# Magnitudes of seismic wave parameters

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 2 7 - 46 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 2.8

The magnitudes of period ${\displaystyle T}$, wavelength ${\displaystyle \mathrm {\lambda } }$, wavenumber ${\displaystyle \mathrm {\kappa } }$, frequency ${\displaystyle f}$, and angular frequency ${\displaystyle \mathrm {\omega } }$ are important in practical situations. Calculate ${\displaystyle T}$, ${\displaystyle \mathrm {\lambda } }$, and ${\displaystyle \mathrm {\kappa } }$ for 15 and 60 Hz for the following velocity situations:

1. weathering, 100 and 500 m/s (minimum and average values);
2. water, 1500 m/s;
3. sands and shales, 2000 (poorly consolidated) and 3300 m/s;
4. limestone, 4300 (porous) and 5500 m/s;
5. salt, 4600 m/s;
6. anhydrite, 6100 m/s.

### Solution

The period ${\displaystyle T}$ equals ${\displaystyle 1/{\it {f}}}$, so ${\displaystyle {\it {{T}=0.067}}}$ s for ${\displaystyle {\it {{f}=15}}}$ Hz and ${\displaystyle {\it {{T}=0.017}}}$ s for ${\displaystyle {\it {{f}=60}}}$ Hz. Also, ${\displaystyle \mathrm {\lambda } =V/f}$, ${\displaystyle \mathrm {\kappa } =2\mathrm {\pi } /\mathrm {\lambda } =2\mathrm {\pi } f/V}$. Using these equations we get the values of ${\displaystyle \mathrm {\lambda } }$ and ${\displaystyle \mathrm {\kappa } }$ in Table 2.8a.

Table 2.8a. Magnitudes of ${\displaystyle T}$, ${\displaystyle \mathrm {\lambda } }$, and ${\displaystyle \mathrm {\kappa } }$.
For ${\displaystyle {\it {{f}=15}}}$ Hz For ${\displaystyle {\it {{f}=60}}}$ Hz
${\displaystyle V}$(km/s) ${\displaystyle T}$(s) ${\displaystyle \mathrm {\lambda } }$(m) ${\displaystyle \mathrm {\kappa } (\mathrm {m} ^{-1})}$ ${\displaystyle T}$(s) ${\displaystyle \mathrm {\lambda } }$(m) ${\displaystyle \mathrm {\kappa } (\mathrm {m} ^{-1})}$
Weathering (min.) 0.1 0.067 7 0.7 0.017 2 4
Weathering (avg.) 0.5 0.067 30 0.2 0.017 8 0.8
Water 1.5 0.067 100 0.063 0.017 25 0.25
Poorly consolidated sandstone-shales at 0.75 km 2.0 0.067 130 0.047 0.017 33 0.19
Tertiary clastics at 3.00 km 3.3 0.067 220 0.029 0.017 55 0.11
Porous limestone 4.3 0.067 290 0.022 0.017 72 0.088
Dense limestone 5.5 0.067 370 0.017 0.017 92 0.069
Salt 4.6 0.067 310 0.020 0.017 77 0.082
Anhydrite 6.1 0.067 410 0.015 0.017 100 0.062