Moho Depth Estimator Calculator
Free Moho depth Calculator for geology & geophysics. Enter variables to compute results with formulas and detailed steps.
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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.
Last reviewed: December 2025
Worked Examples
Example 1: Continental Crust Moho Depth
Example 2: Thin Oceanic Crust Estimation
Background & Theory
The Moho Depth Estimator 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 Moho Depth Estimator 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
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy