## Single-channel spectral ratio method

The seismic wave amplitude spectrum after propagating from traveltime to in a homogeneous attenuating medium are given by:

 (1) (2)

where is the frequency, and are the seismic wave amplitude spectrum after propagating traveltime and , respectively, is the initial amplitude spectrum, and is a factor independent of frequency. Combining equations 1 and 2, we can obtain:

 (3)

Take a natural log of each side of equation 3, we obtain:

 (4)

where and are both constants, and , . Here, can be estimated by the slope of linear regression line. Then, can be estimated by

 (5)

2020-02-10