Seismic applications > Rayleigh waves: SMF filtering

The video shows the following sections:

  • The initial data;
  • The initial data after velocity correction (flattened data);
  • The initial data projected on the first eigenvector (first eigensection);
  • The first eigensection with the choice of the reference frequency. The main frequency of the slow Pseudo-Rayleigh wave is 7 Hz;
  • The first eigensection filtered by a high-pass filter. The low cut-off frequency is the highest frequency of the slow Pseudo-Rayleigh wave;
  • The first eigensection filtered by a low pass filter. The high cut-off frequency is the highest frequency of the slow Pseudo-Rayleigh wave;
  • The residual section. On this section, it is possible to identify the refracted wave, a reflected wave and the air wave preceding the fast Pseudo-Rayleigh wave.

The selected parameters of the SMF filter are 3 for an averaging in distance and 8 for an averaging in frequency. After estimation, the slow wave is put back in its initial position in the plane (x,t). The amplitude spectra obtained by calculating the mean of the modulus Fourier transform of each 47 traces, which make up each section is also presented.

The video also shows the two dimension amplitude spectrum associated to the selected section. The 2D spectra can be normalized in wavenumber k. Above the 2D spectrum, we present 4 eigenvalue curves according to the frequency. The black curve represents the sum of the eigenvalues. The blue curve is the first eigenvalue associated to the first eigenvector (first eigensection), the green curve is associated to the second eigenvalue associated to the second eigenvector (second eigensection). The red curve that is the difference between the black curve and the sum of the blue and green curves represents the sum of the other eigenvalues.