[4] Analysis of some factors that influence imaging

It is worthwhile to analyze the factors which affect the imaging quality and how they do so. We list four main factors: (1) too coarse sampling, (2) uneven sampling intervals or missing data, (3) illumination deficiency, (4) migration operator. All these factors will slow the convergence of iterative migration/inversion algorithms. It is obvious that too coarse sampling produces aliasing. Fig.5 demonstrates that uneven sampling intervals or missing data will cause imaging noise. Because the reflections from the vicinity of a reflecting point can not cancel each other, imaging noise appears. The illumination greatly affects the imaging quality in the case of a complex medium. From the view of the Radon transform and its inverse, if the seismic data set is band-width-unlimited, and the acquisition geometry is continuously distributed around an object body, the object can be uniquely restored with the inverse of the Radon transform. This is theoretically true. According to ray theory tomography, if rays are missing which should pass through the region of interest, the image of the region will be blurred. In fact, this is an amplitude distortion of the image. Therefore, the true medium parameters can never be recovered from real seismic data. The possibility of relative true-amplitude imaging is analyzed later. Propagators describe wave propagation in the background medium. Given the seismic data and the background parameters, only the propagators affect the iterative algorithms. Propagators should characterize wave propagation as accurately as possible. However, commonly used propagators are not so accurate and many wave phenomena are neglected. This can cause amplitude and phase distortion, as well as errors in Hessian calculation. Further, these will slow down the convergence of migration/inversion.