1. MFT: Theoretical Basis
The Multiple Filter Technique (MFT) is a filtering technique (Dziewonski et al., 1969), which is used to obtain the group-velocity dispersion curve from a pre-processed trace (instrument corrected). Following this method, the time in which the envelope of the filtering seismic signal given by:
reaches the maximum, is the group time for the frequency wn selected as center of the Gaussian filter. The group velocity is obtained dividing the epicentral distance by the group time.

2. MFT: Theoretical Basis
The envelope of the filtering seismic signal can be computed as the amplitude of the analytical signal. This amplitude or envelope gn(t) is defined by (Bath, 1974):
The Hilbert transform can be calculated from the Fourier transform, taking into account the following relationships (Brigham, 1988):
where Re denotes the real part and Im denotes the imaginary part.

3. MFT: Flow Chart
Thus, a group-velocity dispersion curve can be computed by means of the procedure shown in the flow chart presented below.

4. MFT: An Example
The above-described filtering process, as an example, has been applied to the trace shown below, which has been instrumentally corrected.
The MFT has been applied for a interval of centre periods Tn from 5 to 100 s, resulting the contour map shown in the next slide.

5. MFT: An Example
Contour map of relative energy normalized to 99 decibels, as a function of period and group time. The white curve denotes the group time inferred from the energy map.

6. MFT: An Example
The group-time curve can be inferred from the energy map. After, the group-velocity curve is calculated from the group times and the epicentral distance, dividing the epicentral distance by the group time for each period.

7. MFT: References MFT: Web Page
Bath M. (1974). Spectral Analysis in Geophysics. Elsevier, Amsterdam.
Brigham E. O. (1988). The Fast Fourier Transform and Its Applications.
Prentice Hall, New Jersey.
Dziewonski A., Bloch S. and Landisman M. (1969). A technique for the
analysis of transient seismic signals. Bulletin of the
Seismological Society of America, 59, No. 1,
MFT: Web Page