# Difference between revisions of "Dictionary:Q(Quality)"

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<b>1</b>. <b>Q</b>uality factor, the ratio of 2π times the peak energy to the energy dissipated in a cycle; the ratio of 2π times the power stored to the power dissipated. The seismic ''Q'' of rocks is of the order of 50 to 300. ''Q'' is related to other measures of absorption (see below): | <b>1</b>. <b>Q</b>uality factor, the ratio of 2π times the peak energy to the energy dissipated in a cycle; the ratio of 2π times the power stored to the power dissipated. The seismic ''Q'' of rocks is of the order of 50 to 300. ''Q'' is related to other measures of absorption (see below): | ||

− | <center>1 | + | <center><math>\frac{1}{Q} = \frac{\alpha V}{\pi f} = \frac{\alpha \lambda}{\pi} = \frac{hT}{\pi} = \frac{\delta}{\pi} = \frac{2\Delta f}{f_\mathrm{r}} </math></center> |

+ | where ''V'', ''f'', ''λ'', and ''T'' are, respectively, velocity, frequency, wavelength, and period (see Sheriff and Geldart, 1995: 60, 177<ref>Sheriff, R. E. and Geldart, L. P., 1995, Exploration Seismology, 2nd Ed., Cambridge Univ. Press.</ref>). The <b>absorption coefficient</b> ''α'' is the term for the exponential decrease of amplitude with distance because of absorption; the amplitude of plane harmonic waves is often written as | ||

+ | <center><math>A\mathrm{e}^{-\alpha x} \sin 2 \pi f ( t - \tfrac{x}{V} ) </math></center> | ||

− | where '' | + | where ''x'' is the distance traveled. The <b>logarithmic decrement</b> ''δ'' is the natural log of the ratio of the amplitudes of two successive cycles. The last equation above relates ''Q'' to the sharpness of a resonance condition; ''f''<sub>r</sub> is the resonance frequency and Δ''f'' is the change in frequency that reduces the amplitude by 1/√2. The <b>damping factor</b> ''h'' relates to the decrease in amplitude with time, |

− | <center> | + | <center><math>A(t) = A_0\mathrm{e}^{-ht} \cos \omega t \ </math></center> |

+ | See also Figure [[Dictionary:Fig_A-2|A-2]]. | ||

+ | [[File:Sega2.jpg|thumb|center|600px|<b>Absorption terminology</b>. Sometimes this terminology is used for attenuation because of factors other than absorption. ''E'' = energy, Δ''E'' = energy lost in one cycle, λ = wavelength, ''f'' = frequency, ''x'' = distance, ''t'' = time, ''A''/''A''<sub>0</sub> = amplitude/(initial amplitude), ''A''<sub>1</sub>/''A''<sub>2</sub>=amplitude/(amplitude one cycle later). (From Sheriff, 1989, p 330<ref>Sheriff, R, 1989, Geophysical methods: Prentice Hall Inc.</ref>)]] | ||

− | + | <b>2</b>. The ratio of the reactance of a circuit to the resistance. <b>3</b>. A term to describe the sharpness of a [[Dictionary:filter|filter]]; the ratio of the midpoint frequency to the bandpass width (often at 3 dB). <b>4</b>. A designation for ''[[Dictionary:Love wave|Love wave]]s'' (q.v.). <b>5</b>. Symbol for the [[Dictionary:Koenigsberger_ratio_(Q)|''Koenigsberger ratio'']] (q.v.). <b>6</b>. See [[Dictionary:Q-type_section|''Q-type section'']]. | |

− | + | ==See also== | |

+ | * [[Dictionary:Attenuation|Attenuation]] | ||

+ | * [[Dictionary:Attenuation factor|Attenuation factor]] | ||

− | + | ==References== | |

− | + | <references /> | |

− |

## Revision as of 06:43, 12 March 2012

**1**. **Q**uality factor, the ratio of 2π times the peak energy to the energy dissipated in a cycle; the ratio of 2π times the power stored to the power dissipated. The seismic *Q* of rocks is of the order of 50 to 300. *Q* is related to other measures of absorption (see below):

where *V*, *f*, *λ*, and *T* are, respectively, velocity, frequency, wavelength, and period (see Sheriff and Geldart, 1995: 60, 177^{[1]}). The **absorption coefficient** *α* is the term for the exponential decrease of amplitude with distance because of absorption; the amplitude of plane harmonic waves is often written as

where *x* is the distance traveled. The **logarithmic decrement** *δ* is the natural log of the ratio of the amplitudes of two successive cycles. The last equation above relates *Q* to the sharpness of a resonance condition; *f*_{r} is the resonance frequency and Δ*f* is the change in frequency that reduces the amplitude by 1/√2. The **damping factor** *h* relates to the decrease in amplitude with time,

See also Figure A-2.

**2**. The ratio of the reactance of a circuit to the resistance. **3**. A term to describe the sharpness of a filter; the ratio of the midpoint frequency to the bandpass width (often at 3 dB). **4**. A designation for *Love waves* (q.v.). **5**. Symbol for the *Koenigsberger ratio* (q.v.). **6**. See *Q-type section*.