Principle of prestack migration based on the full elastic two‐way wave equation

Abstract

The acoustic approximation in seismic migration is not allowed when the effects of wave conversion cannot be neglected, as is often the case in data with large offsets. Hence, seismic migration should ideally be founded on the full elastic wave equation, which describes compressional as well as shear waves in solid media (such as rock layers, in which shear stresses may play an important role). In order to cope with conversions between those wave types, the full elastic wave equation should be expressed in terms of the particle velocity and the traction, because these field quantities are continuous across layer boundaries where the main interaction takes place. Therefore, the full elastic wave equation should be expressed as a matrix differential equation, in which a matrix operator acts on a full wave vector which contains both the particle velocity and the traction. The solution of this equation yields another matrix operator. This full elastic two‐way wave field extrapolation operator describes the relation between the total (two‐way) wave fields (in terms of the particle velocity and the traction) at two different depth levels. Therefore it can be used in prestack migration to perform recursive downward extrapolation of the surface data into the subsurface (at a “traction‐free” surface, the total wave field can be described in terms of the detected particle velocity and the source traction). Results from synthetic data for a simplified subsurface configuration show that a multiple‐free image of the subsurface can be obtained, from which the angle‐dependent P-P and P-SV reflection functions can be recovered independently. For more complicated subsurface configurations, full elastic migration is possible in principle, but it becomes computationally complex. Nevertheless, particularly for the 3-D case, our proposal has improved the feasibility of full elastic migration significantly compared with other proposed full elastic migration or inversion schemes, because our method is carried out per shot record and per frequency component.

An excitation potential imaging condition for elastic reverse time migration

“…On the other hand, the full elastic wave equation takes the compressive (P-) and shear (S-) wave propagation on the subsurface into account (Wapenaar et al, 1987). This is more consistent with actual earth materials.…”

“…Many researchers have previously explored this aspect (e.g., Baysal et al, 1983;Chang and McMechan, 1986, 1994Du and Qin, 2009;Levin, 1984;Sun and McMechan, 2001;Sun et al, 2006;Wapenaar et al, 1987;Sava, 2008, 2009;Yan and Xie, 2012;Yoon and Marfurt, 2006;Zhe and Greenhalgh, 1997). However, some problems still remained.…”

Imaging strategies using focusing functions with applications to a North Sea field

“…a direct wave) in the imaging condition eliminates some crosstalk between source-side wavefields and unrelated events in the receiver-side wavefield (Wapenaar et al 1987;da Costa Filho et al 2015).…”

Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

“…Because seismic waves propagate through the earth as a superposition of P-and S-wave modes, an elastic wave equation is usually more accurate for wavefield extrapolation than an acoustic wave equation. Wave mode decoupling can not only help elastic imaging to produce physically interpretable images, which characterize reflectivities of various reflection types (Wapenaar et al, 1987;Dellinger and Etgen, 1990;Yan and Sava, 2008), but it can also provide more opportunity to mitigate the parameter trade-offs in elastic waveform inversion (Wang and Cheng, 2015).…”