# Radiolocation errors because of velocity variations

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 7 221 - 252 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 7.1

Ground conductivity affects radio-wave velocity because of currents induced in the earth. Range calculations assuming that travel is over normal seawater thus may be in error if this is not true. What errors are involved for travelpaths over the terrains in Table 7.1a?

Table 7.1a. Radio-wave velocities over various terrains.
Terrain Velocity (km/s)
Seawater 299 670
Freshwater 299 250
Farmland 299 400
Dry sand 299 900
Mountains 298 800

### Background

Radio-navigation methods are used to determine distances in marine surveys and the velocity is generally assumed to be that over saltwater.

### Solution

Let ${\displaystyle V_{S}}$ be velocity over normal seawater and ${\displaystyle V_{T}}$ velocity over other terrains. If we use ${\displaystyle V_{S}}$ to calculate ranges, the error in range calculations will be ${\displaystyle \Delta x=t\left(V_{S}-V_{T}\right)}$ and the relative error is ${\displaystyle \Delta x/x=1000\left(1-V_{T}/V_{S}\right)}$ m/km. When ${\displaystyle V_{T}, the error will be positive, meaning that the calculated range is too great. The results are shown in Table 7.1b.

Table 7.1b. Location errors for various terrains.
Terrain Velocity (km/s) Error (m/km)
Seawater 299 670 0.0
Freshwater 299 250 1.4
Farmland 299 400 0.9
Dry sand 299 900 –0.8
Mountains 298 800 2.9