According to different findings (e.g., Ciraolo et al. 2007; Mannucci et al. 1998), the GPS receiver measurements are important to estimate the electron density along a ray path between a GPS satellite and receiver on the ground.
The relationship between these data and the electron density can be described by (1) where N s) is the electron density distribution, and p represents a ray path between the satellite and the ground receiver.
Each curve corresponds to a time sequence of the TEC along a ray path between a satellite and a receiver, and the large variability of the curves is related to differing look angles of the GPS satellites and receiver clock biases, among other factors.
We consider the slant TEC, STEC i,j,k, measured along a ray path between satellite-i and receiver-j at a time epoch k for i = 1,2,…, s, j = 1,2,…,r, k = 1,2,…,t, where s is the number of the available satellite, r is the number of the receiver, and t is the number of the time series data.
The attenuation factor (t^) for the P- or S-wave propagating into a three-dimensionally heterogeneous structure may be represented as t^ = mathop int limits_{text{ray path}}^ frac{{{text{d}}s}}{{v_{{left( {x,y,z} right)}} Q_{{left( {x,y,z} right)}} }}, (4 where (v) is the seismic velocity (Thurber 1983), and the integration is performed along a ray path between the event and the station.
Using the Fast Onboard Recording of Transient Events satellite (FORTÉ), it has been shown that trans-ionospheric pulsed radio-frequency (RF) signals carry sufficient information to infer the peak electron density of the ionosphere, in addition to the total electron content along a ray path between a source and a receiver.
As originally stated, the path taken by a ray of light between two fixed points in an arrangement of mirrors, lenses, and so forth, is that which takes the least time.
In order to evaluate these areas, we take a look at a distance between a ray and the center of the object.
Wodehouse once noted that it was seldom difficult to tell the difference between a ray of sunshine and a Scotsman with a grievance.
Let denote the angle between a ray from the origin to the sound source and a ray from the origin to the point of observation (left or right ear) on the surface of the sphere as shown in Figure 1.
