Description
Evaluate r²/sqrt((1-r²)²+(2 × damping × r)²) using separate stable forms below and above r=1.
Wave calculations relate angle, speed, distance, frequency, or attenuation under a specified propagation model. A local ray or amplitude term assumes the relevant geometry and medium rather than deriving them from observations.
Evaluate r²/sqrt((1-r²)²+(2 × damping × r)²) using separate stable forms below and above r=1.
When to use this tool
Use Geophone Natural Frequency Response Ratio when you need a local wave-propagation term with explicit parameters.
How to use the tool and how it works
- Enter frequencyRatio, dampingRatio. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read amplitudeRatio. Use the output convention below.
Require nonnegative frequencyRatio and dampingRatio except the undamped resonance r=1, damping=0. Evaluate r²/sqrt((1-r²)²+(2 × damping × r)²) using separate stable forms below and above r=1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| frequencyRatio | Nonnegative measurement frequency divided by the natural frequency. | Required. Finite number; minimum 0. |
| dampingRatio | Nonnegative dimensionless supplied damping ratio. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| amplitudeRatio | Amplitude Ratio | Required. Finite number. |
{
"input": {
"frequencyRatio": 1,
"dampingRatio": 0.5
},
"output": {
"amplitudeRatio": 1
}
}Limitations and assumptions
- FrequencyRatio is applied/natural frequency and damping is dimensionless; this is the stated second-order normalized amplitude model, not measured geophone calibration, phase response, or an instrument-specific correction.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a full forward model or inversion when the medium, interfaces, or travel paths are unknown. Verify angular convention, physical units, and amplitude-versus-energy interpretation.
References
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