Abstract
AbstractThe Ricker wavelet has been widely used in the analysis of seismic data, as its asymmetrical amplitude spectrum can represent the attenuation feature of seismic wave propagation through viscoelastic homogeneous media. However, the frequency band of the Ricker wavelet is not analytically determined yet. The determination of the frequency band leads to an inverse exponential equation. To solve this equation analytically a special function, the Lambert W function, is needed. The latter provides a closed and elegant expression of the frequency band of the Ricker wavelet, which is a sample application of the Lambert W function in geophysics and there have been other applications in various scientific and engineering fields in the past decade. Moreover, the Lambert W function is a variation of the Ricker wavelet amplitude spectrum. Since the Ricker wavelet is the second derivative of a Gaussian function and its spectrum is a single-valued smooth curve, numerical evaluation of the Lambert W function can be implemented by a stable interpolation procedure, followed by a recursive computation for high precision.
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