Seismic Attenuation Calculator
Our geology & geophysics calculator computes seismic attenuation accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
A = A0 x exp(-pi x f x t / Q) | t* = t / Q
Seismic amplitude decays exponentially with the product of frequency and travel time, divided by the quality factor Q. The t-star parameter represents the integrated attenuation along a ray path. Higher Q means less attenuation; higher frequency and longer travel time mean more attenuation.
Worked Examples
Example 1: Teleseismic P-wave Attenuation
Problem:A P-wave with f = 1 Hz and initial amplitude 100 travels for 200 seconds through mantle with Q = 500.
Solution:A = 100 x exp(-pi x 1 x 200 / 500)\nA = 100 x exp(-1.2566)\nA = 100 x 0.2846 = 28.46
Result:Final amplitude = 28.46 (71.5% loss, -10.9 dB)
Example 2: Near-surface Attenuation
Problem:A 10 Hz wave in sediments with Q = 50 travels 5 km at 2 km/s.
Solution:t = 5/2 = 2.5 s\nA/A0 = exp(-pi x 10 x 2.5 / 50)\nA/A0 = exp(-1.5708) = 0.2079
Result:79.2% amplitude loss (Q = 50 is highly attenuating)
Frequently Asked Questions
What is seismic attenuation?
Seismic attenuation is the loss of wave energy as seismic waves travel through the Earth. This energy loss occurs through two main mechanisms: intrinsic attenuation (anelastic absorption converting wave energy to heat) and scattering attenuation (redirection of energy by heterogeneities). Attenuation causes wave amplitudes to decrease with distance beyond what geometric spreading alone would predict, and it preferentially removes higher frequencies, making distant seismograms appear lower in frequency.
What is the seismic quality factor Q?
The quality factor Q is a dimensionless parameter that describes how efficiently seismic energy propagates through a medium. A high Q value (like 1000-5000 in the deep mantle) means low attenuation and efficient wave propagation. A low Q value (like 50-200 in partially molten zones) indicates high attenuation. Q is defined as 2 times pi times the ratio of energy stored to energy lost per cycle. It is inversely proportional to the attenuation coefficient.
How does frequency affect seismic attenuation?
Higher frequency seismic waves are attenuated more strongly than lower frequency waves because the attenuation per wavelength is roughly constant for a given Q value. Since higher frequencies have shorter wavelengths, they undergo more attenuation cycles per unit distance. This frequency-dependent attenuation acts as a natural low-pass filter, which is why distant earthquakes are recorded primarily at low frequencies and why high-frequency signals are only observable at short distances.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy