Non-surface Consistency Error Analysis Based On Finite-frequency Snell's Law

At present, the static correction methods which are widely used in industry are based on the Surface Consistency Hypothesis. Surface Consistency Hypothesis supposes seismic rays travel in low-speed layer vertically. And with the seismic exploration transfer from placid basins and central regions towards the surface geology complex regions, mountains, deserts and other typical complex surfaces does not conform to the surface consistency hypothesis, Sudden changes of surface in rugged areas disarrange travel time of seismic waves, and make it more difficult to explore in these areas.Now,almost all the static correction and ray tracing method are based on Snell's law and fermat's principle, which assumes that the reflected waves have the characteristics of high frequencyies, tending to infinity. This assumption has achieved certain success in the actual production, however, the frequencies of the artificial seismic wave are not infinitely large quantities, We have developed a new approach to computing raypaths, using a modification of Snell that we call it limited frequency Snell's law. The results are more consistent with the paths and times got by applying the band-limited signals in real data than the paths and times obtained by using high-frequency approximations.Based on it's theoretical study, The Limited frequency Snell's Law is applied to the error analysis of non-surface consistent static correction. The performances of the Snell's Law and the limited-frequency Snell's Law for several classi cal non-surface consistent models are compared on the relationships between the non-surfac econsistent static correction errors and the depth of the datum, the thickness of the weatherin g layer, the thickness of the bedrock, the offset, and the specific value of the velocity of t he weathering and the velocity of the bedrock by forward modeling on computer. Conclusio ns, which can help us to give suggestions on the parameter selecting for the calculation of st atic correction and to reduce the static correction error, can be drawn from the above analysis.