Ricker wavelet

The Ricker wavelet, also known as the Mexican hat wavelet or the second derivative of a Gaussian, is a zero-phase wavelet used extensively in geophysics, particularly in seismic data processing and interpretation. Its defining characteristic is its simple, symmetric shape in both the time and frequency domains.

The wavelet is derived from the second derivative of a Gaussian function. This derivation ensures that the Ricker wavelet has a zero mean and a dominant frequency. The zero mean property means that the positive and negative lobes of the wavelet integrate to zero, which can be beneficial in avoiding artificial DC shifts in the processed data. The dominant frequency refers to the frequency at which the wavelet has its maximum amplitude in the frequency spectrum.

The wavelet is typically parameterized by its peak or dominant frequency. Increasing the peak frequency of a Ricker wavelet results in a narrower pulse in the time domain, providing higher temporal resolution. Conversely, decreasing the peak frequency results in a broader pulse and lower temporal resolution.

The Ricker wavelet is widely used to model seismic reflections in subsurface imaging. The assumption is that sharp contrasts in acoustic impedance (the product of density and seismic velocity) between different rock layers generate seismic reflections that can be approximated by Ricker wavelets. By convolving a reflectivity series (representing these impedance contrasts) with a Ricker wavelet, seismologists can create synthetic seismograms that mimic real-world seismic data.

Advantages of the Ricker wavelet include its simplicity, ease of implementation, and its close resemblance to the shape of many observed seismic reflections. However, a major limitation is its perfect symmetry and zero-phase nature, which may not always accurately represent the complexities of real-world seismic wave propagation and reflection phenomena. In practice, more sophisticated wavelets with non-zero phase characteristics are sometimes employed to better capture the nuances of seismic data.