Cruz Danilo Santos, de Araújo João M, da Costa Carlos A N, da Silva Carlos C N
Programa de Pós-Graduação em Ciência e Engenharia do Petróleo, Universidade Federal do Rio Grande do Norte, Natal 59064-741, Brazil.
Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal 59064-741, Brazil.
Entropy (Basel). 2021 May 13;23(5):599. doi: 10.3390/e23050599.
Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.
全波形反演是获取高分辨率地下信息的一种有利技术。在石油工业中，主要是在储层表征方面，通常将来自井的信息用作先验信息，以减少所得结果的模糊性。为此，我们建议在全波形反演的形式体系中添加一个相对熵项。在这种情况下，熵将仅仅是正则化的一个名称，并将起到帮助收敛到全局最小值的作用。熵在反问题中的应用通常涉及问题的公式化，以便能够使用统计概念。为避免这一步骤，我们建议对全波形反演进行确定性应用。我们将讨论相对熵的一些方面，并展示三种不同的方法，通过在反问题中利用熵来添加先验信息。我们使用动态加权方案通过熵来添加先验信息。其理念是，先验信息有助于在反演过程开始时找到全局最小值的路径。在所有情况下，先验信息都可以非常快速地纳入全波形反演中，并引导反演得到期望的解。当我们将构成熵的对数加权纳入反问题时，我们将抑制低强度波动并锐化点事件。因此，相对于全波形反演添加熵可以提供具有更好分辨率的结果。在BP 2004模型中存在盐的区域，通过对合成数据利用相对熵添加先验信息，我们取得了显著的改进。我们将表明，在全波形反演形式体系中通过熵添加的先验信息将被证明是一种避免局部最小值的方法。
