ABSTRACT In this paper, we develop a general approach to integrating petrophysical models in three‐dimensional seismic full‐waveform inversion based on the Gramian constraints. In the framework of this approach, we present an example of the frequency‐domain P‐wave velocity inversion guided by an electrical conductivity model. In order to introduce a coupling between the two models, we minimize the corresponding Gramian functional, which is included in the Tikhonov parametric functional. We demonstrate that in the case of a single‐physics inversion guided by a model of different physical type, the general expressions of the Gramian functional and its gradients become simple and easy to program. We also prove that the Gramian functional has a non‐negative quadratic form, so it can be easily incorporated in a standard gradient‐based minimization scheme. The developed new approach of seismic inversion guided by the known petrophysical model has been validated by three‐dimensional inversion of synthetic seismic data generated for a realistic three‐dimensional model of the subsurface.

中文翻译：

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使用 Gramian 约束将已知岩石物理模型纳入地震全波形反演

摘要 在本文中，我们开发了一种基于 Gramian 约束的在三维地震全波形反演中集成岩石物理模型的通用方法。在这种方法的框架内，我们展示了一个由电导率模型引导的频域 P 波速度反演的例子。为了在两个模型之间引入耦合，我们最小化了相应的 Gramian 泛函，该泛函包含在 Tikhonov 参数泛函中。我们证明，在由不同物理类型的模型引导的单物理反演的情况下，Gramian 泛函及其梯度的一般表达式变得简单且易于编程。我们还证明了 Gramian 泛函具有非负二次形式，所以它可以很容易地合并到一个标准的基于梯度的最小化方案中。由已知岩石物理模型引导的新开发的地震反演方法已通过对真实地下三维模型生成的合成地震数据进行三维反演验证。