Mathematics · Mathematical Physics

Seismic Geometric-Spreading Intensity source distance Solver

Rearrange the seismic geometric-spreading intensity relationship and solve for source distance.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
source distance120
Reconstructed ideal spherical-wave intensity16.666667

Calculation steps

  1. Use b=√(a/c) with ideal spherical-wave intensity=16.666666666666668 and source intensity-distance-squared coefficient=240000.
  2. source distance=119.99999999999999.
  3. Substitution into c=a/b² reconstructs 16.66666666666667.

Understand Seismic Geometric-Spreading Intensity: solve source distance

One idea, three depths

Choose how deeply to explain Seismic Geometric-Spreading Intensity: solve source distance

Seismic Geometric-Spreading Intensity: solve source distance: Rearrange the seismic geometric-spreading intensity relationship and solve for source distance.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Seismic Geometric-Spreading Intensity: solve source distance to answer this question: rearrange the seismic geometric-spreading intensity relationship and solve for source distance? Enter ideal spherical-wave intensity and source intensity-distance-squared coefficient; the calculator shows source distance. For example: source intensity-distance-squared coefficient=240000 and source distance=120 produce ideal spherical-wave intensity=16.666666666666668. The answer tells you source distance.

Age 15Explain it to a 15-year-oldConnect it to the formula

Ideal spherical-wave intensity equals a source coefficient divided by distance squared. This page isolates source distance and verifies it in the original relationship. The rule is b=√(a/c). Its input values are ideal spherical-wave intensity, source intensity-distance-squared coefficient, and the main result is source distance. For example: source intensity-distance-squared coefficient=240000 and source distance=120 produce ideal spherical-wave intensity=16.666666666666668.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated seismic geometric-spreading intensity: solve source distance relation over the valid real-number domain stated below. The implemented relation is b=√(a/c), evaluated from ideal spherical-wave intensity, source intensity-distance-squared coefficient to produce source distance. Ideal spherical-wave intensity equals a source coefficient divided by distance squared. This page isolates source distance and verifies it in the original relationship. Real seismic waves experience layered spreading, attenuation, scattering, radiation pattern, free-surface effects, focusing, and mode conversion.

Inputs and valid domain

  • ideal spherical-wave intensity must be a finite real number.
  • source intensity-distance-squared coefficient must be a finite real number.

Important boundary: Real seismic waves experience layered spreading, attenuation, scattering, radiation pattern, free-surface effects, focusing, and mode conversion.

The formula

b=√(a/c)

How the calculator works through it

It substitutes ideal spherical-wave intensity, source intensity-distance-squared coefficient into the formula and exposes every numerical step above. The main output is source distance, accompanied by Reconstructed ideal spherical-wave intensity.

Read the result correctly

The source distance is the direct answer to “rearrange the seismic geometric-spreading intensity relationship and solve for source distance.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

source intensity-distance-squared coefficient=240000 and source distance=120 produce ideal spherical-wave intensity=16.666666666666668.

Where this model stops being reliable

Real seismic waves experience layered spreading, attenuation, scattering, radiation pattern, free-surface effects, focusing, and mode conversion.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Seismic Geometric-Spreading Intensity: solve source distance works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Seismic Geometric-Spreading Intensity: solve source distance uses b=√(a/c). You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

  • Ratios, units and dimensional meaning

    Tracking ratios and units keeps the Seismic Geometric-Spreading Intensity: solve source distance result physically interpretable instead of merely numerical.

    Review this foundation about 5 min

Optional enrichment

  • Vectors and physical direction

    Vector language extends Seismic Geometric-Spreading Intensity: solve source distance when magnitude and direction must be treated separately.

    Review this foundation about 6 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read ideal spherical-wave intensity, source intensity-distance-squared coefficient.
  2. Evaluate the principal relationship: b=√(a/c).
  3. Return source distance and check the domain conditions described above.
Python
            from math import *

def seismic_geometric_spreading_intensity_solve_b(c, a) -> float:
    return sqrt((a / c))

assert abs(seismic_geometric_spreading_intensity_solve_b(16.666666666666668, 240000) - 119.99999999999999) < 1e-6 * max(1.0, abs(119.99999999999999))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double seismic_geometric_spreading_intensity_solve_b(double c, double a) {
    return sqrt((a / c));
}

int main(void) {
    const double expected = 119.99999999999999;
    const double actual = seismic_geometric_spreading_intensity_solve_b(16.666666666666668, 240000);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double seismic_geometric_spreading_intensity_solve_b(double c, double a) {
    return std::sqrt((a / c));
}

int main() {
    constexpr double expected = 119.99999999999999;
    const double actual = seismic_geometric_spreading_intensity_solve_b(16.666666666666668, 240000);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double seismic_geometric_spreading_intensity_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global seismic_geometric_spreading_intensity_solve_b
section .text

seismic_geometric_spreading_intensity_solve_b:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-16]
    divsd xmm0, [rbp-8]
    movsd [rbp-32], xmm0
    sqrtsd xmm0, [rbp-32]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = seismic_geometric_spreading_intensity_solve_b(c, a)
    result = sqrt((a / c));
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, a_] := Sqrt[(a / c)];
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

University Physics Volume 3

Read OpenStax University Physics: Quantum Mechanics
Cite this book
APA 7
Ling, S. J., Sanny, J., & Moebs, W. (2016). University physics volume 3. OpenStax. https://openstax.org/books/university-physics-volume-3/pages/1-introduction
MLA 9
Ling, Samuel J., et al. University Physics Volume 3. OpenStax, 2016, https://openstax.org/books/university-physics-volume-3/pages/1-introduction.
Chicago author-date
Ling, Samuel J., Jeff Sanny, and William Moebs. 2016. University Physics Volume 3. Houston, TX: OpenStax. https://openstax.org/books/university-physics-volume-3/pages/1-introduction.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Seismic Geometric-Spreading Intensity source distance Solver. MW SysArc Tools. https://math.mwsysarc.com/mathematical-physics/seismic-geometric-spreading-intensity-source-distance-solver

MLA 9

MW SysArc. “Seismic Geometric-Spreading Intensity source distance Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/mathematical-physics/seismic-geometric-spreading-intensity-source-distance-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Seismic Geometric-Spreading Intensity source distance Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/mathematical-physics/seismic-geometric-spreading-intensity-source-distance-solver.

Harvard

MW SysArc (2026) ‘Seismic Geometric-Spreading Intensity source distance Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/mathematical-physics/seismic-geometric-spreading-intensity-source-distance-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_seismic_geometric_spreading_intensity_solve_b_2026,
  author = {{MW SysArc}},
  title = {Seismic Geometric-Spreading Intensity source distance Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/mathematical-physics/seismic-geometric-spreading-intensity-source-distance-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Seismic Geometric-Spreading Intensity source distance Solver
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/mathematical-physics/seismic-geometric-spreading-intensity-source-distance-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Seismic Geometric-Spreading Intensity: solve source distance do?

Rearrange the seismic geometric-spreading intensity relationship and solve for source distance.

How does the Seismic Geometric-Spreading Intensity: solve source distance work?

The calculator applies b=√(a/c). Ideal spherical-wave intensity equals a source coefficient divided by distance squared. This page isolates source distance and verifies it in the original relationship.

What can I learn from the Seismic Geometric-Spreading Intensity: solve source distance?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

MW SysArc Certified