前言

主要记录下常用各种子波函数以及对应的图形。

Ricker子波

$ S(t)=(1-2\pi^2f^2t^2)exp(-\pi^2f^2t^2) $

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function [w] = ricker(fpeak,t,tdelay)
w = exp(-pi^2*fpeak^2*(t-tdelay).^2).*(1-2*pi^2*fpeak^2*(t-tdelay).^2);
return

ricker.png

Ricker子波的一阶导数：

$$S(t)=2\pi^2f^2t(2\pi^2f^2t^2-3)exp(-\pi^2f^2t^2)$$

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function [w] = ricker1(fpeak,t,tdelay)
 w = 2*pi^2*fpeak^2*(t-tdelay).*(2*pi^2*fpeak^2*(t-tdelay).^2-3).*...
     exp(-pi^2*fpeak^2*(t-tdelay).^2);
return

ricker-deri.png

最小相位子波

$$S(t)=texp(-3.5ft)sin(2\pi ft)$$

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function [w] = min_phase(fpeak,t,tdelay)
w = (t-tdelay).*exp(-3.5*fpeak*(t-tdelay)).*sin(2*pi*fpeak*(t-tdelay));
return

min_phase.png

Gauss子波的导数：

$$S(t)=-A\pi^2f^2texp(-\pi^2f^2t^2)(3-2\pi^2f^2t^2)$$

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function [w] = gauss1(fpeak,t,tdelay)
w =-pi^2*fpeak^2*(t-tdelay).*exp(-pi^2*fpeak^2*(t-tdelay).^2).*...
    (3-2*pi^2*fpeak^2*(t-tdelay).^2);
return

gauss1.png

参考资料

罗焕宏.基于单程波算子的地震波场模拟及叠前深度偏移[D].中国石油大学,2010