Crustal Thickness From Receiver Functions Calculator
Free Crustal thickness receiver functions Calculator for geology & geophysics. Enter variables to compute results with formulas and detailed steps.
Formula
H = tPs / (sqrt(1/Vs² - p²) - sqrt(1/Vp² - p²))
Crustal thickness H is calculated from the Ps conversion delay time (tPs), average crustal P-wave (Vp) and S-wave (Vs) velocities, and the teleseismic ray parameter (p). The Vp/Vs ratio determines Vs from Vp.
Worked Examples
Example 1: Continental Crust Estimation
Problem: A seismic station records a Ps delay of 4.5 seconds. Average crustal Vp is 6.3 km/s, Vp/Vs = 1.73, and ray parameter is 0.06 s/km. Calculate crustal thickness.
Solution: Vs = 6.3 / 1.73 = 3.642 km/s\ntermVs = sqrt(1/3.642² - 0.06²) = sqrt(0.07539 - 0.0036) = 0.2679\ntermVp = sqrt(1/6.3² - 0.06²) = sqrt(0.02520 - 0.0036) = 0.1471\nH = 4.5 / (0.2679 - 0.1471) = 4.5 / 0.1208 = 37.25 km
Result: Crustal thickness H = 37.25 km
Example 2: Thin Oceanic Crust
Problem: An ocean-bottom seismometer shows tPs = 1.0 s with Vp = 6.8 km/s, Vp/Vs = 1.80, and p = 0.05 s/km.
Solution: Vs = 6.8 / 1.80 = 3.778 km/s\ntermVs = sqrt(1/3.778² - 0.05²) = sqrt(0.07007 - 0.0025) = 0.2600\ntermVp = sqrt(1/6.8² - 0.05²) = sqrt(0.02163 - 0.0025) = 0.1384\nH = 1.0 / (0.2600 - 0.1384) = 1.0 / 0.1216 = 8.22 km
Result: Crustal thickness H = 8.22 km (typical oceanic crust)
Frequently Asked Questions
What are receiver functions in seismology?
Receiver functions are time series computed from teleseismic earthquake recordings that isolate the response of Earth structure directly beneath a seismometer. They are created by deconvolving the vertical component from the radial (or transverse) component of a three-component seismogram. This process removes the effects of the earthquake source and instrument response, leaving only the P-to-S converted waves and their reverberations generated at subsurface discontinuities such as the Moho. The most prominent phase in a receiver function is the Ps conversion at the crust-mantle boundary, which arrives after the direct P wave by a time delay that depends on crustal thickness and seismic velocities.
How is crustal thickness calculated from receiver functions?
Crustal thickness is calculated from the time delay between the direct P-wave arrival and the P-to-S (Ps) converted phase at the Mohorovicic discontinuity. The fundamental equation is H = tPs / (sqrt(1/Vs^2 - p^2) - sqrt(1/Vp^2 - p^2)), where H is crustal thickness, tPs is the Ps delay time, Vs and Vp are average crustal S-wave and P-wave velocities, and p is the ray parameter. Additional constraints come from the PpPs and PsPs+PpSs reverberation phases, which provide independent thickness estimates. The H-kappa stacking method by Zhu and Kanamori (2000) simultaneously estimates both crustal thickness (H) and Vp/Vs ratio (kappa) by stacking amplitudes at predicted arrival times.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
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