CN1271863A - 获取多相介质中物理特性的优化模型的方法 - Google Patents

获取多相介质中物理特性的优化模型的方法 Download PDF

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CN1271863A
CN1271863A CN00106821A CN00106821A CN1271863A CN 1271863 A CN1271863 A CN 1271863A CN 00106821 A CN00106821 A CN 00106821A CN 00106821 A CN00106821 A CN 00106821A CN 1271863 A CN1271863 A CN 1271863A
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F·富尼耶
J·J·鲁瓦耶
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    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
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Abstract

本发明的方法可以通过变换,借助与介质中观测或测量的数据结构一致的更为定量的变换参数特性(例如标准偏差和相关长度)获得物理量的优化模型,该物理量代表了分层多相介质(该介质的阻抗与例如在其中传播的波有关)。通过定义这些参数的内在依赖性,有利于指导解释者选择用于参数所考虑的数值。最终的模型相对借助于纯粹经验选择而言得到了改进。

Description

获取多相介质中物理特性的优化模型的方法
本发明涉及获取多相介质中物理特性的优化模型的方法。
按照本发明的方法可以对波传播涉及的地下区域的阻抗建模，并且由此获取底土图像，从而更加精确地定位产生这些阻抗变化的非连续性。本发明适于定位碳氢化合物储层。
现在众所周知的是储层模型的精度和可靠性很大程度上取决于不同性质兼容数据的综合，这或多或少与所研究储层的性质相关。许多调查表明，地震数据能起作用的部分用于把储存的图象强制在钻井所处空间之间。
将地震数据综合入储层模型的一般方法是根据地震振幅估计声波或弹性波的阻抗并将它们转换为储层性质。
在各种逆转换算法中，利用先验模型的技术要求对数据和先验模型在优化中的各种影响的加权参数进行选择。
本申请人提交的专利EP-354,112(US-4,972,383)和EP-889,331描述了一种称为Interwell方法的方法，它可以获取代表地下区域声波阻抗变化的至少二维模型，它与观测或测量得到的数据(地质数据、堆积后地震数据或其他通过钻井获得的数据)匹配最好。它包括通过将钻井数据与已知结构或地层数据结合构造先验阻抗模型。特别是沿着地层单元内的相关表面沿着钻井Kriging已知的阻抗。地震层给出了地层单元的几何结构并且通过根据沉积模式跟随限定的表面完成相关性(平行于顶层或地面的协调)。随后通过考虑测得的地震振幅更新钻井间的初始阻抗分布。为此通过使两项代价函数最小迭代完成：
F＝Fs+Fg，这里
Fs为定义为某些指标的地震项，其代表从模型获得的合成轨迹与实际地震轨迹(堆积前轨迹、堆积后轨迹)振幅的差值的某种范数；而
fg为地理项，它测量先验模型与标准模型的差值。
优化阻抗模型根据两项的权重进行折衷。假定这种误差是随机变量，其指数协方差为σ2，相关长度为λ，这些权重与变换参数有关(即Fs与信噪比有关而Fg与相关长度λ和关于先验模型的误差的方差σ2有关)。
Fs的权重通常根据实际振幅估计。相反，相关长度为λ和标准偏差σ由用户根据他对先验模型的置信度而定义。但是由于对先验模型的置信度取决于数据的质量、钻井的数量和位置以及阻抗场的空间性态，所以不应太过于由经验估计。
本发明的方法可以通过变换，借助与介质中观测或测量的数据结构一致的更为定量的变换参数特性(例如标准偏差和相关长度)获得物理量的优化模型，该物理量代表了分层多相介质(该介质的阻抗与例如在其中传播的波有关)。通过定义这些参数的内在依赖性，有利于指导解释者选择用于参数所考虑的数值。最终的模型相对借助纯粹靠经验选择而言得到了改进。
它包含：从一定数量介质点测量、记录或观测获得的已知数据构造先验模型；以及通过考虑先验模型，根据要寻求的模型与已知数据之间的差值使代价函数最小化而构造优化模型。
本方法的特征在于先验模型的构造包括通过用kriging方法处理沿不连续性(分层方向)方向不同介质点物理量已知值之间的协方差(Cz)得到相关性，先验模型中物理量值的不确定性与介质中沿这些方向的各点相应的值有关，按照控制变换参数的协方差模型(Cε)，所述模型包括平稳协方差项(Cz)，它仅仅依赖于该点与非平稳协方差项之间的距离矢量(h)，非平稳协方差项取决于点的位置和分别与其他点之间的距离。
按照第一实施例，为了比普通先验模型更为精确地定义变换参数，平均协方差(Cε)被确定和调整至(已知类型的)平稳指数协方差模型。
按照第二实施例，为了获得变换参数的局部值(λx，σx)，在所有点上将协方差项(Cε)调整至平稳指数模型。
通过以下结合附图对本发明的描述，可以理解本发明的其他特征和优点，其中：
图1A、1B示出了三口钻井W1、W2和W3附近相关平面内kriging误差的两个协方差栅格，分别对应两种不同的距离矢量h，表示不确定协方差的非平稳性质；
图2示出了用介质标准变换参数获得的阻抗模型的实例；以及
图3示出了借助本发明方法获得的阻抗模型实例，其变换参数被更好调整至不确定协方差的性态。
由于通过kriging法构造先验模型，所以我们研究了主要控制地质项Fg权重的kriging误差的理论协方差。在普通kriging法中，如果Z为阻抗场而Z先验为kriging化阻抗场Z*，则误差表示如下：
ε(x)＝Z(x)-Z*(x)
如果x和y表示介质内距离为h的两个点，则误差ε(x)的协方差Cε(x，y)表示如下：h
Cε(x，y)＝Cz( h)-tβ(x)Kβ(x+ h)
这里K为kriging矩阵，β(x)和β(x+ h)为横坐标x和x+ h上的kriging权重，而 h为x至y的距离矢量，而tβ为权重β的转置。
两点x与y之间的理论误差协方差Cε(x，y)以允许构造先验模型的初始kriging协方差Cz( h)的形式出现，协方差大部分是各向同性的并且依赖于距离 h，由依赖于距离 h和所考虑点x位置的非平稳项tβ(x)Kβ(x+ h)修正。在远离钻井处，以初始协方差Cz( h)为主，而随着靠近钻井，第二项变得越来越重要。
以下以三口竖井的实际场例子描述这种性态。对于储层的分层单元，沿基部的平行表面，借助普通的指数模型(相关长度为750米，阻抗标准偏差为1122g/cm3.m/s)对阻抗作kriging化处理。如图1A和1B所示，计算两个距离矢量的相关误差的协方差。
方法包括选择与变换过程中综合的可用数据定量兼容的变换参数。最简单的途径无需变换算法修正，包括计算用于调整平稳指数协方差(专家已知的类型)的平均误差协方差
Figure A0010682100051
以自动获取平均变换参数
Figure A0010682100052
和
另一种方式是通过计算该点位置x的合适的校正项tβ(x)Kβ(x+ h)(它必需加入平稳项Cz( h))完成任意点的局部调整，并且通过借助平稳指数协方差逼近局部协方差确定局部变换参数λ＝λ和σ＝σ。
本方法容易使解释者采用kriging误差的空间性态来调整分配给地质项Fg的权重。
在上述实例中，本方法用于建模与传播的波(弹性波、电磁波等)有关的阻抗形式。显然本方法也可以用于建模其他形式的物理量，例如孔隙度、渗透率、饱和度等或与钻井测试有关的量。广义而言，本方法可以用于专家熟知的贝叶斯型变换模型。

Claims (4)

1.一种方法，它可以通过变换获得代表分层多相介质的物理量的优化模型，它包含：从借助与介质中一定数量点上的测量、记录或观测获得的已知数据构造先验模型，以及通过考虑先验模型，根据要寻求的模型与已知数据之间差值使代价函数最小化构造优化模型，其特征在于先验模型的构造包括通过用kriging方法处理沿不连续性(分层方向)方向不同介质点物理量已知值之间的协方差(Cz)得到相关性，先验模型中物理量值的不确定性与介质中沿这些方向的各点相应的值有关，按照控制变换(λ，σ)参数的协方差模型(Cε)，所述模型包括平稳协方差项(Cz)，它仅仅依赖于该点与非平稳协方差项之间的距离矢量(h)，非平稳协方差项取决于点的位置(x)和与其他点之间的距离( h)。
2.如权利要求1所述的方法，其特征在于为了定义变换参数(λ，σ)，确定调整至平稳指数协方差模型的平均协方差(Cε)。
3.如权利要求1所述的方法，其特征在于为了定义变换参数的局部值(λx，σx)，在所有点上将协方差项(Cε)调整至平稳指数模型。
4.如权利要求1所述的方法，其特征在于选择变换参数以定义与下述公式定义的误差协方差模型兼容的变换参数(λ，σ)：
Cε(x，y)＝Cz( h)-tβ(x)Kβ(x+ h)
这里x和y为介质内距离为 h的任意两点，K为kriging矩阵，β(x)和β(x+ h)为横坐标x和x+ h上的kriging权重，而 h为两点之间的距离矢量。
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