Computing dip-angle gathers using Poynting vector for elastic reverse time migration in 2D transversely isotropic media

Highlights

• An efficient algorithm based on the Poynting vector is proposed to obtain the dip-angle gathers for elastic reverse time migration.

• We use the optical flow method to improve the stability of the proposed algorithm.

• We use the dip-angle gathers to improve the imaging quality for anisotropic elastic reverse time migration.

Abstract

Angle-domain common-image gathers (ADCIGs) have wide applications in seismic imaging. For isotropic elastic reverse time migration (ERTM), we can produce dip-angle ADCIGs by using conventional Poynting vectors. Seismic anisotropy widely occurrs in Earth materials, such as in the shales and fractured reservoirs. ERTM based on the isotropic elastic wave equation is unable to accurately image anisotropic structures, leading to noise, discontinuous reflection events and mispositioning in migration results. Hence, conducting ERTM and generating dip-angle ADCIGs for anisotropic media require solving the anisotropic elastic wave equation. However, it is challenging to compute the gathers using the conventional Poynting vector for anisotropic elastic media. In this study, we derive the group and phase Poynting vectors, in which we use the optical flow method to stabilize the phase-related Poynting vectors. This approach admits efficient calculation of dip-angle ADCIG in anisotropic media. It also suppresses noise in anisotropic ERTM. The results of numerical experiments demonstrate the effectiveness of the proposed method.

Introduction

Angle-domain common-imaging gathers (ADCIGs) have become an important tool for seismic interpretation, velocity modeling, and amplitude variation with angle analysis (Sava and Alkhalifah, 2013, Dafni and Symes, 2016a, Liu, 2019). In recent years, scattering-angle ADCIGs, which have crucial applications in seismic imaging, and dip-angle ADCIGs, also got increasing attention, which can be used to enhance image quality for Kirchhoff migration (Dafni and Reshef, 2014) and implement stationary-phase procedures for prestack time migration (PSTM) (Xu and Zhang, 2017). Furthermore, the dip-angle ADCIGs are used to identify the seismic diffractions and reflections by their distinct responses (Moser and Howard, 2008, Klokov and Fomel, 2012). Moreover, incorporating information about the dip-angle and scattering-angle gathers presents significant advantages in the postmigration seismic process (Dafni and Reshef, 2014, Dafni and Reshef, 2015). For wave-equation migration, Dafni and Symes (2016b) computed the dip-angle ADCIGs by using Radon transform operators for a subsurface-offset extended image. They devised a specularity filter to obtain high-quality images by suppressing noise and non-specular signals in the dip domain. However, the computational cost is high for estimating gathers using the subsurface-offset gathers. To improve efficiency, Liu (2019) proposed to compute the dip-angle ADCIGs using the Poynting vector for isotropic ERTM. He used the specular filter of Dafni and Symes (2016b) to suppress migration artifacts for the ERTM images. These studies are examples of important applications of dip-angle ADCIGs in seismic migration.

Existing dip-angle ADCIGs calculation methods for wave-equation migration were developed for the case of isotropic media, whereas few studies have been conducted on dip-angle ADCIGs for anisotropic media. Anisotropy is present in a wide range of crustal rocks (Thomsen, 1986), including sedimentary rock sequences. Over the past several years, a lot of research has been conducted on acoustic RTM, in which pure P-waves are propagated using the pseudoacoustic equations in transversely isotropic (TI) media (Alkhalifah, 1998, Alkhalifah, 2000, Alkhalifah, 2014, Zhang and Zhang, 2008, Fletcher et al., 2009, Du et al., 2010, Duveneck and Bakker, 2011, Zhang et al., 2011, Li et al., 2017). In recent years, the increased use of the multi-component acquisition techniques, has lead to developments in elastic reverse-time migration (ERTM). A lot of research has been focused on ERTM (Yan and Sava, 2008, Duan and Sava, 2015, Wang and McMechan, 2015, Du et al., 2017, Li et al., 2018, Yu et al., 2018). Actually, anisotropy is an elastic feature prevalent in solids, requiring information not associated with the P-waves alone (Kazei and Alkhalifah, 2019, Wang et al., 2019), and the accuracy of imaging and inversion will improve with considering the elastic nature of the Earth (Oh and Alkhalifah, 2016). Therefore, this study investigates the implementation of ERTM using the anisotropic elastic wave equation (Yu et al., 2016, Wang et al., 2016, Hu et al., 2018, Wang et al., 2019) along with dip-angle ADCIGs, which are also needed for accurate computation of anisotropic ERTM.

Here, we employ the Poynting vector to generate the dip-angle ADCIGs due to its straightforward computation during wavefield extrapolation. However, the calculation of the dip-angle gathers for isotropic ERTM (Liu, 2019) cannot be extended directly to the anisotropic case. In isotropic media, the phase-velocity and group-velocity directions coincide with each other, whereas they differ in anisotropic media (Tsvankin, 2001, Yan and Dickens, 2016, Lu et al., 2019). Because of the reflection characteristics follow Snell’s law in the form of phase-velocity angle (Yan and Dickens, 2016), this angle must be used to compute the scattering and dip angles and to generate ADCIGs. The group-velocity angle may be used to compute ADCIGs for isotropic ERTM. However, we cannot estimate the Poynting vectors using ray (energy) components of the wave in anisotropic media, like in isotropic media. In this case, if the elastic Poynting vectors (Červený, 2000) correspond to the group-velocity direction, we need to transform the angles from group-velocity to the phase-velocity (Yan and Dickens, 2016, Lu et al., 2019) in order to generate ADCIGs. However, the process of relation between the group and phase velocities is complex (Yan and Dickens, 2016, Lu et al., 2019). To address this problem in computing dip gathers in anisotropic media, we develop a method that uses the estimated phase-related Poynting vectors to generate dip-angle ADCIGs. However, the Poynting vector method is often unstable to compute the wave propagation directions. To stabilize the Poynting vector directions, we adopt the optical flow (Zhang, 2014, Zhang et al., 2018) method to efficiently and accurately calculate dip-angle ADCIGs.

The main contents of this paper include the following aspects. First, we derive the group-related and phase-related Poynting vectors from the anisotropic elastic wave equation, and analyze their difference. Then, we apply the optical flow algorithm to stabilize the Poynting vector calculations, and effectively generate the dip-angle ADCIGs for anisotropic ERTM. Next, we perform several numerical tests on the developed scheme. Finally, we share our conclusions of the study.