Imaging conditions for elastic reverse time migrationImaging conditions for elastic RTM

Abstract

Elastic reverse time migration (RTM) has the ability to retrieve accurately migrated images of complex subsurface structures by imaging the multicomponent seismic data. However, the imaging condition applied in elastic RTM significantly influences the quality of the migrated images. We evaluated three kinds of imaging conditions in elastic RTM. The first kind of imaging condition involves the crosscorrelation between the Cartesian components of the particle-velocity wavefields to yield migrated images of subsurface structures. An alternative crosscorrelation imaging condition between the separated pure wave modes obtained by a Helmholtz-like decomposition method could produce reflectivity images with explicit physical meaning and fewer crosstalk artifacts. A drawback of this approach, though, was that the polarity reversal of the separated S-wave could cause destructive interference in the convertedwave image after stacking over multiple shots. Unlike the conventional decomposition method, the elastic wavefields can also be decomposed in the vector domain using the decoupled elastic wave equation, which preserves the amplitude and phase information of the original elastic wavefields. We have developed an inner-product imaging condition to match the vector-separated Pand S-wave modes to obtain scalar reflectivity images of the subsurface. Moreover, an auxiliary P-wave stress image can supplement the elastic imaging. Using synthetic examples with a layered model, the Marmousi 2 model, and a fault model, we determined that the inner-product imaging condition has prominent advantages over the other two imaging conditions and generates images with preserved amplitude and phase attributes. INTRODUCTION With the improvement of computation capacity and acquisition technology, elastic imaging (Yan and Sava, 2008; Du et al., 2017), and inversion (Feng and Schuster, 2017; Wang et al., 2018a) with multicomponent seismic data has already become increasingly feasible. Elastic imaging has the capability of providing more opportunities in understanding the subsurface through reflection images associated with S-waves (e.g., PS, SP, and SS images) as compared with acoustic imaging with single-component seismic data. Assuming no attenuation in the subsurface, the converted-wave images also have a higher resolution than the P-wave images because the converted waves have shorter wavelengths (Yan and Sava, 2008). Similar to the acoustic imaging technique, the elastic imaging technique includes three kinds of schemes: ray-based migrations (Kuo and Dai, 1984; Hokstad, 2000), one-way wave-equation migrations (Wu, 1994; Xie and Wu, 2005), and elastic reverse time migration (RTM) (Chang and McMechan, 1987, 1994). Among these elastic migration schemes, elastic RTM, which uses the two-way elastic wave equation for the propagation of elastic wavefields, is capable of accurately repositioning various kinds of seismic events (e.g., scattering, prismatic, and converted waves) into their actual geologic position in the subsurface and has no dip-angle limitation. For these reasons, elastic RTM is the most promising migration algorithm for multicomponent seismic data in complex geologic conditions. Elastic RTM was initially performed by Sun and McMechan (1986) for elastic seismic data recorded in vertical seismic profiles. Chang and McMechan (1987, 1994) implement 2D and 3D elastic RTM for multicomponent seismic data based on the excitation-time imaging condition (Chang and McMechan, 1986). However, in their imaging algorithm, the scattered Pand S-waves are imaged simultaneously, which produces subsurface images with unclear physical meaning and serious crosstalk artifacts created by the unseparated wave modes. Manuscript received by the Editor 17 March 2018; revised manuscript received 9 November 2018; published ahead of production 08 December 2018; published online 07 March 2019. Northeast Petroleum University, School of Earth Science, Daqing 163318, China. E-mail: [email protected]; [email protected] (corresponding author). © 2019 Society of Exploration Geophysicists. All rights reserved. S95 GEOPHYSICS, VOL. 84, NO. 2 (MARCH-APRIL 2019); P. S95–S111, 18 FIGS., 1 TABLE. 10.1190/GEO2018-0197.1 D ow nl oa de d 09 /1 3/ 19 to 1 .1 91 .1 10 .2 03 . R ed is tr ib ut io n su bj ec t t o SE G li ce ns e or c op yr ig ht ; s ee T er m s of U se a t h ttp :// lib ra ry .s eg .o rg / To decrease the crosstalk artifacts and make the images characterize explicit physical meaning, there are two practical RTM schemes used to migrate elastic seismic events. One is the scalar RTM for elastic seismic data implemented by Sun and McMechan (2001). This scheme first requires decomposition of the elastic seismic data recorded at the earth’s surface into the Pand S-wave components, and then two scalar RTMs are implemented to reposition the separated data using a respective migration velocity model. Although the mature scalar RTM technique with the separated Pand S-waves data can produce subsurface images that clearly describe the reflectivity of the pure wave modes at physical property interfaces, there are two issues in this procedure that require further investigation. One is that the separation of multicomponent seismic data recorded at the earth’s surface is often imperfect and may induce potential artifacts because of the lack of the vertical partial derivative. Another is that the scalar RTM does not accurately cope with the converted relationship of the wave modes and neglects the vector essence of the elastic wavefields. Another practical scheme separates the extrapolated elastic wavefields into pure Pand S-wave modes by the Helmholtz-like decomposition method before implementing an imaging condition (Yan and Sava, 2008; Du et al., 2012; Duan and Sava, 2015; Li et al., 2016; Wang et al., 2017), in which the decomposition method can be carried out by computing the divergence and curl of the extrapolated elastic wavefields in the isotropic case. This scheme is theoretically superior to the scalar RTM scheme because these constructed source and receiver wavefields using the full elastic wave equation are capable of characterizing the propagation of the elastic wavefields in elastic earth media very well. It not only correctly accounts for the wave-mode conversion and keeps the vector characteristics of the input multicomponent seismic data, but it also effectively avoids the crosstalk artifacts by using the wavefielddecomposition method. Nevertheless, this scheme still has two drawbacks. One is that the converted-wave image undergoes a polarity-reversal problem, which can lead to destructive interference when stacking multiple shots (Du et al., 2012). Additionally, in the 3D case, only if the 3C S-wave separated by the curl operator is scalarized (Du et al., 2014; Gong et al., 2018), the scalar reflection images associated with Swaves (e.g., PS, SP, and SS images) can be constructed by the conventional crosscorrelation imaging condition. There are some approaches to correct the polarity-reversal problem in the commonsource domain (Du et al., 2012; Duan and Sava, 2015; Li et al., 2016; Wang et al., 2017) and in the angle domain (Rosales and Rickett, 2001; Rosales et al., 2008). Unfortunately, these correction approaches in the common-source domain frequently rely on the propagation directions calculated by the Poynting vector or polarization vector in the time-space domain, which will become invalid when complex multipathings are involved (Ren et al., 2017). Although other straightforward correction schemes realized in the angle domain are more precise than those in the common-source domain, they rely on complicated angle-decomposition procedures and have a high computational cost. Consequently, without great effort toward overcoming this unfavorable factor, it is difficult to obtain a satisfactory converted-wave image. Another drawback in this scheme is that the conventional wavefield decomposition approach by calculating the divergence and curl operators involves the spatial derivatives on the displacement or particle-velocity components, which will lead to a π∕2 phase shift (Sun et al., 2001). Moreover, the amplitudes of the separated Pand S-waves are changed by 1∕VP and 1∕VS (VP is the P-velocity and VS is the S-velocity), respectively (Sun et al., 2011). Therefore, we must correct these separated waves before applying an imaging condition to obtain accurate angle-dependent image amplitudes. Recently, a novel decoupled elastic wave equation proposed by Ma and Zhu (2003) has been extensively used in elastic RTM (Xiao and Leaney, 2010; Zhang and McMechan, 2011; Gu et al., 2015; Wang and McMechan, 2015; Gong et al., 2016). According to the Helmholtz decomposition theory (Aki and Richards, 1980), the conventional coupled elastic wave equation can be decomposed into Pand S-wave component equations, which together are called the decoupled elastic wave equation. These two equations can accurately describe the decoupled Pand S-wave propagation, which retains the vector feature of the input elastic wavefields. According to Ma and Zhu’s (2003) derivations, Zhang et al. (2007) construct a decoupled version of Virieux’s (1986) staggered-grid stressvelocity formulation, in which the particle velocities of the Pand S-waves are solved simultaneously. Xiao and Leaney (2010) also introduce the auxiliary Pand S-wave stresses to decompose the coupled elastic wavefields in the vector domain. Unlike the conventional Helmholtz-like decomposition method that uses the divergence and curl operators, a valuable advantage of the decoupled elastic wave equation is that it can accurately preserve the amplitude and phase information of the input elastic wavefields. However, because the output wavefields from the decoupled elastic wave equation are both vectorial, a special imaging condition needs to be developed to exploit these decoupled vector wavefields as the input to generat