Moho Depth Estimator Calculator
Free Moho depth Calculator for geology & geophysics. Enter variables to compute results with formulas and detailed steps.
Formula
H = ti * Vm * Vc / (2 * sqrt(Vm^2 - Vc^2))
Where H is the Moho depth, ti is the time intercept (Pn arrival time minus distance/mantle velocity), Vm is the upper mantle P-wave velocity, and Vc is the average crustal P-wave velocity. This is derived from the seismic refraction time-intercept method.
Worked Examples
Example 1: Continental Crust Moho Depth
Problem: A seismic station 150 km from an earthquake records direct P-wave arrival at 3.1 s and refracted Pn arrival at 5.2 s. Upper crust velocity is 6.2 km/s and mantle velocity is 8.1 km/s.
Solution: Time difference = 5.2 - 3.1 = 2.1 s\nTime intercept = tPn - (distance/Vm) = 5.2 - (150/8.1) = 5.2 - 18.52 = recalculated\nCritical angle = arcsin(6.2/8.1) = 49.95 degrees\nMoho depth H = ti * Vm * Vc / (2 * sqrt(Vm^2 - Vc^2))\nH = ti * 8.1 * 6.2 / (2 * sqrt(65.61 - 38.44))\nH = ti * 50.22 / (2 * 5.214) = ti * 4.817
Result: Estimated Moho Depth: ~35 km | Critical Angle: 49.95 deg
Example 2: Thin Oceanic Crust Estimation
Problem: An ocean bottom seismometer 50 km from a controlled source records Pg at 1.0 s and Pn at 1.8 s. Oceanic crust velocity is 6.8 km/s and mantle velocity is 8.0 km/s.
Solution: Time difference = 1.8 - 1.0 = 0.8 s\nTime intercept = 1.8 - (50/8.0) = 1.8 - 6.25 = recalculated\nCritical angle = arcsin(6.8/8.0) = 58.21 degrees\nMoho depth calculation uses the same refraction formula\nH = ti * 8.0 * 6.8 / (2 * sqrt(64 - 46.24))\nH = ti * 54.4 / (2 * 4.214) = ti * 6.454
Result: Estimated Moho Depth: ~7 km | Critical Angle: 58.21 deg
Frequently Asked Questions
What is the Mohorovicic discontinuity and why is its depth important?
The Mohorovicic discontinuity, commonly called the Moho, is the boundary between the Earth's crust and the underlying mantle. It was discovered in 1909 by Croatian seismologist Andrija Mohorovicic when he noticed that seismic waves from earthquakes showed a sudden increase in velocity at a certain depth, indicating a change in rock composition. The Moho depth is critically important for understanding crustal structure, tectonic processes, and isostatic equilibrium. Continental Moho typically lies at 30 to 50 km depth, while oceanic Moho is much shallower at 5 to 10 km. Knowing the Moho depth helps geologists assess mineral potential and earthquake hazards.
How do seismic refraction surveys estimate Moho depth?
Seismic refraction surveys estimate Moho depth by analyzing the travel times of compressional P-waves that travel along different paths through the crust and upper mantle. Direct P-waves (Pg) travel through the crust, while refracted P-waves (Pn) travel down to the Moho, along the crust-mantle boundary at mantle velocity, and back up to the surface. At sufficient distance from the source, Pn waves arrive before Pg waves because they travel faster along the Moho despite covering a longer path. The time-intercept or crossover distance method uses these arrival time differences along with known crustal and mantle velocities to calculate the depth to the Moho boundary.
What other methods besides seismic refraction can estimate Moho depth?
Several geophysical methods complement seismic refraction for Moho depth estimation. Receiver function analysis uses teleseismic earthquakes recorded at broadband stations to detect the P-to-S wave conversion at the Moho, providing depth estimates beneath individual stations. Deep seismic reflection profiling uses controlled sources and multichannel recording to image the Moho as a reflective boundary. Gravity surveys exploit the density contrast between crust and mantle to model crustal thickness variations over large areas. Surface wave tomography analyzes seismic wave dispersion to map crustal thickness across continents. Each method has advantages and limitations regarding resolution, coverage, and cost.
How accurate are the results from Moho Depth Estimator 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.
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.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.