Magnitudes of seismic wave parameters

Problems in Exploration Seismology and their Solutions

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

Problem 2.8

The magnitudes of period $T$, wavelength $\mathrm {\lambda }$, wavenumber $\mathrm {\kappa }$, frequency $f$, and angular frequency $\mathrm {\omega }$ are important in practical situations. Calculate $T$, $\mathrm {\lambda }$, and $\mathrm {\kappa }$ 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 $T$ equals $1/{\it {f}}$, so ${\it {{T}=0.067}}$ s for ${\it {{f}=15}}$ Hz and ${\it {{T}=0.017}}$ s for ${\it {{f}=60}}$ Hz. Also, $\mathrm {\lambda } =V/f$, $\mathrm {\kappa } =2\mathrm {\pi } /\mathrm {\lambda } =2\mathrm {\pi } f/V$. Using these equations we get the values of $\mathrm {\lambda }$ and $\mathrm {\kappa }$ in Table 2.8a.

Table 2.8a. Magnitudes of $T$, $\mathrm {\lambda }$, and $\mathrm {\kappa }$.

		For ${\it {{f}=15}}$ Hz			For ${\it {{f}=60}}$ Hz
	$V$(km/s)	$T$(s)	$\mathrm {\lambda }$(m)	$\mathrm {\kappa } (\mathrm {m} ^{-1})$	$T$(s)	$\mathrm {\lambda }$(m)	$\mathrm {\kappa } (\mathrm {m} ^{-1})$
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

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Table of Contents (book)

Also in this chapter

• The basic elastic constants
• Interrelationships among elastic constants
• Magnitude of disturbance from a seismic source
• Magnitudes of elastic constants
• General solutions of the wave equation
• Wave equation in cylindrical and spherical coordinates
• Sum of waves of different frequencies and group velocity
• Potential functions used to solve wave equations
• Boundary conditions at different types of interfaces
• Boundary conditions in terms of potential functions
• Disturbance produced by a point source
• Far- and near-field effects for a point source
• Rayleigh-wave relationships
• Directional geophone responses to different waves
• Tube-wave relationships
• Relation between nepers and decibels
• Attenuation calculations
• Diffraction from a half-plane

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