Frequencies of the Ricker wavelet
Frequencies of the Ricker wavelet
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DOI：
10.1190/geo2014-0441.1
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发表时间：
2015-03-01
期刊：
影响因子：
3.3
通讯作者：
Wang, Yanghua
中科院分区：
文献类型：
--
作者：
Wang, Yanghua
Ricker小波理论上是考虑牛顿粘性效应的Stokes微分方程组的解，适用于粘弹性均匀介质中传播的地震波。本文定义了Ricker小波的时间域宽度和频域带宽，并利用Lambert W函数对其进行了解析展开量。我们确定了中心频率，即频带的几何中心，接近于使用功率谱统计估计的平均频率，而不是一些已发表的文献中使用的幅度谱。我们还证明了与平均频率的标准差并不像文献所说的那样是Ricker小波频谱的半带宽。此外，我们在数学上建立了理论频率(中心频率和半带宽)与数值测量(平均频率及其标准差)之间的关系，并根据Ricker小波的峰值频率解析地产生了每个频率量。
The Ricker wavelet is theoretically a solution of the Stokes differential equation, which takes into account the effect of Newtonian viscosity, and is applicable to seismic waves propagated through viscoelastic homogeneous media. In this paper, we defined the time-domain breadth and the frequency-domain bandwidth of the Ricker wavelet and developed quantities analytically in terms of the Lambert W function. We determined that the central frequency, the geometric center of the frequency band, is close to the mean frequency statistically evaluated using the power spectrum, rather than the amplitude spectrum used in some of the published literature. We also proved that the standard deviation from the mean frequency is not, as suggested by the literature, the half-bandwidth of the frequency spectrum of the Ricker wavelet. Moreover, we established mathematically the relationships between the theoretical frequencies (the central frequency and the half-bandwidth) and the numerical measurements (the mean frequency and its standard deviation) and produced each of these frequency quantities analytically in terms of the peak frequency of the Ricker wavelet.