Analysis Of One-way Wave Equation Migration Algorithm

One-way wave equation migration is an extremely effective seismic migration imaging algorithm, with the method of classic Kirchhoff integral migration, it avoid the hypothesis of the asymptotic wave equation. Compared with reverse-time migration, one-way wave equation is efficient, and saves the computer memory space. One-way wave equation migration is mainly about the equation of square root operator (i.e. phase-shift operator), use different methods of singularities, fit differential phase shift operators are approaching, in order to improve the calculation precision of one-way wave equation, and enhance the ability to complex geological conditions. This article is mainly aimed at the method of different transmission shift operator and impulse responses of one-way equation, and analysis a series of related dynamic properties of migration imaging. According to the phase shift operator of one-way wave equation methods, we can divide it into three different methods: the frequency domain (ω-kdomain), time - space domains (t-xdomain) and mixed domains (ω-xdomain). The algorithm ofω-kdomain is simpler, we can directly recursive calculation according to the extrapolating. Extrapolating of t-xdomain algorithm contains 2D convolution computation, we can use FFT to manage in theω-xdomain, only use one convolution. Nowωplays a part of parameter. In theω-xdomain we also use FFT conversion,ω-x domain and t-x domain method is a relatively simple extrapolation, only consider for smooth surface that it is independent on time. Whenω-xfield changes toω-kdomain, although simplified calculation, but lost flexibility, and lateral velocity variation cannot handle. The biggest advantage in theω-xdomain is aimed at that different frequency components can use different effective, in addition, the wavelet is calculated, has a good flexibility and adaptability.Under the condition of uneven medium, impulse response analysis method, different direction due to the t-xdomain of wave propagation, its velocity different wave field rays not perpendicular to face, including from Persia array of semicircle arc shape closed curve which areas for development, this area was invalid part. Disperse phenomenon is in phase shift operator due to the t-xdomain of solving the approximate expansion. Considering the resolution of the wavelet controlled by three factors, through the comparison between the mixed domain and t-xdomain finite difference method,ω-kdomain has a high resolution of wavelet, but t-xdomain finite difference method of oscillation amplitudes tail in the initial sampling points bigger error, so the mixed domain has an advantage in improving the resolution of wavelet. Through the spectrum analysis, it shows that the one-way wave operators applicationω-kdomain to earthquake has advantages of lighting, but because of the calculation principle , its speed limit is only in the case without change of lateral velocity. Mixed domain operator can reserve energy though relatively weak, but its complex geological conditions for earthquake lighting has good effect. t-xdomain can complex medium environment, and maintain relatively mixed domain method more energy, but this kind of method is limited, only can use in some of the application of geological model said illumination analysis.By understanding the different algorithms of adaptive, can provide a reference basis for practical production, also provide information for further improved algorithm. Due to the accuracy of the migration imaging decision in actual geological conditions and taking the compensation method is also selected processing method. Under the principle of classical significance on the migration technology can simply to spread effect is relatively wave propagation lag compensation, accurately reflect the phase information, but did not consider wave field amplitude adjustment problems. Aim at one-way wave, geophysicists raise that we can use the theory of true amplitude improving traditional one-way equation method. This paper introduces the theory of one-way wave equation under the algorithms and process improvements based on true amplitude. It sufficiently shows that, true amplitude one-way equation is exact, rotate, and enough to provide more accurate and more meaningful data for seismic exploration.