On Some Problems In Kirchhoff-type Migration

Limited aperture true amplitude migration as the development of classical Kirchhoff-type migration can recover both the amplitude and wavelet, which makes sence for inversion of seismic lithologic parameters. However, there are still some problems with the method. The author choose some typical problems to study including the ture amplitude weight function, migration aperture, amplitude and pulse distortion, and migration resolution. The weight and aperture are two critical parameters that work together for imaging. Optional expressions are given about these two parameters. Ture amplitude Kirchhoff-type migration is proposed based on different theoritical approaches, which lead to the different notations of the weight. The author summarizes the weight functions in related articles, firstly sorted them by4ways, then the author show how to build relationship among them by paraxial ray properties. As to the numerical calculation, the weight can be get by three methods of Green’s function amplitude, derivatives of traveltime or projected paraxial ray parameters. These three methods have both advantages and disadvantages. People need to select the appropriate method according to the accuracy in practice. The paper even extends the sight to the use of weight in multi-component technology and anisotropic medium. Different directional characteristics are analyzed on the weight by pluse response from single trace. This is meaningful to study the weight’s action mechanism when the ture amplitude is recovered. To study the migration aperture, the author focuses on the aperture effect, from which the aperture size, location, are determined. Numerical method works much better than empirical formulas. Besides qualitative analysis about the instinct amplitude and pulse distortion, several suggestions are given on how to improve the migration resolution. At last, some simple sythetic examples in2-D and2.5-D models are presented.