The optimization approach to lithological tomography: Combining seismic data and petrophysics for porosity prediction
The optimization approach to lithological tomography: Combining seismic data and petrophysics for porosity prediction
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DOI：
10.1190/1.1801944
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发表时间：
2004-09
期刊：
影响因子：
3.3
通讯作者：
M. Bosch
中科院分区：
文献类型：
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作者：
M. Bosch
最小二乘模型优化方法通常用于通过用非线性模型拟合地球物理数据来估计物理介质属性。我把这个公式扩展到联合估计介质的物理性质和岩性描述。将岩石物理信息纳入反演方案中，通过描述岩性和介质物理之间的地质统计关系，提供了岩性和介质物理之间的耦合。由此产生的过程迭代地调整联合模型，以同时拟合地球物理数据，岩石物理统计介质描述，和岩性的先验信息，下面的方程推导出牛顿的优化方法。虽然需要更多的计算来合并附加信息并估计模型更新，但是线性化方程的代数系统可以被适当地变换以保持在常规逆公式的相同维度内。在岩石物理变换是线性的特定情况下（即，提供物理参数的期望值的岩性参数的函数），岩性反演方程等效于常规反演的相应方程，随后进行岩石物理学逆变换。我说明的方法与合成的例子孔隙度阻抗估计从零偏移距地震数据，使用Wyllie变换构造孔隙度和阻抗之间的统计关系。当测试模型的孔隙度范围处于岩石物理变换的非线性部分时，岩性反演的效果明显优于常规反演。当孔隙度范围在变换的几乎线性部分时，两种方法的性能是等同的。
Least-squares model optimization methods are commonly used to estimate physical media properties by fitting geophysical data with nonlinear models. I extend this formulation to joint estimation of physical properties and lithological description of the media. Incorporation of petrophysical information within the inversion scheme provides the coupling between lithology and media physics by describing the geostatistical relation between them. The resulting procedure adjusts iteratively the joint model to simultaneously fit geophysical data, the petrophysical statistical medium description, and prior information on the lithology, following equations derived for the Newton’s optimization method. Although more calculations are required to incorporate the additional information and estimate the model update, the algebraic system of linearized equations can be transformed appropriately to remain within the same dimensions of the conventional inverse formulation. In the particular case when the petrophysical transform is linear (i.e., the function of lithological parameters that provides the expected values of the physical parameters), the lithological inversion equations are equivalent to the corresponding equations of a conventional inversion followed with the inverse petrophysical transform. I illustrate the methodology with synthetic examples of porosity-impedance estimation from zero offset seismic data, using Wyllie’s transform to construct the statistical relationship between porosity and impedance. When the porosity range of the test models is on the nonlinear part of the petrophysical transform, the lithological inversion performs significantly better than the conventional inversion. When the porosity range is on an almost linear part of the transform, the performances are equivalent for both approaches.