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Related Artists:. Trace Drum N Bass. Alternative Names:. To order by phone:. Call quoting EIL. Why you should buy from us. Laura buried in new stock arrivals. If the speed of sound is not constant, the rays follow curved paths rather than straight ones. The computational technique known as ray tracing is a method used to calculate the trajectories of the ray paths of sound from the source.
Ray theory is derived from the wave equation when some simplifying assumptions are introduced and the method is essentially a high-frequency approximation. The method is sufficiently accurate for applications involving echo sounders, sonar, and communications systems for short and medium short distances.
These devices normally use frequencies that satisfy the high frequency conditions. This article demonstrates that ray theory also can be successfully applied for much lower frequencies approaching the regime of seismic frequencies. This article presents classical ray theory and demonstrates that ray theory gives a valuable insight and physical picture of how sound propagates in inhomogeneous media.
However, ray theory has limitations and may not be valid for precise predictions of sound levels, especially in situations where refraction effects and focusing of sound are important. There exist corrective measures that can be used to improve classical ray theory, but these are not discussed in detail here.
Recommended alternative readings include the books. A number of realistic examples and cases are presented with the objective to describe some of the most important aspects of sound propagation in the oceans. This includes the effects of geographical and oceanographic seasonal changes and how the geoacoustic properties of the sea bottom may limit the propagation ranges, especially at low frequencies. The examples are based on experience from modeling sonar systems, underwater acoustic communication links and propagation of low frequency noise in the oceans.
There exist a number of ray trace models, some are tuned to specific applications, and others are more general. In this chapter the applications and use of ray theory are illustrated by using Plane Ray, a ray tracing program developed by the author, for modeling underwater acoustic propagation with moderately range-varying bathymetry over layered bottom with a thin fluid sedimentary layer over a solid half with arbitrary geo-acoustic properties.
However, the discussion is quite general and does not depend on the actual implementation of the theory. Figure 1 shows a small segment of a ray path and the coordinate system. When the speed of sound varies with depth the ray paths will bend and the rays propagate along curved paths. The radius of curvature R is defined as the ratio between an increment in the arc length and an increment in the angle. Figure 1 shows that the radius of curvature is.
Taking the derivative of Eq. The positive or negative sign of the gradient determines whether the sign of R is negative or positive, and thereby determines if the ray path curves downward or upward. A small segment of a ray path in a isotropic medium with arc length ds.
The ray parameter is not constant when the bathymetry varies with range. For the coordinates of the running point at r 2 , z 2 along the ray path, the horizontal distance is.
Left: The sound speed profile. Right: A portion of a ray traveling from point r 1 , z 1 to r 2 , z 2. The acoustic intensity of a ray can, according to ray theory, be calculated using the principle that the power within a ray tube remains constant within that ray tube. At a reference distance r 0 from the source, the intensity is I 0. At horizontal distance r, the intensity is I.
In terms of the perpendicular cross section dL of the ray tube, the power is. Since the power in the ray tube does not change, we may equate Eq. Instead of using Eq. The last expression in Eq. With respect to the reference distance r 0 , the transmission loss TL is defined as.
By inserting Eq. In this treatment the transmission loss includes only the geometric spreading loss. Therefore bottom and surface reflection losses and sea water absorption loss must be included separately. The geometric transmission loss in Eq. The first term represents the horizontal spreading of the ray tube and results in a cylindrical spreading loss.
The second and third terms represent the vertical spreading of the ray tube and are influenced by the depth gradient of the sound speed. The first condition signifies a turning point where the ray path becomes horizontal; the second condition occurs at points where an infinitesimal increase in the initial angle of the ray produces no change in the horizontal range traversed by the ray.
The locus of all such points in space is called a caustic. In both cases there is focusing of energy by refraction and where classical ray theory incorrectly predicts infinite intensity.
Caustics and turning points will be discussed further in section 8. From Eq. By applying Eqs. In practice, the sound speed profile is often given as measured sound speeds at relatively few depth points.
It is therefore advisable to use an interpolation scheme that is consistent with the usual behavior of the sound speed profile to increase the number of depth points to an acceptable high density. The examples in this article are generated using the ray trace program PlaneRay that has been developed by the author [ 7 - 8 ].
However, any other ray programs with similar capabilities could have been use and the discussion is therefore valid for ray modeling in general.
Other models frequently used and are the Bellhop model [ 9 ], and the models [ 10 - 11 ]. Figure 5 shows an example of ray modeling. The sound speed profile is shown at the left panel and the rays from a source at 50 m depth is shown in the right panel, which also shows the bathymetry and the thickness of the sediment layer over the solid half space. Sound speed profile and ray traces for a typical case. The source depth is m and the red dotted line indicates a receiver line at a depth of 50 m.
To calculate the acoustic field it is necessary to have an efficient and accurate algorithm for determination of eigenrays. An eigenray is defined as a ray that connects a source position with a receiver position. The PlaneRay model uses a unique sorting and interpolation routine for efficient determination of a large number of eigenrays in range dependent environments.
This approach is described by the two plots in Figure 6 , which displays the ray history as function of initial angle at the source. All facts and features of the acoustic fields such as the transmission loss, transfer function and time responses are derived from the ray traces and their history The two plots show the ranges and travel times to where the rays cross the receiver depth line marked by the red dashed line in Figure 5.
A particular ray may intersect the receiver depth line, at several ranges. For instance at the range of 2 km, there are 11 eigenrays and from Figure 6 the initial angles of these rays are approximately found to be 5.
However, the values found in this way are often not sufficiently accurate for the determination of the sound field. Further processing may therefore be required to obtain accurate results. The graphs of Figure 6 are composed of independent points, but it is evident that the points are clustered in independent clusters or groups. This property is used for sorting the points into branches of curves that represents different ray history. These branches are in most case relatively continuous and therefore amenable to interpolation.
An additional advantage of this method is that the contribution of the various multipath arrivals can be evaluated separately, thereby enabling the user to study the structure of the field in detail. Ray history of the initial ray tracing in Figure 5 showing range left and travel time right to the receiver depth as function of initial angel at the source. In most cases the eigenrays are determined by one simple interpolation yields values that are sufficiently accurate for most application, but the accuracy increases with increasing density of the initial angles at the cost of longer computation times.
Figure 7 shows examples of eigenrays traces with rays a receiver located at 2. Eigenrays from a source at m depth to a receiver at 50 m depth and distance of 2.
Sound absorption is important for long range propagation especially at higher frequencies. The absorption increases with frequencies and is dependent on temperature, salinity, depth and the pH value of the water. There exists several expressions for acoustic absorption in sea water; one of the preferred options is the semi-empirical formulae by Francoise and Garrison [ 12 ]. Figure 8 shows sound absorption as function of frequency in sea water using this expression for the values given in the figure caption.
The various contributions to the absorption are also indicated. Ray tracing is greatly simplified when no rays are traced into the bottom, but stops at the water-bottom interface.
This avoids tracing of multiple reflections in layered bottoms. Instead the boundary conditions at the sea surface and the bottom can be approximately satisfied by the use of plane wave reflection coefficient. A simple and useful bottom model is assuming a fluid sedimentary layer over a homogeneous solid half space. The reflection coefficient of a bottom with this structure is. The reflection coefficient between the water and the sediment layer, r 01 , is given as.
The wave attenuations are 0. The small, but significant, reflection loss at lower angles is caused by shear wave conversion and bottom absorption In this case the attenuation is about 1 dB in the frequency band around 50 Hz to Hz. For a sea surface with ocean waves there will be diffuse scattering to all other direction than the specular direction, which result in a reflection loss that in the first approximation can be modeled by the coherent rough surface reflection coefficient.
Bottom reflection loss dB as function of frequency and incident angle for a 2 m sediment layer over solid rock. The parameters are given in the text.
Figure 10 shows the rough surface reflection loss as function of grazing angle, calculated for a wave height of 0. Reflection loss dB of rough surface with rms. Optical shines through well and he hit a level of sci fi minimalism on Sphere that was out of this world really.
Sonar is a monstrous classic techstep but Sphere is nonetheless a great tune and a bit underrated imo. Sonar is better than Sphere, hands down. However Sphere is still a great tune. Trace's "Sonar" tune is dark and heavy. Also a Mampi Swift tape from at Helter Skelter Excellent tune! Credit also to Optical on this excellent number. This record is well worth tracking down on the excellent Prototype recordings label.
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