Seismic Attenuation Calculator
Our geology & geophysics calculator computes seismic attenuation accurately. Enter measurements for results with formulas and error analysis.
Calculator
Adjust values & calculateLow Q (50-200): high attenuation | High Q (500-5000): low attenuation
Formula
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.
Last reviewed: December 2025
Worked Examples
Example 1: Teleseismic P-wave Attenuation
Example 2: Near-surface Attenuation
Background & Theory
The Seismic Attenuation Calculator applies the following established principles and formulas. Earth science calculators draw on a wide range of measurement scales and physical principles that quantify natural phenomena across geological, atmospheric, and hydrological systems. Earthquake magnitude is most precisely described by the Moment Magnitude Scale (Mw), which replaced the original Richter scale for larger events. Mw is calculated as Mw = (2/3) log10(M0) − 10.7, where M0 is the seismic moment in dyne-centimeters. The Richter scale, while still referenced colloquially, is a local magnitude (ML) measurement derived from peak seismograph amplitude at a standard 100 km distance. Wind intensity is classified using the Beaufort Scale, a 13-point empirical scale (0–12) relating wind speed in knots to observable sea and land effects, with Beaufort 12 corresponding to hurricane-force winds above 64 knots. Tropical cyclone intensity is further categorized by the Saffir-Simpson Hurricane Wind Scale, which assigns Categories 1 through 5 based on sustained wind speed, correlating with expected structural damage. Mineral hardness is quantified on the Mohs scale (1–10), comparing scratch resistance relative to reference minerals from talc (1) to diamond (10). Soil composition analysis measures the proportions of sand, silt, and clay by particle size, alongside organic matter content, bulk density, and porosity, which together determine engineering and agricultural suitability. Seismic wave velocity in rock varies by material: P-waves travel at approximately 5–7 km/s in granite and 1.5 km/s in water, while S-waves travel at roughly 60% of P-wave speeds. Atmospheric pressure decreases with altitude according to the barometric formula: P = P0 × exp(−Mgh / RT), where M is molar mass of air, g is gravitational acceleration, h is altitude, R is the universal gas constant, and T is temperature in Kelvin. Standard sea-level pressure is 101,325 Pa. Tidal calculations use harmonic analysis of gravitational forcing by the Moon and Sun, with the principal lunar semidiurnal tidal constituent (M2) having a period of approximately 12.42 hours.
History
The history behind the Seismic Attenuation Calculator traces back through the following developments. The systematic study of Earth's structure and processes spans millennia, but the scientific foundations were laid in the seventeenth century. In 1669, Danish naturalist Nicolas Steno published his principles of stratigraphy, establishing the laws of superposition, original horizontality, and lateral continuity — foundational rules for reading rock layers that remain in use today. Scottish geologist James Hutton introduced the concept of uniformitarianism in 1788, proposing that geological processes observable in the present have operated throughout Earth's history at broadly consistent rates. This idea of deep time challenged prevailing biblical chronologies and set the stage for modern geology. Charles Lyell systematized these ideas in his landmark three-volume work Principles of Geology, published beginning in 1830, which directly influenced Charles Darwin's thinking on biological evolution during the voyage of the Beagle. The nineteenth century saw growing curiosity about continental shapes, but a coherent theory awaited Alfred Wegener, a German meteorologist who proposed continental drift in 1912, arguing that the continents had once formed a supercontinent he called Pangaea. His evidence included matching fossil records and geological formations across the Atlantic, but his mechanism was disputed for decades. The theory gained acceptance in the 1960s when seafloor spreading was confirmed through paleomagnetic studies, and plate tectonics emerged as the unifying framework of modern geoscience. The United States Geological Survey was established by Congress in 1879 to classify public lands and examine the geological structure, mineral resources, and products of the national domain. The twentieth century brought instrumental advances, including the global seismograph network deployed after World War II, initially to monitor nuclear tests, which dramatically improved earthquake detection and characterization. Satellite Earth observation began in earnest with the Landsat program launched in 1972, enabling continuous global monitoring of land use, glacier retreat, and vegetation patterns. Today, GPS networks, LIDAR scanning, and ocean-floor mapping provide centimeter-scale precision for tracking tectonic motion, sea level rise, and volcanic deformation in near real time.
Frequently Asked Questions
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.
How accurate are the results from Seismic Attenuation Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Why might my result differ from another tool or reference?
Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy