Estimation of phase and group velocities for multi-modal ground roll using the ‘ phase shift ’ and ‘ slant stack generalized S transform based ’ methods-猫眼课题宝

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2011

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R. Askari;R. Ferguson;K. DeMeersman

相速度和群速度是多道地波分析（MASW）勘探中决定剪切波速度的两个重要因素。在这项研究中，我们提出了两种不同的方法。分别采用相移法和基于倾斜叠加广义S变换的方法估计相速度和群速度。相移法利用傅立叶域倾斜叠加的思想来估计相速度。基于倾斜叠加广义S变换的方法是在广义S变换的基础上，利用时频域的倾斜叠加思想。这些方法是鲁棒的估计相速度和群速度的地面滚动是多模态的。我们预计，通过反演的相速度和群速度的多模态地滚，更好地估计近地表剪切波速度将是可获得的。引言工程研究中最重要的目标之一是估算近地表的土壤刚度（Xia等人，2002年a）。由于土的刚度和剪切波速的相关性，剪切波速的准确估计是工程研究中的一个关键因素。虽然地震折射法是用于横波速度估计的常规方法之一（Palmer，1980），但是它们不能估计地质结构复杂的S速度（Xia等人，2002 b）或隐藏层（速度小于上层的层）存在（Sheriff和Geldart，1986）。作为折射方法的替代，分散表面波（瑞利波和洛夫波）的分析是用于估计剪切波速度的公知过程（例如，Evison等人，1959; Stokoe等人，1988; KeilisBorok，1989; Lay和Wallace，1995; Xia等人，1999年）。该方法是基于从真实的数据计算的面波频散曲线（相速度或群速度曲线）到垂直剪切波速度剖面的反演。一些研究表明，该方法克服了折射方法的缺陷，例如地质复杂性（Xia等人，2002 b）或隐藏层的存在（Feng et al.，2005年）。由于表面波方法是基于相速度和群速度对剪切波速度剖面的反演，因此为了真实地估计频散曲线而进行的数据处理是非常关键的。已经开发了许多算法来解决这个问题-p变换（McMechan和Yedlin，1981）、小波变换（Kulesh等人，2005; Holschneider等人，二○ ○五年; Kulesh等人，2008）和用于相速度的广义S变换（Askari和Ferguson; 2011），以及窄带通滤波（Herrmann，1973）、小波变换（Kulesh等人，2005; Holschneider等人，2005）和群速度的广义S变换（Askari和Ferguson，2011）。Askari，Ferguson，and DeMeersman 2 CREWES Research Report - Volume 23（2011）多道面波分析（MASW）是一种基于多道地震记录地滚的面波方法，用于近地表研究（Park，1999）。在这项研究中，我们提出了两种方法估计的相速度和群速度的MASW调查分别。相移（Park等人，1998）是一种基于从一个道到另一个道的傅立叶相位谱差的估计来估计相速度的方法。然后，我们介绍了一种基于广义S变换（Pinnegar和Mansinha，2003）的倾斜叠加模型来估计多通道地滚的群速度。考虑时距域u（t，x）中包含地滚的地震记录，每条记录道的傅里叶变换表示为U（x，t）= u（x，t）edt。(1)上面的等式可以重写为：

Phase and group velocities are two important factors that determine shear wave velocity in Multi-channel Analysis of Surface Wave (MASW) surveys. In this study, we present two different methods. The phase shift method and the slant stack generalized S transform based method for the estimation of the phase and group velocities respectively. The phase shift method uses the idea of the slant stack in the Fourier domain to estimate the phase velocity. The slant stack generalized S transform based method uses the slant stack idea in the time-frequency domain based on the generalized S transform. These methods are robust to estimate phase and group velocities where ground roll is multimodal. We anticipate that, through inversion of the phase and group velocities of multimodal ground rolls, a better estimation of near surface shear wave velocity will be obtainable. INTRODUCTION One of the most important goals in engineering studies is the estimation of soil rigidity for the near surface (Xia et al., 2002a). Due to the dependency of soil rigidity and shear wave velocity, accurate estimation of shear wave velocity is a key factor in engineering studies. Although, seismic refraction methods are one of the conventional methods used for shear wave velocity estimation (Palmer, 1980), they fail to estimate S-velocity where geological structure is complex (Xia et al., 2002b) or where hidden layers (a layer whose velocity is less than its upper layer) are present (Sheriff and Geldart, 1986). As an alternative to the refraction methods, the analysis of dispersed surface waves (Rayleigh and Love waves) is a well-known procedure to estimate shear wave velocity (e.g. Evison et al., 1959; Stokoe et al., 1988; KeilisBorok, 1989; Lay and Wallace, 1995; Xia et al., 1999). The method is a based on the inversion of a surface wave dispersion curve (either phase or group velocity curves) calculated from a real data to a vertical shear wave velocity profile. Some studies indicate that the method overcomes the pitfalls of the refraction methods such as geological complexity (Xia et al., 2002b) or the presence of hidden layers (Feng et al., 2005). Since surface wave methods are based on the inversion of phase and group velocities to a shear wave velocity profile, the processing of data in order to truly estimate a dispersion curve is very crucial. Many algorithms have been developed to address this issue -p transform (McMechan and Yedlin, 1981), the wavelet transform (Kulesh et al., 2005; Holschneider et al., 2005; Kulesh et all, 2008) and the generalized S transform (Askari and Ferguson; 2011) for phase velocity, and narrow band-pass filtering (Herrmann, 1973), the wavelet transform (Kulesh et al., 2005; Holschneider et al., 2005) and the generalized S transform (Askari and Ferguson, 2011) for group velocity. Askari, Ferguson, and DeMeersman 2 CREWES Research Report — Volume 23 (2011) Multi-channel Analysis of Surface Waves (MASW) is a surface wave method based on multi-channel seismic recorded ground roll for near surface studies (Park, 1999). In this study, we present two methods for the estimation of the phase and group velocities for the MASW survey respectively. The phase shift (Park et al., 1998) is a method which is based on the estimation of the Fourier phase spectrum difference from one trace to another for the estimation of the phase velocity. Then, we introduce a slant stack model based on the generalized S transform (Pinnegar and Mansinha, 2003) to estimate the group velocity of multi-channel ground roll. PHASE SHIFT METHOD Considering a seismic record in the time-offset domain u(t,x) containing the ground roll, the Fourier transform for each trace is expressed U(x, ) = u(x, t)e dt. (1) The equation above could be rewritten as

Estimation of phase and group velocities for multi-modal ground roll using the ‘ phase shift ’ and ‘ slant stack generalized S transform based ’ methods

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