# موجة ريكر

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{{#category_index:R|Ricker wavelet}} موجة صفرية الطور، وهي المشتقة الثاني للدالة الغاوسية أو المشتقة الثالث لدالة كثافة الاحتمال النظامية. وغالبًا ما يتم استخدام مويجة ريكر كمويجة مدمجة ذات المرحلة الصفرية في صناعة النمذجة وتصنيع مخطط الزلازل الاصطناعية. انظر الشكل R-14. وسميت نسبة لعالم الجيوفيزياء الأمريكي نورمان إتش ريكر (1896–1980) ،.

FIG. R-14. Ricker wavelet. (a) Time-domain and (b) frequency-domain representations.

The amplitude f(t) of the Ricker wavelet with peak frequency fM at time t is given by,

${\displaystyle f(t)=(1-2\pi ^{2}f_{_{M}}^{2}t^{2})e^{-\pi ^{2}f_{_{M}}^{2}t^{2}}}$.

The frequency domain representation of the wavelet is given by,

${\displaystyle F(f)={\frac {2}{\sqrt {\pi }}}{\frac {f^{2}}{f_{M}^{3}}}e^{-{\frac {f^{2}}{f_{M}^{2}}}}}$

Where,

${\displaystyle T_{D}={\frac {\sqrt {6}}{\pi f_{M}}}}$ and ${\displaystyle T_{R}=T_{D}/{\sqrt {3}}}$.

The mean frequency ${\displaystyle f_{mean}={\frac {2}{\sqrt {\pi }}}f_{M}}$ and the median frequency ${\displaystyle f_{median}=1.08f_{M}}$.

Sometimes the period (somewhat erroneously referred to occasionally as the wavelength) is given as 1/f, but since it has mixed frequencies, this is not quite correct, and for some wavelets is not even a good approximation. In fact, the Ricker wavelet has its sidelobe minima at

${\displaystyle \pm {\frac {\sqrt {3/2}}{f_{_{M}}\pi }}}$

These minima have the value

${\displaystyle A_{\mathrm {min} }=-{\frac {2}{e^{3/2}}}}$