P Wave Azimuthal Residual Vector Sum Split
Summarize the first azimuthal harmonic of P-wave residuals and use a least-squares cosine/sine fit to separate systematic directional variation from residual scatter.
Description
Summarize the first azimuthal harmonic of P-wave residuals and use a least-squares cosine/sine fit to separate systematic directional variation from residual scatter.
P Wave Azimuthal Residual Vector Sum Split is a focused tool for the following task. Summarize the first azimuthal harmonic of P-wave residuals and use a least-squares cosine/sine fit to separate systematic directional variation from residual scatter. It reports |Σr·û|, φ_sys, rand% from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use P Wave Azimuthal Residual Vector Sum Split
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.
- az_i
- Required list. Station azimuths.
- r_i
- Required list. Signed P residuals.
The cited overview of Seismic wave supplies background for the terminology and domain context used by this tool.1
How P Wave Azimuthal Residual Vector Sum Split works
Summarize the first azimuthal harmonic of P-wave residuals and use a least-squares cosine/sine fit to separate systematic directional variation from residual scatter. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- |Σr·û| (s)
- Returned number in s. Magnitude of the residual-weighted direction sum.
- φ_sys (°)
- Returned number in °. Azimuth of the systematic component.
- rand% (%)
- Returned number in %. Share of variance not explained by the systematic term.
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
-
Seismic wave — Wikipedia contributors
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