Tri Station Circle Epicenter Least Squares Solver
Epicenter from three S-P distance circles via Gauss-Newton least squares.
Description
Epicenter from three S-P distance circles via Gauss-Newton least squares.
Tri Station Circle Epicenter Least Squares Solver is a focused tool for the following task. Epicenter from three S-P distance circles via Gauss-Newton least squares. It reports x₀, y₀, rms from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use Tri Station Circle Epicenter Least Squares Solver
Use this seismology calculation to reproduce a stated convention, screen observations, or compare scenarios whose units, coordinate conventions, catalog selection, and model assumptions are known.
- x_i
- Required list. Station eastings (km).
- y_i
- Required list. Station northings (km).
- d_i
- Required list. Hypocentral-projected distances.
The cited overview of Seismometer supplies background for the terminology and domain context used by this tool.1
How Tri Station Circle Epicenter Least Squares Solver works
Epicenter from three S-P distance circles via Gauss-Newton least squares. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- x₀ (km)
- Returned number in km. Estimated easting.
- y₀ (km)
- Returned number in km. Estimated northing.
- rms (km)
- Returned number in km. Circle-fit residual RMS.
Limitations and assumptions
- Earth structure, source geometry, path effects, site response, instrument response, catalog completeness, uncertainty, and the fitted range can dominate the accuracy of simplified seismic calculations.
- Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.
Alternative or Complementary approaches
For analysis or hazard decisions, retain uncertainty and provenance and compare the result with waveform processing, calibrated regional models, and guidance from qualified seismologists or the responsible agency.
References
-
Seismometer — Wikipedia contributors
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