P-S波反射系数的一种小角度近似

从Aki和Richards在弱反差条件下给出的P-S波反射系数近似公式出发,提出了一种在小角度入射范围内的P-S波反射系数近似公式.为了得到该近似公式,对原公式中的角度项进行了二项式展开,直接利用入射角代替入射角的正弦.不同模型的计算表明,该近似在小角度入射范围内相当于Aki和Richards的原近似公式,在大角度时有一定改善.新的近似公式形式简单、涉及的弹性参数较少,容易应用到反演当中.另外,利用一阶小角度近似结果可以对横波阻抗进行反演.

AN SMALL INCIDENT ANGLE APPROXIMATION OF REFLECTION COEFFICIENT OF P-S WAVE

On the basis of the P-S wave reflection coefficient equation given by Aki & Richards for weak contrast media, a new approximation formula for the small incident angle is presented. For the purpose of formulating the new equation, binomial expansion is applied to the factors related to incident and transmission angles, and the sine of the incident angle is replaced by incident angle directly. Thanks to its simple form and few elastic parameters, the new equation can be easily employed to the parameter inversion. Calculation results on different models show that it is equivalent to the original equation by Aki & Richards when the incident angle is small and can make some improvement when the angle is somewhat larger. In addition, the first order approximation form can invert the shear wave impedance.