Geophysics Calculators
Free geophysics calculators: seismic wave velocity, seismic refraction, moment magnitude, fault slip rate, gravity anomaly, geothermal gradient, heat flow.
Geophysics Calculators - Seismic Waves, Rock Properties, and Earthquake Magnitude
Geophysics applies the physics of waves and elastic materials to Earth’s interior, from how fast seismic energy travels through rock, to how strongly it reflects off a buried boundary, to how large the earthquake was that generated it in the first place. CalculatorPod’s geophysics calculators cover the foundational relationships seismologists, exploration geophysicists, and earth-science students reach for constantly.
Twenty-Five Geophysics Calculators
Seismic Refraction Depth Calculator - Depth to a refracting layer boundary from crossover distance and the direct- and refracted-wave velocities picked off a travel-time curve, with a chart of the direct and refracted travel-time lines and the crossover point marked.
P-Wave and S-Wave Velocity Calculator - Derives seismic P-wave and S-wave velocities from a rock’s bulk modulus, shear modulus, and density (Vp = sqrt((K + 4/3G)/rho), Vs = sqrt(G/rho)), with the Vp/Vs ratio, Poisson’s ratio, and a chart of both velocities versus density.
Seismic Impedance and Reflection Coefficient Calculator - Acoustic impedance (Z = rho x V) for two rock layers and the normal-incidence reflection coefficient (R = (Z2-Z1)/(Z2+Z1)) at their boundary, with automatic polarity flagging and a chart of R versus impedance contrast.
Richter Magnitude Calculator - Estimates local (Richter) earthquake magnitude from maximum seismogram amplitude and epicentral distance, with a chart showing how the same recorded amplitude implies a larger magnitude at greater distance.
Moment Magnitude Calculator - Seismic moment and moment magnitude (Mw = (2/3)(log10(M0) - 9.1)) from fault rupture length, width, average slip, and crustal shear modulus, with a chart of magnitude versus average slip.
Seismic Energy Release Calculator - Total radiated seismic energy and TNT-equivalent tonnage from earthquake magnitude using the Gutenberg-Richter relation (log10(E) = 1.5M + 4.8), with a log-scale chart showing energy’s explosive growth with magnitude.
Earthquake Intensity (MMI) Estimator - Estimates Modified Mercalli Intensity from peak ground acceleration using the Wald et al. (1999) empirical relation, with a Roman numeral intensity label and a chart of estimated MMI versus PGA.
Fault Slip Rate and Recurrence Interval Calculator - Long-term fault slip rate (SR = D_total / T) and the average earthquake recurrence interval (RI = D_event / SR) from a fault’s total accumulated offset, time span, and characteristic event slip, with a chart of recurrence interval versus slip rate.
Plate Tectonic Velocity Calculator - Linear plate motion velocity (v = omega x R x sin(Delta)) from a plate’s Euler pole angular rotation rate and angular distance from that pole, with a chart of velocity versus angular distance.
Gravity Anomaly (Bouguer) Calculator - Bouguer gravity anomaly from observed gravity, latitude, elevation, and rock density using the 1967 International Gravity Formula plus free-air and Bouguer slab corrections, with a chart of normal gravity versus latitude.
Free-Air Gravity Correction Calculator - Free-air gravity anomaly from observed gravity, latitude, and elevation using the 1967 International Gravity Formula plus the free-air correction alone, with no rock-density term, suited to marine and airborne surveys, and a chart of normal gravity versus latitude.
Geoid Undulation Estimator - Geoid undulation N (N = h - H) from a GPS-measured ellipsoidal height and a leveled orthometric (mean sea level) height, with a plain-language note on whether the geoid sits above or below the reference ellipsoid there.
Geothermal Gradient Calculator - Geothermal gradient in degrees C per kilometer from a surface and a measured borehole temperature, with temperature extrapolated to any target depth and a chart of temperature versus depth.
Heat Flow Density Calculator - Crustal heat flow density (q = k x G) from a rock’s thermal conductivity and the local geothermal gradient, via Fourier’s law of heat conduction, with a plain-language continental/elevated/volcanic classification note.
Curie Point Depth Calculator - The depth at which crustal rock reaches the Curie temperature and loses ferromagnetism (D = (T_curie - T_surface) / G) from a simple linear geotherm, with a chart of the genuinely inverse Curie depth versus gradient relationship.
Earth Magnetic Field Declination Estimator - Dipole-approximation magnetic declination from a site’s latitude and longitude and the geomagnetic pole position, with a prominent caveat that real-world declination requires NOAA’s World Magnetic Model.
Electrical Resistivity of Earth Layers Calculator - Apparent ground resistivity from a Wenner four-electrode array survey reading (rho_a = 2pia*V/I), with realistic millivolt/milliamp field inputs and a plain-language clay/sand/bedrock classification note.
Isostasy and Crustal Thickness Calculator - Compute Airy crustal root depth and total crust thickness under mountains or ocean basins from elevation and densities, with a Pratt comparison and root chart.
Seismic Reflection Two-Way Travel Time Calculator - Two-way travel time (TWT = 2h/V, in ms) from reflector depth and average velocity, or reflector depth from a picked TWT, with a chart of TWT versus depth marking your reflector and showing slower and faster velocity lines.
Tsunami Wave Speed Calculator - Tsunami wave speed (c = sqrt(g x d)) from ocean depth in m/s and km/h, with travel time over a distance and wavelength from the wave period, and a chart of speed versus depth.
Tsunami Runup Height Estimator - Estimate tsunami runup height from offshore wave height, depths and beach slope using Green’s law shoaling and Synolakis runup, with a chart of runup versus beach slope.
Volcanic Eruption Energy Estimator (VEI) - Estimate the VEI class, dense-rock mass and thermal energy of a volcanic eruption from tephra volume, with TNT and Hiroshima equivalents.
Stress Drop in Earthquake Source Calculator - Estimate the static stress drop of an earthquake in MPa and bar from seismic moment (or Mw) and source radius, or from corner frequency, with a log-log chart of stress drop versus radius.
Attenuation Quality Factor Calculator - Find seismic quality factor Q from amplitude decay, or predict the amplitude left after a travel time, with attenuation coefficient and charts.
Ground Motion Prediction Equation Calculator - Estimate median peak ground acceleration (g and m/s2) and shaking intensity from earthquake magnitude and distance using the Joyner-Boore attenuation relation, with a PGA-versus-distance chart.
For general wave-speed and acoustic tools, see the Physics subcategory’s Speed of Sound Calculator.
Frequently Asked Questions
How does seismic refraction surveying find the depth to a rock layer?
A refraction survey plots first-arrival travel time against distance from the source for a line of receivers, producing two straight segments, a shallower-slope line for the direct wave and a steeper-slope line for the wave refracted along the faster underlying layer. The distance where those two lines cross, the crossover distance, together with both wave velocities read off the line slopes, gives the depth to the refracting boundary. The Seismic Refraction Depth Calculator solves for that depth directly.
What determines seismic wave speed through rock?
A rock's elastic properties, its bulk modulus (resistance to compression) and shear modulus (resistance to shape distortion), together with its density, set both its P-wave and S-wave velocity. The P-Wave and S-Wave Velocity Calculator computes both directly from these three properties.
Why do seismic waves reflect at rock layer boundaries?
A wave partially reflects whenever it crosses a boundary between two materials with different acoustic impedance (density times velocity). The Seismic Impedance and Reflection Coefficient Calculator quantifies exactly how much of the wave reflects versus transmits at any such boundary.
How is earthquake magnitude estimated from a single seismogram?
Local (Richter) magnitude uses the maximum recorded trace amplitude, corrected for how much the seismic wave attenuated over the distance from the earthquake to the recording station. The Richter Magnitude Calculator applies this correction automatically.
Is the Richter scale still used today?
Modern seismology primarily reports moment magnitude for large earthquakes since it doesn't saturate at high values the way local (Richter) magnitude does, but local magnitude remains standard for small-to-moderate regional earthquakes and is what the historical "Richter scale" name refers to.
How is fault recurrence interval estimated from slip rate?
Recurrence interval is a typical single-earthquake displacement divided by the fault's long-term slip rate (RI = D_event / SR). The Fault Slip Rate and Recurrence Interval Calculator derives both directly from a fault's accumulated offset and elapsed time.
What is an Euler pole and why does plate velocity vary across a plate?
Under the rigid-plate rotation model, an entire tectonic plate rotates about a single Euler pole at one shared angular rate, but linear surface velocity depends on distance from that pole (v = omega x R x sin(Delta)), so different points on the same plate move at different speeds. The Plate Tectonic Velocity Calculator computes this directly.
Why is Bouguer anomaly usually negative over mountains?
Mountain ranges are typically isostatically compensated by a low-density crustal root at depth, and that mass deficit outweighs the visible topographic mass excess, producing a negative Bouguer anomaly. The Gravity Anomaly (Bouguer) Calculator applies the free-air and Bouguer slab corrections needed to compute it.
What is the difference between free-air anomaly and Bouguer anomaly?
Free-air anomaly corrects observed gravity for elevation only, while Bouguer anomaly goes further and also subtracts the gravitational pull of the rock mass beneath the station using a density value. The Free-Air Gravity Correction Calculator computes the elevation-only version, standard for marine and airborne surveys.
What is geoid undulation?
Geoid undulation is the vertical distance between the geoid, Earth's true equipotential surface approximating mean sea level, and a reference ellipsoid such as WGS84, computed simply as N = h - H from a GPS ellipsoidal height and a leveled orthometric height. The Geoid Undulation Estimator converts between the two directly.
How is geothermal gradient calculated from borehole data?
Geothermal gradient is the temperature rise between the surface and a measured depth, divided by that depth in kilometers, and it can then be used to extrapolate temperature to other depths assuming a locally linear geotherm. The Geothermal Gradient Calculator performs both steps from a surface and a borehole temperature reading.
How is crustal heat flow density calculated from conductivity and gradient?
Heat flow density follows Fourier's law of heat conduction applied to the crust, q = k x G, where k is the rock's thermal conductivity and G is the geothermal gradient, and a convenient unit cancellation lets the result come out directly in mW/m2. The Heat Flow Density Calculator also classifies the result as typical continental, elevated, or very high.
What is Curie point depth and how is it estimated?
Curie point depth is the depth at which crustal rock reaches the Curie temperature of its dominant magnetic mineral and loses ferromagnetism, estimated under a simple linear geotherm as D = (T_curie - T_surface) / G. The Curie Point Depth Calculator computes it directly and charts its inverse relationship with geothermal gradient.
How is magnetic declination estimated from location alone?
A simplified dipole model estimates declination as the great-circle bearing from a site to the geomagnetic north pole, though this first-order approximation can differ substantially from the real, non-dipole magnetic field. The Earth Magnetic Field Declination Estimator computes this dipole estimate while clearly flagging it as distinct from NOAA's authoritative World Magnetic Model.
How is ground resistivity measured with a Wenner electrode array?
A Wenner survey injects current through the outer two of four equally spaced, collinear electrodes and measures the resulting voltage across the inner two, then applies the geometric-factor formula rho_a = 2*pi*a*(V/I) to convert that reading into apparent resistivity. The Electrical Resistivity of Earth Layers Calculator performs this conversion directly from field-realistic millivolt and milliamp inputs.