# Difference between revisions of "Effect of station angle on location errors"

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− | == Problem == | + | == Problem 7.2 == |

If the error in Shoran time measurements is <math>\pm 0.1 \mu s</math>, what is the the size of the parallelogram of error in Figure 7.2a when (a) <math>\theta=30^{\circ}</math> and (b) <math>\theta=150^{\circ}</math>? Take the velocity of radio waves as <math>3\times 10^{5}</math> km/s. | If the error in Shoran time measurements is <math>\pm 0.1 \mu s</math>, what is the the size of the parallelogram of error in Figure 7.2a when (a) <math>\theta=30^{\circ}</math> and (b) <math>\theta=150^{\circ}</math>? Take the velocity of radio waves as <math>3\times 10^{5}</math> km/s. | ||

## Latest revision as of 15:36, 8 November 2019

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 7 |

Pages | 221 - 252 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Contents

## Problem 7.2

If the error in Shoran time measurements is **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \pm 0.1 \mu s}**
, what is the the size of the parallelogram of error in Figure 7.2a when (a) **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \theta=30^{\circ}}**
and (b) **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \theta=150^{\circ}}**
? Take the velocity of radio waves as **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3\times 10^{5}}**
km/s.

### Background

Shoran is a radio-navigation device which measures the 2-way traveltime between the point of observation and a fixed station. Using two fixed stations, the point of observation can be located by swinging arcs centered at the two stations; for large distances the arcs become nearly straight lines.

The traveltimes are subject to error **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \pm \Delta t}**
, so the ranges are **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V\left(t_{i} \pm \Delta t\right)}**
, **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle i=1}**
, 2. Swinging the four arcs corresponding to these time values, we get a *parallelogram of error* such as that in Figure 7.2a; the location lies somewhere inside this parallelogram.

### Solution

In Figure 7.2a, the error in range **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =AM=AN=AP=AQ}**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} =\left(3\times 10^{8}\ \mathrm{m/s}\right)\left(1\times 10^{-7}\ \mathrm{s}\right)=30\ \mathrm{m}. \end{align} }**

.

The long diagonal **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =2AR=2AQ/\sin15^{\circ} = 2\times 30/\sin15^{\circ} =230}**
m.

The short diagonal **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =2AS=2\times 30/\cos 15^{\circ} =60}**
m.

To get the figure for **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \theta =150^{\circ} }**
we merely reverse the arrow on **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \textit{AB}}**
or **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \textit{AC}}**
; therefore the error values are the same as for **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 30^{\circ}}**
.

## Continue reading

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Radiolocation errors because of velocity variations | Transit satellite navigation |

Previous chapter | Next chapter |

Characteristics of seismic events | Reflection field methods |

## Also in this chapter

- Radiolocation errors because of velocity variations
- Effect of station angle on location errors
- Transit satellite navigation
- Effective penetration of profiler sources
- Directivity of linear sources
- Sosie method
- Energy from an air-gun array
- Dominant frequencies of marine sources
- Effect of coil inductance on geophone equation
- Streamer feathering due to cross-currents
- Filtering effect of geophones and amplifiers
- Filter effects on waveshape
- Effect of filtering on event picking
- Binary numbers