Thin-bed thickness calculation formula and its approximation using peak frequency

Quantitative thickness estimation below tuning thickness is a great challenge in seismic exploration. Most studies focus on the thin-beds whose top and bottom reflection coefficients are of equal magnitude and opposite polarity. There is no systematic research on the other thin-bed types. In this article, all of the thin-beds are classified into four types： thin-beds with equal magnitude and opposite polarity, thin-beds with unequal magnitude and opposite polarity, thin-beds with equal magnitude and identical polarity, and thin-beds with unequal magnitude and identical polarity. By analytical study, an equation describing the general relationship between seismic peak frequency and thin-bed thickness was derived which shows there is a Complex implicit non-linear relationship between them and which is difficult to use in practice. In order to solve this problem, we simplify the relationship by Taylor expansion and discuss the precision of the approximation formulae with different orders for the four types of thin-beds. Compared with the traditional amplitude method for thin-bed thickness calculation, the method we present has a higher precision and isn＇t influenced by the absolute value of top or bottom reflection coefficient, so it is convenient for use in practice.

在调节厚度下面的量的厚度评价是在地震探索的大挑战。的大多数研究焦点薄床系数相等的大小和相反的极性是其顶和底部思考。另外的薄床的类型上没有系统的研究。在这篇文章，所有薄床被分类进四种类型：与不相等的大小和相同极性与相等的大小和相反的极性薄床、与不相等的大小和相反的极性薄床、与相等的大小和相同极性薄床、薄床。由分析学习，描述在地震山峰频率和薄床的厚度之间的一般关系的一个方程被导出它在那里的表演并且哪个是在他们之间的一种复杂含蓄的非线性的关系是困难的在实践使用。以便解决这个问题，我们由泰勒扩大简化关系并且为四种类型与不同订单讨论近似公式的精确薄床。与为薄床的厚度计算的传统的振幅方法相比，方法我们在场有更高的精确并且没被顶或底部思考系数的绝对值影响，它因此对在实践的使用方便。