Prestack Reverse-time Migration In TTI Media

The thin interbed produced by depositing periodically and the fracture arranged directionally lead to anisotropy. They can be described by the model of VTI and HTI respectively, which are collectivelly known as TI media. Under the field of stress from outside, the symmetry axis of TI media will be inclined, and then it will become TTI media, which generally develops in high dip angle structures of salt and its flank in which anisotropy exists. If the traditional isotropic or VTI reverse-time migration operator was used, the migration artifacts would appear in the final imaging results. The TTI reverse-time migration that anisotropy and the alteration of symmetry axis orientation are considered can produce higher-quality imaging profile. With the double-way wave equation as the theretical basis, principlly, it can make turning wave、prism wave、diffracted wave and mutiple energy focus and constring, imaging accuratly, and take full advantage of the abundant wave-field information. In this paper, we mainly discuss and analysis TTI reverse-time migration method.The establishment and modeling of TTI two-oder coupled qP-wave equations. Used the constitutive equations、motion differential equations and geometric equations, and combined with TTI elastic matrix, we deduced TTI elasto-dynamic equations of motions. Because of the limitation of TTI reverse-time migration implementation procedure, some simplified method must be developed. Therefore, we futher intrduce the main methods and thought to decomposite anisotropic elastic wave field. Based on the condition of acoustic assumption, in this paper, we elabrate the derivation of TTI qP-wave equations. Start from anisotropic qP-qSV wave exact dispersion relationship, the TTI two-order couple qP-wave equations given by Duveneck are derivated in detail with the obviouse physical meaning. After that, we build regular difference discrete format of second time derivative and ten space derivative of the equation, analysis its stable condition, and then implement numerical modeling combined with PML. Compared with the results of TTI elastic wave equations numerical modeling, it proves that TTI qP-wave equation can simulate the propagation characteristics of P-wave accurately and effectively. As for the problem of qSV-wave artifacts and numerical stability existed in TTI reverse-time migration, we discuss some efficient solutions. Synthetic examples verify the validity of methods. Prestack reverse time migration in TTI media. Firstly, we introduce the fundamental principle of reverse-time migration, and analysis the mechanism of production and coping strategy of low-frequency noise. In order to save computer memory space, we state the essence of random boundary condition and how to realize it in reverse-time migration. What is the important, it is extended to TTI media. Based on TTI two-order coupled qP-wave equations, we build TTI qP-wave double-way migration operator. The final imaging results got by using isotropic and anisotropic migration operator, respectively, show the efficiency and adaptability of it. Furthermore, we also realize the TTI elastic wave equation reverse-time migration, especially combined with random boundary condition and it achieve satisfactory results.