{"title":"An efficient method of predicting S-wave velocity using sparse Gaussian process regression for a tight sandstone reservoir","authors":"","doi":"10.1016/j.jappgeo.2024.105480","DOIUrl":null,"url":null,"abstract":"<div><p>The shear wave (S-wave) velocity plays a crucial role in interpreting the lithology in seismic data, identifying fluids and predicting reservoirs. However, S-wave velocity is often unavailable due to the high cost of measurement and technical constraints. Conventional methods exhibit limitations that potentially impact the accuracy or efficiency on predicting S-wave velocity. Moreover, these methods always ignore the uncertainty quantification associated with the predicted results. This paper proposes a sparse Gaussian process regression (SGPR) method to predict the S-wave velocity in tight sandstone reservoirs. SGPR is a highly efficient regression technique that is based on the Gaussian process regression (GPR) method. In the SGPR method, inducing inputs are introduced to approximate the kernel matrix to decrease the computational complexity. A sparse set of inducing inputs and kernel hyperparameters are optimized through minimizing the Kullback-Leibler (KL) divergence between the exact posterior distribution and the approximate one. In this study, we select several types of logging data, which include porosity, water saturation, shale content, lithology and P-wave velocity, as the inputs for the SGPR method to predict S-wave velocity. To validate its effectiveness, we use the SGPR method to predict S-wave velocity in tight sandstone and compare the results with those from the GPR method, the bidirectional long short-term memory (BiLSTM) method and the Xu-White model. Additionally, we conduct cross-validation to demonstrate the robustness of the SGPR method. Our findings indicate that the SGPR method presents better performance and significant advantages about the accuracy and efficiency. Moreover, the SGPR method offers uncertainty quantification for the predicted S-wave velocity.</p></div>","PeriodicalId":54882,"journal":{"name":"Journal of Applied Geophysics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Geophysics","FirstCategoryId":"89","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926985124001964","RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"GEOSCIENCES, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The shear wave (S-wave) velocity plays a crucial role in interpreting the lithology in seismic data, identifying fluids and predicting reservoirs. However, S-wave velocity is often unavailable due to the high cost of measurement and technical constraints. Conventional methods exhibit limitations that potentially impact the accuracy or efficiency on predicting S-wave velocity. Moreover, these methods always ignore the uncertainty quantification associated with the predicted results. This paper proposes a sparse Gaussian process regression (SGPR) method to predict the S-wave velocity in tight sandstone reservoirs. SGPR is a highly efficient regression technique that is based on the Gaussian process regression (GPR) method. In the SGPR method, inducing inputs are introduced to approximate the kernel matrix to decrease the computational complexity. A sparse set of inducing inputs and kernel hyperparameters are optimized through minimizing the Kullback-Leibler (KL) divergence between the exact posterior distribution and the approximate one. In this study, we select several types of logging data, which include porosity, water saturation, shale content, lithology and P-wave velocity, as the inputs for the SGPR method to predict S-wave velocity. To validate its effectiveness, we use the SGPR method to predict S-wave velocity in tight sandstone and compare the results with those from the GPR method, the bidirectional long short-term memory (BiLSTM) method and the Xu-White model. Additionally, we conduct cross-validation to demonstrate the robustness of the SGPR method. Our findings indicate that the SGPR method presents better performance and significant advantages about the accuracy and efficiency. Moreover, the SGPR method offers uncertainty quantification for the predicted S-wave velocity.
剪切波(S 波)速度在解释地震数据中的岩性、识别流体和预测储层方面起着至关重要的作用。然而,由于测量成本高和技术限制,通常无法获得 S 波速度。传统方法的局限性可能会影响预测 S 波速度的准确性或效率。此外,这些方法总是忽略与预测结果相关的不确定性量化。本文提出了一种稀疏高斯过程回归(SGPR)方法,用于预测致密砂岩储层中的 S 波速度。SGPR 是一种基于高斯过程回归(GPR)方法的高效回归技术。在 SGPR 方法中,引入了诱导输入来近似核矩阵,以降低计算复杂度。通过最小化精确后验分布与近似后验分布之间的 Kullback-Leibler (KL) 发散,对稀疏的诱导输入和核超参数集进行优化。在本研究中,我们选择了几种类型的测井数据,包括孔隙度、水饱和度、页岩含量、岩性和 P 波速度,作为 SGPR 方法预测 S 波速度的输入。为了验证其有效性,我们使用 SGPR 方法预测致密砂岩中的 S 波速度,并将结果与 GPR 方法、双向长短期记忆(BiLSTM)方法和 Xu-White 模型的结果进行比较。此外,我们还进行了交叉验证,以证明 SGPR 方法的稳健性。我们的研究结果表明,SGPR 方法性能更好,在准确性和效率方面具有显著优势。此外,SGPR 方法还能对预测的 S 波速度进行不确定性量化。
期刊介绍:
The Journal of Applied Geophysics with its key objective of responding to pertinent and timely needs, places particular emphasis on methodological developments and innovative applications of geophysical techniques for addressing environmental, engineering, and hydrological problems. Related topical research in exploration geophysics and in soil and rock physics is also covered by the Journal of Applied Geophysics.