A Global SOFAR Channel Wave Speed Map

Triangulating an ocean acoustic event requires an accurate estimate of the propagation time between a remote source and the receiving hydrophone. It is dependent on the speed of sound over the path taken, which is affected by water temperature, salinity, and pressure. The sound speed reaches a minimum at a particular depth depending on those local values, called the SOFAR deep sound channel because sounds above or below that depth tend to refract back into the channel. This allows a very low loss over great distances if a sound enters the SOFAR channel. Using the World Ocean Atlas data set allows computing the SOFAR depth and speed with useful accuracy on a quarter degree global grid. With an estimate of speed variations, it is then a matter of integrating the average speed over any path of interest. The speed map is used to generate a map of travel times for each hydrophone location.

There are various sound models, but they are in general agreement on the computation. Sound speed at sea level is close to about 1.5 km/sec in salt water, but may slow to 1.45 km/s in the SOFAR channel. For trans-oceanic signals, that can become a difference of several minutes in expected arrival time, or an error of hundreds of kilometers when matching up arrivals to locate an origin.

A first attempt at profiling particular paths was with the handy Ocean Data View (ODV) tool which can directly load World Ocean Atlas WOA-v13 from its graphical interface. It has the ability take a section profile slice of sound speed vs depth between two ocean locations to generate a pseudocolor image. To find the speed minimum along then required external code. While unable to export the path data directly, it was found that the exportable .png image color index values could be pegged to the speed range.

Ocean Data View application showing a sound speed profile over a path.

A simple image processing routine followed the minima and integrated a path speed result.

Sound speed profile from H01S to implosion event. Estimate = 1.4767 km/s

The early signal matching here used that manual method to profile the speed over key paths. To generate the cartographic maps, speeds to about a dozen points around the Indian Ocean were used with MATLAB to fit a smooth 2d surface for interpolation. As accuracy became more critical or signal matching, interpolating speeds on the full WOA grid was a logical next step. WOA-v13 annualized average data for March was chosen and imported to MATLAB, and SOFAR speed/depth were then computed on the grid. The result was projected with an equiangular plate carrée projection base map. The floating point values are stored as an array for later use, but can also be saved into a lossless 16 bit .png image file.

SOFAR Speed Map – Red = Speed, Cyan = Depth
Speed range = 1405.768-1548.136 m/s, Depth range = 0 – 2100 m.

Knowing the range of values in each channel, the 16-bit image itself can be loaded as a dataset. The previous graphical method of getting the propagation time between two locations is now a matter of feeding the coordinates to a code function that integrates over a line on the map. Using accurate geodesics, a best estimate of propagation speed and time can be displayed, along with the section profile:

Sound speed stats by integration between two locations on the SOFAR map. (H01 and the Southern Event).

The next step of precomputing a path speed map takes about 10 minutes of processing for each hydrophone or T-wave seismometer. Here is a graphical path-speed map for hydrophone H08:

SOFAR path speed map to hydrophone array H08S.

The path speed array can now be utilized in future code for rapid calculation of propagation times. For visualization, the array is added as the green channel to complete the H08 SOFAR speed / pathspeed / depth map image:

The H08s path speed visualized as the green channel with the speed-depth map.

Future work will incorporate the hydrophone path speed data arrays for more accurate acoustic event mapping.