# Numerical Modeling of Scholte Wave in Acoustic-Elastic Coupled TTI Anisotropic Media
## 1 Introduction  
Numerical modeling of acoustic-elastic coupled media is critical to the interpretation of shallow sea seismic data, and the accurate numerical simulation is of great significance for the later data processing and parameters inversion [1; 2]. However, the accurate simulation of the fluid-solid interface and construction of the Scholte waves are very challenging and are the signature problems in this research [3; 4; 5; 6; 7]. An additional challenge is the introduction of anisotropy in the research, and the assumption of isotropy can lead to the wrong imaging of underground structures and the reduction of resolution [8; 9; 10; 11]. Scholte waves are generated at a fluid-solid interface. Their energy is mainly distributed in the fluid, while the energy decays with depth in the solid [12; 13; 14; 15; 16; 17]. Similarly, there are also leaked Rayleigh waves at a fluid-solid interface, whose energy decays with depth in the solid with propagation characteristics similar to head waves [18]. Numerical studies have summarized the physical aspects of Scholte waves [19; 20; 21; 22]. If the value of the fluid sound velocity \(C_{f}\) is between the solid shear wave velocity \(C_{s}\) and the longitudinal wave velocity \(C_{L}\), Scholte waves can be generated at a fluid-solid interface. If \(C_{f}<C_{s}\), leaked Rayleigh waves are generated. If the acoustic impedance mismatch is large, the Scholte wave velocity is close to \(C_{f}\). Scholte waves do not decay along the direction of propagation, but lose energy in 3D due to geometric effect. There are two wavefield simulation approaches for modeling wave propagation in acoustic-elastic coupled media: (1) the partitioned approach [23; 24; 25; 26], where the acoustic wave equation and the elastic wave equation are used to describe wave propagation influid and solid phases, respectively. The partitioned method needs accurate kinematic and dynamic boundary conditions. A fluid-solid interface is usually treated with special mesh and coordinate mapping to match the two boundary conditions [27; 28; 29]; (2) the monolithic approach [30; 31; 32; 33; 34], where the elastic velocity-stress equation governs the wavefield in two-phase media without providing specific boundary conditions. Based on the wave equation, the synthetic pressure field is substituted into the first-order elastic velocity-stress equation; the first-order acoustic-elastic coupled equation is derived [33; 34]. The equation has accurate kinematic and dynamic characteristics, successfully simulates Scholte waves, and solves the artifact problem at the fluid-solid interface [31]. With the development of the research, vertical transverse isotropy (VTI) was introduced into the acoustic-elastic coupled equation [35]. It is now accepted that anisotropy media exists widely. Increasingly practical work has introduced anisotropy [36; 37], which greatly improved the imaging quality of underground structures and the interpretability of data [38; 39]. Anisotropy is also essential for the research of acoustic-elastic coupled media. Researchers demonstrated the presence of anisotropy in the salt floor of the Gulf of Mexico from seismic imaging using ocean-bottom data and borehole data [40]. Combined with the minute finite difference method (MFD) and fully staggered mesh (FSGs), the wavefield of VTI acoustic-elastic coupled media is accurately simulated [29]. Here, we define the underwater solid media as TTI (Tilted Transverse Isotropy) media, which is a type of transversely isotropic (TI) media with a tilted axis of symmetry. TTI media have different velocities along the axis of symmetry and perpendicular to the axis of symmetry. It can be seen as a tilted form of VTI (Vertical Transverse Isotropy) media with a vertical axis of symmetry. And we describe Scholte waves in 3D integrally to understand characteristics of the Scholte wave. In this paper, we adopt the monolithic approach to simulate the wavefield of acoustic-elastic coupled TTI media.