means for spatial (two dimensional) interpolation of variables. As presented in a companion paper, interpolation is accomplished by means of fitting consecutive bilinear surface into a regression model with known break points and adjustable smoothing terms defined by means of angles formed by those bilinear surface. Additionally, the second version of the methodology (BSSE) incorporates, in an objective manner, the influence of an explanatory variable available at a considerably denser dataset. In the present study, both versions are explored and illustrated using both synthesized and real world (hydrological) data, and practical aspects of their application are discussed. Also, comparison and validation against the results of commonly used spatial interpolation methods (inverse distance weighted, spline, ordinary kriging and ordinary cokriging) are performed in the context of the real world application. In every case, the method’s efficiency to perform interpolation between data points that are interrelated in a complicated manner was confirmed. Especially during the validation procedure presented in the real world case study, BSSE yielded very good results, outperforming those of the other interpolation methods. Given the simplicity of the approach, the proposed mathematical framework’s overall performance is quite satisfactory, indicating its applicability for diverse tasks of scientific and engineering hydrology and beyond.

Editor Z. W. Kundzewicz; Associate editor A. Carsteanu     

Interpolation of runoff applying objective methods

The paper treats the problem of interpolating annual runoff from regular streamflow measurements in a regional scale applying objective methods. These methods are adapted to point processes like temperature and precipitation. Modifications are needed to account for the fact that streamflow is an integrated process following the hierarchical structure of river systems. The most straightforward method is therefore to relate the interpolation to the existing river network. For theoretical reasons it is preferable to interpolate the lateral inflow rather than the flow in the river itself. Procedures for the interpolation with the different approaches are developed and discussed. Special attention is put on the question how the equation of continuity can be satisfied. The Laagen drainage basin in southern Norway is used as a test area. The data consist of annual observations of streamflow and digital map information on river networks and drainage basin boundaries.     

Reconstruction of the near‐offset gap in marine seismic data using seismic interferometric interpolation

In conventional seismic exploration, especially in marine seismic exploration, shot gathers with missing near‐offset traces are common. Interferometric interpolation methods are one of a range of different methods that have been developed to solve this problem. Interferometric interpolation methods differ from conventional interpolation methods as they utilise information from multiples in the interpolation process. In this study, we apply both conventional interferometric interpolation (shot domain) and multi‐domain interferometric interpolation (shot and receiver domain) to a synthetic and a real‐towed marine dataset from the Baltic Sea with the primary aim of improving the image of the seabed by extrapolation of a near‐offset gap. We utilise a matching filter after interferometric interpolation to partially mitigate artefacts and coherent noise associated with the far‐field approximation and a limited recording aperture size. The results show that an improved image of the seabed is obtained after performing interferometric interpolation. In most cases, the results from multi‐domain interferometric interpolation are similar to those from conventional interferometric interpolation. However, when the source–receiver aperture is limited, the multi‐domain method performs better. A quantitative analysis for assessing the performance of interferometric interpolation shows that multi‐domain interferometric interpolation typically performs better than conventional interferometric interpolation. We also benchmark the interpolated results generated by interferometric interpolation against those obtained using sparse recovery interpolation.     

医学图像三维重建的插值方法研究

本文从算法的形成过程、基本原理和步骤、适用范围和局限性、以及可能的改进方法等对现有三维重建的插值方法作了评述。探讨了各种插值方法之间的内在联系，分析了存在局限性的本质原因。对插值问题的进一步研究方向提出了看法。     

Smart averaging interpolation algorithm comparative test

In many practical cases, it is necessary to characterize the explored area with a regular set of geodata. Regular matrix data (e.g., ordinary maps) are calculated via existing data interpolation and extrapolation. For low frequency (oversampled) data acquired within a dense profile net (e.g., seismic three‐dimensional structural or gravity mapping), this procedure is mathematically more or less stable and, to a certain extent, unique since we might neglect discrepancies resulting from different interpolations. The situation is quite different for high‐resolution and high‐frequency contaminated data (e.g., raw seismic attributes or geochemistry measurements) represented by sparse profiling. Considering the variety of exploration cases, the investigation of different interpolation algorithm efficiency seems very important. Since it is impossible to compare all algorithms by means of formal mathematics, we have designed a test program. A representative set of seismic attribute maps has been artificially destroyed by introducing blank values (from 20% up to 95%) and then restored by different interpolation algorithms— bicubic, bilinear, nearest neighbor, and “smart averaging.” Smart averaging interpolation is done in a “live” window. The position, form, and size of the window are determined by some mathematical criterion on a trial‐and‐error basis. Discrepancies between restored and initial (true) data have been assessed and analysed. It is shown that the total (absolute) efficiency and comparative (relative) efficiency of the algorithms depend mostly upon the initial interpolant data characteristics. Identifying the best interpolation algorithm for all interpretive cases seems impossible. Some aspects of data processing are discussed in connection with interpolation accuracy.     

Interpolation of runoff applying objective methods

The paper treats the problem of interpolating annual runoff from regular streamflow measurements in a regional scale applying objective methods. These methods are adapted to point processes like temperature and precipitation. Modifications are needed to account for the fact that streamflow is an integrated process following the hierarchical structure of river systems. The most straightforward method is therefore to relate the interpolation to the existing river network. For theoretical reasons it is preferable to interpolate the lateral inflow rather than the flow in the river itself. Procedures for the interpolation with the different approaches are developed and discussed. Special attention is put on the question how the equation of continuity can be satisfied. The Laagen drainage basin in southern Norway is used as a test area. The data consist of annual observations of streamflow and digital map information on river networks and drainage basin boundaries.