二维位场向上延拓和向下延拓的样条函数法

本文用样条函数法实现了二维位场的向上延拓和向下延拓,向上延拓用样条函数法计算泊松积分,向下延拓用样条函数法求解第一类Ｆｒｅｄｈｏｌｍ积分方程。模型和实例计算表明,本文方法正确可行且精度高。     

一种三维重、磁异常的向上延拓的近似计算

本文利用立体角求和的方法对向上延拓进行近似计算。方法假设边界平面上第一小元域内的场值对延拓值的贡献与小元域对延拓点所张的立体角有关。求出立体角就能够求出延拓系数。实例计算表明减少了边缘的损失,其结果可与原有的积分延拓方法相比拟。     

二维位场向上延拓与向下延拓的样条函数法

本文用样条函数法实现了二维位场的向上延拓和向下延拓，向上延拓用样条函数法计算泊松积分，向下延拓用样条函数法求解第一类Ｆｒｅｄｈｏｌｍｔｍ积分方程。模型和实例计算表明，本文方法正确可行且精度高。     

用三维积分插值法延拓程序计算二维单剖面的试验情况

三维积分插值法延拓是一种根据某个已知的观测平面上的位场值,来近似地计算场源以上空间任意一点位场的方法。在磁力重力勘探资料解释中应用较广。大家知道三维积分插值法向上延拓的近似公式为:     

基于互相关成像条件的保幅高斯束逆时偏移

常规的逆时偏移算法都是基于双程波动方程的数值解法,实际上利用Kirchhoff积分进行波场延拓,也可以实现逆时偏移。以Kirchhoff积分为基础,采用高斯束叠加积分表示的格林函数来表示正反向延拓波场,将正反向延拓波场进行保幅的互相关得到地下成像。保幅高斯束逆时偏移方法结合了射线类偏移方法的高计算效率和逆时波动方程偏移的高精度,能很好地处理焦散点、陡倾角等问题,并且具有面向目标成像的能力,并消除了偏移过程中的几何扩散效应和入射角变化引起的振幅误差。     

用叠加求和方法进行位场延拓和变换(上)

在重磁数据处理中,目前空间域的延拓方法,效果良好。但也各自存在某些不足,积分插值法边部丢点较多,在数据少时便无法进行计算;其所用下延插值函数取4次多项式,不能反映在场源界面奇异的客观规律;一些归结为解线性方程组以     

重力全梯度张量的延拓

以傅里叶变换为基础,证明了重力全梯度张量满足拉普拉斯方程,进而实现了梯度张量的延拓计算.三维断层模型试验结果表明,基于傅里叶变换的梯度张量向上延拓计算在理论上是严密且可以实现的,计算误差主要是由有限的积分范围所致,延拓高度越高则误差越大.而梯度张量的向下延拓则属于不适定问题.一般情况下,当延拓高度大于三倍点距时即出现严重的振荡现象,导致有用梯度张量信息的淹没.结合黑龙江省虎林盆地的梯度张量,验证了梯度张量延拓的实用性.     

二维位场曲面延拓的等效源法

在任意起伏地形条件下,重磁位场解析延拓(简称曲面延拓)原理、方法的研究是位场解释理论中一个难度较大的重要课题,许多物探工作者做了大量工作,其中布哈塔卡尼亚(B.K.Bhattacharyya,1979)等人提出的方法比较成功地解决了曲面延拓中的“上延拓”问题;“下延拓”问题,由于问题本身的复杂性,一直还没有令人满意的解决办法. 本文所论述的解析延拓原理和方法适用于任意起伏地形条件下的解析延拓,既可以作“上延拓”,也可以作“下延拓”.限于篇幅,本文只讨论二维问题.     

优选延拓技术及其在中国布格重力异常图处理上的应用

从维纳滤波原理出发 ,应用多层格林等效层模型精确模拟实测重磁场的径向对数功率谱 ,实现了重磁场在频率域的优选延拓。通过理论模型实验 ,证实了优选延拓算子具有向上延拓时不过分衰减低频信号、向下延拓时不过分突出或压制高频信号的选择性功能。根据优选向上延拓可以保证低频成分不衰减的性质 ,能够较为精确地提取区域异常 ,进而分离出局部异常。利用优选向下延拓可以对指定波段放大 ,而对其他波段保持全通的特征可以实现对某一深度或尺度的局部异常有选择地增强。运用优选延拓技术对中国大陆布格重力异常进行了增强与分离处理 ,获得了基于最佳滤波原理计算的中国大陆区域重力异常、剩余重力异常和带通重力异常。为研究中国大陆表层的岩石物性结构及平面分布特征提供了新的资料 ,同时也说明了优选延拓技术具有广阔的应用领域     

矿产预测中重磁异常变换的若干问题 二、向上延拓的作用及问题

在矿产预测中,对大面积观测的重磁数据作向上延拓处理,似乎已是一种例行作法。但在作向上延拓处理时,究竟延拓几种高度?具体的高度是多少?倒是值得研究和探讨的问题。有一位野外队的同志打算对 10000 km2的数据作向上延拓,并准备从 0．5 km到 50 km,共延拓七个高度。他问我这样作是否合适?     

重力异常三维反演——视密度成像方法技术的应用

将起伏地形上测量的重力异常,延拓至平均水平面;对平面上的重力场进行不同深度层源的切割分离;再将各层的重力场向下延拓至相应的深度,并反演出该深度层的密度结构.以此得到的密度,反映该深度层密度的近似分布,故称为视密度成像.在重力场的曲面向下延拓过程中,采用了新的延拓方法——迭代法,延拓深度大,延拓过程稳定;且不需解线性代数方程组,避开了制约三维反演实用化的计算时间的瓶颈问题.在主频1.73 GHz的微机上,完成71×81数据点反演的计算时间为10 s.以新疆一个地区的实例说明这种方法的反演效果.     

位场向下延拓的导数迭代法

针对向下延拓的不适定问题,提出了一种新的位场向下延拓方法-导数迭代法。从位场垂向一阶导数的定义出发,将观测面和向上延拓、向下延拓同等高度平面上的位场值近似联系起来,采用迭代法进行逐次逼近,推导出空间域位场向下延拓的导数迭代法的递推公式。考虑到空间域向上延拓积分方程实现的复杂性,对递推公式进行快速傅里叶变换,整理得到波数域中的导数迭代公式,同时证明了该方法的收敛性。模型检验和实例分析均表明迭代法相对直接FFT法具有稳定性强和下延深度大的优点。     

复小波变换反演重力异常

对国外最新研究位场连续复小波变换理论的一系列文章进行了系统归纳、推导与总结,推出了板状体重力场的小波变换系数解析式.对齐次场源形成的重力场进行柯西小波变换,等效于重力场向上延拓和求导两种运算相结合,并服从小波变换双尺度定律.利用小波变换系数模沿极值轴线的变化特征同时反演重力场源的几何形状、埋深、倾角.独立编写了所有程序,并对不同理论模型进行了大量计算,对所有结果进行了分析与讨论.此法为重力场反演提供了一条新的途径,实用于重磁资料自动化处理、反演与解释.     

利用位场连续复小波变换识辨磁场源(下)

基于齐次位场源的位场柯西小波变换，等效于位场向上延拓和求导两种运算相结合原理，建立了不同的理论模型，并编写了所有程序，通过合成资料的大量计算，对所有结果进行了验证与讨论。利用小波变换系数模沿极值轴线的变化特征，可以同时反演位场源的几何形状、埋深、倾角。实用于重磁资料自动化处理与解释，为磁场反演提供了一条新的途径。     

重力场向下延拓的三阶Adams-Bashforth公式法

重力场向上延拓是稳定且收敛的过程,而向下延拓是不稳定且发散的过程。为此,本文提出一种重力场向下延拓新方法。首先,对重力场及其垂向一阶导数向上延拓,得到不同高度的重力场垂向导数;然后,基于求解微分方程的三阶Adams-Bashforth多步法,推导出稳定的向下延拓公式;最后,为验证本文方法,将其分别应用于模型数据和实际数据。理论模型试验及误差曲线表明,相对于经典下延方法——傅里叶变换下延法和积分迭代下延法,新方法三阶Adams-Bashforth公式法下延过程稳定,边界效应不明显,下延深度可达5倍点距,下延结果与真实值的相对误差更小,结果更准确。将本文方法应用于加拿大某区实测航空重力数据,得到有效且准确的下延结果,能够识别和圈定一些细小异常特征。     

高精度重力资料的密度界面反演

Parker-Oldenburg法(PO)界面反演方法的核心算子是向下延拓,由于该算子的不稳定性,限制了PO反演法在重力密度界面反演应用中的发展.利用徐世浙提出的一种精度高、稳定性好的向下延拓的迭代法进行PO反演中的向下延拓,改进了PO反演中的稳定性.把改进的PO反演方法应用到理论模型和莺歌海基底反演中,均取得了较好的结果.     

The crustal structure of the Sahel Basin (eastern Tunisia) determined from gravity and geothermal gradients: implications for petroleum exploration

An analysis of Bouguer gravity anomaly data and geothermal gradient data obtained from bottom hole and drill stem tests temperature is used to determine the crustal structure of the Sahel Basin in eastern Tunisia and its role in the maturation and location of the large number of oil and gas fields in the region. The regional Bouguer gravity anomaly field is dominated by gradual increase in values from the northwest to southeast and is may be caused by crustal thinning as revealed by regional seismic studies. In addition, higher geothermal gradients in the same region as the Bouguer gravity anomaly maximum add an additional constraint for the existence of crustal thinning in the region. A detailed analysis of the Bouguer gravity anomaly data was performed by both upward continuation and horizontal gradients. These two techniques were combined to show that the study area consists of two structural regions: (1) the North–South Axis (NOSA)–Zeramedine region which is characterized by northwest-dipping, northeast-striking faults, thicker crust (30–31 km) and low geothermal gradients, and (2) the Mahres–Kerkennah region which is characterized by vertical, northwest-striking faults, thinner crust (28–29 km) and higher geothermal gradients. The correlation of a variety of features includes mapped and geophysically defined faults, volcanic rocks, a thinned crust and high geothermal gradients within the same location as known oil and gas fields indicate that the faults are a major factor in the location of these petroleum accumulations.     

基于位场分离方法的极地冰盖重力异常剥离：以模型试验为例

为了提高极地重力数据处理的质量,降低巨厚冰层对重力数据解释的影响,将极地大陆冰盖引起的重力异常从叠加异常中剥离出来成为极地重力数据处理的重要步骤之一。针对该问题,本文建立两个极地大陆冰层构造模型,对不同模型进行正演获得对应布格重力异常,再尝试利用三种位场分离方法,包括趋势分析法、向上延拓法和优化滤波法,对冰层引起的重力异常进行剥离试验,基于模型试验结果对比分析不同位场分离方法对极地冰层重力效应剥离的应用效果。模型试验结果显示,趋势分析法在冰层界面起伏较平缓情况下效果较好,但当冰层界面起伏复杂时难以用数学表达式精确拟合区域场,因此易在结果中引入虚假异常;向上延拓法在局部场源较浅的异常分离中效果较好,但由于极地模型冰盖深度较深及延拓高度选取不合理,在试验中出现了分离不足的情况;优化滤波法在相对复杂模型中分离效果相对好,但由于频段选取的主观性,使得该方法也易出现分离不足或过度情况。综合上述模型试验表明,在剥离极地冰盖引起的重力异常时,由于极地冰盖厚度起伏等地质情况复杂多变,应结合实际地质情况及其他可获得的地球物理资料进行综合分析,选择适用于具体情况的分离方法。     

MATLAB programs for the synthetic models

The separation of residual gravity anomaly from regional gravity has considerably been studied for many years in gravity explorations. In addition, it is considered as a critical step in gravity data inversion. Some techniques have been developed for regional–residual anomaly separation both in space and frequency domains. One of these techniques for computing the regional anomaly is nonlinear filtering. In this paper, some techniques such as low-pass filtering, Butterworth, upward continuation, and nonlinear filtering are used to on synthetic gravity data in present of random noise and noise free for the purpose of residual–regional anomaly separation. The obtained results of techniques are compared with each other. The results have shown that separation methods are so efficient where synthetic models are located in shallow depth. Moreover, it is found that in comparison with other separation techniques, nonlinear filtering is more efficient in residual–regional anomaly separation and upward continuation technique is more efficient than Butterworth filter and low-pass filter. In addition, all of the obtained results have shown that Butterworth and low-pass filters are the same.     

Regional geological and tectonic structures of the North Sea area from potential field modelling

The spatial distribution of large-scale crustal domains and their boundaries are investigated in the North Sea area by combining gravity, magnetic and seismic data. The North Sea is situated on the plates of three continents, Avalonia, Laurentia and Baltica, which collided during the Caledonian orogeny in the middle Palaeozoic. The location and continuation of the collisional sutures are debated. We apply filters and transformations to potential field data to focus on the crystalline crust and uppermost mantle on a regional scale in order to extract new information on continental sutures. The transformations reveal intrinsic features of crustal transitions between the Caledonian plates and their relation to later extensional structures. The transformations include the Hough Transform applied to the gravity field, calculation of fractional derivatives and integrals of the gravity and magnetic fields, the pseudogravity field and the horizontal gradient field as well as upward continuation. The results indicate a fundamental difference between the lithosphere of Avalonia, Laurentia and Baltica. The location of the Mesozoic rift system (the Central Graben and Viking Graben), may have been partly determined by the presence of the sutures between these three plate, indicative of extensional reactivation of compressional structures. A significant lineament across the entire North Sea between Scotland and North Germany indicates that the lower crust of Baltica provenance may extend as far south-westward as to this lineament. Comparison of the power spectra of the gravity field in five selected areas shows significant differences in the long wavelength components between the areas north and south of the lineament corresponding to differences in crustal properties. This lineament could represent the suture between lithosphere of Caledonian origin (Avalonia) versus lithosphere of Precambrian origin (Baltica) in the lower crust and upper mantle. If this is the case, the lineament is the missing link in the reconstruction of the triple plate collision.