{"title":"An efficient pseudoelastic pure P-mode wave equation and the implementation of the free surface boundary condition","authors":"Xinru Mu, Tariq Alkhalifah","doi":"10.1111/1365-2478.13610","DOIUrl":null,"url":null,"abstract":"<p>Based on the elastic wave equation, a pseudoelastic pure P-mode wave equation has been recently derived by projecting the wavefield along the wavefront normal direction. This pseudoelastic pure P-mode wave equation offers an accurate simulation of P-wave fields with accurate elastic phase and amplitude characteristics. Moreover, considering no S-waves are involved, it is computationally more efficient than the elastic wave equation, making it an excellent choice as a forward simulation engine for P-wave exploration. Here, we propose a new pseudoelastic pure P-mode wave equation and apply the stress image method to it to implement the free surface boundary condition. The new pseudoelastic wave equation offers significantly improved computational efficiency compared to the previous pseudoelastic wave equation. Additionally, the wavefields simulated by this new pseudoelastic wave equation exhibit clear physical interpretations. We evaluate the accuracy of the new wave equation in simulating elastic P-waves by employing a model with high-velocity contrasts. We find that this new equation, which purely admits P-waves, though having exact amplitude and phase behaviour as the elastic waves for transmission components, the amplitudes slightly suffer in the scattering scenario. The difference in amplitude between the elastic and our pseudoelastic increases as the contrast in velocity at the interface (interlayer velocity ratio) increases, especially the S-wave velocities. This has negative implications on scattering from the free surface boundary condition or the sea bottom interface, especially if the shear wave velocity below the surface or the sea bottom is high. However, in cases where, like for land data in the Middle East, the transition to a free surface is smoother, the accuracy of the pseudoelastic equation is high. In all cases, regardless of the interlayer velocity ratio, the accuracy of the pseudoelastic wave equation in simulating the elastic case, for scattered waves, exceeds that of the acoustic wave equation in phase and amplitude.</p>","PeriodicalId":12793,"journal":{"name":"Geophysical Prospecting","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geophysical Prospecting","FirstCategoryId":"89","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/1365-2478.13610","RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
Based on the elastic wave equation, a pseudoelastic pure P-mode wave equation has been recently derived by projecting the wavefield along the wavefront normal direction. This pseudoelastic pure P-mode wave equation offers an accurate simulation of P-wave fields with accurate elastic phase and amplitude characteristics. Moreover, considering no S-waves are involved, it is computationally more efficient than the elastic wave equation, making it an excellent choice as a forward simulation engine for P-wave exploration. Here, we propose a new pseudoelastic pure P-mode wave equation and apply the stress image method to it to implement the free surface boundary condition. The new pseudoelastic wave equation offers significantly improved computational efficiency compared to the previous pseudoelastic wave equation. Additionally, the wavefields simulated by this new pseudoelastic wave equation exhibit clear physical interpretations. We evaluate the accuracy of the new wave equation in simulating elastic P-waves by employing a model with high-velocity contrasts. We find that this new equation, which purely admits P-waves, though having exact amplitude and phase behaviour as the elastic waves for transmission components, the amplitudes slightly suffer in the scattering scenario. The difference in amplitude between the elastic and our pseudoelastic increases as the contrast in velocity at the interface (interlayer velocity ratio) increases, especially the S-wave velocities. This has negative implications on scattering from the free surface boundary condition or the sea bottom interface, especially if the shear wave velocity below the surface or the sea bottom is high. However, in cases where, like for land data in the Middle East, the transition to a free surface is smoother, the accuracy of the pseudoelastic equation is high. In all cases, regardless of the interlayer velocity ratio, the accuracy of the pseudoelastic wave equation in simulating the elastic case, for scattered waves, exceeds that of the acoustic wave equation in phase and amplitude.
最近,在弹性波方程的基础上,通过沿波面法线方向投影波场,推导出了伪弹性纯 P 模波方程。这种伪弹性纯 P 模式波方程可以精确模拟 P 波场,并具有精确的弹性相位和振幅特征。此外,考虑到不涉及 S 波,它在计算上比弹性波方程更高效,因此是 P 波探索前向模拟引擎的绝佳选择。在此,我们提出了一种新的伪弹性纯 P 模波方程,并将应力图像法应用于该方程,以实现自由表面边界条件。与之前的伪弹性波方程相比,新的伪弹性波方程大大提高了计算效率。此外,新的伪弹性波方程模拟的波场具有清晰的物理解释。我们通过使用一个高速对比模型来评估新波方程模拟弹性 P 波的准确性。我们发现,这种纯粹接纳 P 波的新方程虽然在传输成分上与弹性波具有完全相同的振幅和相位行为,但在散射情况下振幅略有减弱。随着界面速度对比(层间速度比)的增大,尤其是 S 波速度的增大,弹性波与我们的伪弹性波之间的振幅差异也会增大。这对自由表面边界条件或海底界面的散射有负面影响,尤其是当表面或海底下面的剪切波速度较高时。然而,在一些情况下,如中东地区的陆地数据,向自由表面的过渡比较平滑,伪弹性方程的精确度很高。在所有情况下,无论层间速度比如何,伪弹性波方程在模拟弹性情况下的散射波时,其相位和振幅精度都超过声波方程。
期刊介绍:
Geophysical Prospecting publishes the best in primary research on the science of geophysics as it applies to the exploration, evaluation and extraction of earth resources. Drawing heavily on contributions from researchers in the oil and mineral exploration industries, the journal has a very practical slant. Although the journal provides a valuable forum for communication among workers in these fields, it is also ideally suited to researchers in academic geophysics.