The Santa Barbara Channel Experiment (SBCX)

Optimal RAM Mesh Parameters in the SBCX Environment

Motivation

Source localization through Matched Field Processing (MFP) requires one to repeatedly simulate the acoustic field propagating from a candidate source position to a known receiver array. For each iteration, the candidate source position is changed slightly. The simulated pressure field at the receiver (known as the ``replica,'') is correlated with the actual received field; the correlation results for all candidate source positions are plotted on an ambiguity surface. Generally, the candidate source position with the highest correlation indicates the location of the acoustic source.

Accuracy of the model used to simulate the received pressure field is extremely important to successful localization. Several model types exist; it is useful to divide them into categories. Range-independent models treat the ocean floor as flat, whereas range-dependent models have the capability of handling bathymetric variations in range. Modeling the acoustic path as a waveguide allows for one to use an eigenvector/value approach. Decomposition of the pressure field into a series of orthonormal modefunctions allows one to rapidly calculate the pressure field at any point in the waveguide. Unfortunately, this technique works well only when the propagation environment can be modeled as a waveguide; the accuracy of results degrades as range-dependent effects (varying bathymetry) are introduced into the waveguide. Another technique involves using the Parabolic Equation (PE) to simulate the pressure field through a range dependent environment. Rather than decompose the acoustic pressure field, the PE solution solves for the field marching in steps from source to receiver. It provides improved accuracy over normal mode methods in range-dependent environments, at the expense of increased computational time.

The Santa Barbara Channel Experiment featured a range-dependent environment which lent itself toward the use of PE methods for acoustic field calculations. Before running simulations, the proper parameters for PE replica calculations were established. Of great importance were the , or marching step interval, and , the depth interval. These two parameters determined the granularity of the acoustic field calculation using PE. If these parameters were too large, the simulated pressure field would not be accurate. Too small, and too much time would be spent computing the field for the desired accuracy.

To help determine the proper setting for , a comparison was made between normal mode (NM) and parabolic equation (PE) simulations. In both cases, an identical range-independent environment was used. One assumed the NM pressure field to be correct in the range-independent case; the parameters used in the PE simulation would be altered until they matched the pressure field in the NM solution.

Green's function

Comparison of the PE and NM pressure field output required one to decompose simulation outputs. The pressure field is represented by Green's function, G(r,z_s,z_r). NM simulation codes output the eigenvalues (wavenumbers), k_l and eigenfunctions (modeshapes), (z) of the waveguide. Together with the source and receiver depths, z_s and z_r, as well as their intermediate range, r, they can be combined to form Green's function,

P(r,z_s,z_r,)

Comparison of G_pe and G_nm is easier if the exponential carrier, e^jkr is removed. For the parabolic equation method, one would drop the exponential term in Equation 2. One cannot drop the exponential term inside the summation of the normal mode solution and obtain the same result. Rather, suppression of the carrier can be achieved if both Green's functions are multiplied by e^-jk₀r, where k₀ is a nominal wavenumber. In this simulation, with c₀ = 1480 m/sec.

Simulation environment

The baseline propagation environment used in the simulations was a range independent waveguide with an isovelocity sound profile. A single source was positioned at 30 meters in depth. Bottom properties similar to those found in the Santa Barbara Channel Experiment were used.

Figure 1: Simulation environment used for comparison between KRAKEN and RAM

Layer	Depth	Pressure speed	Shear speed	Density	Attenuation
	(m)	cp (m/sec)	cs (m/sec)	(g/cm3)	(dB/)
Water	0.0	1500	0	1.00	0.00
	197.7	1500	0	1.00	0.00
Sediment 1	197.7	1560	0	1.85	0.18
	286.7	1821	0	1.85	0.18
Sediment 2	286.7	1862	0	1.88	0.03
	586.7	2374	0	1.88	0.03
Bottom	586.7	2374	0	2.03	0.04

Parameter variation

With the simulation parameters established, the comparison between normal mode and parabolic equations was performed. KRAKEN was used for normal mode simulation, and RAM employed in the parabolic equation case. The objective of the simulations was to determine what parameter to use in the PE simulation. The parameter was fixed at 5 meters. Simulations were performed with set to 1, 0.5, 0.25, and 0.125 meters.

Simulation results

An error metric was constructed as a function of range. The pressure fields for both NM and PE were compared by averaging their differences across depth,

Figure 2: Difference between pressure fields generated by KRAKEN and RAM, averaged over depth

From the scale indicated, the plots show little difference in accuracy between simulations across frequencies. One can qualitatively see the error decreases as frequency increases. Unfortunately, the density of the results give little insight into the effect of changes in .

Figure 3: Pressure field simulation variations at 7.5 and 15 km

Figure 3 shows the pressure field generated by Equations 3 and 4 as a function of depth, for 100, 250, and 400 Hz, at 7.5 and 15 km. The dark blue ``Kraken'' line is assumed to be correct; one desires RAM to match it as closely as possible. For 100 Hz, only the green 1.0 m line fails to match the Kraken line. As one increases frequency to 250 Hz, the differences between spacing becomes more distinct, with 1.0 m still not matching, but small mismatches in smaller increments. At 400 Hz, the only line which consistently follows the Kraken line is the 0.125 m line.

Recommendations

From Figure 3 it is easy to see that 1 meter mesh spacing is not adequate for accurate pressure field calculation. At 100 Hz, accurate results may be obtained out to 15 km using 0.5 meter spacing. At 250 Hz, 0.125 spacing would be prudent, while closer spacing would be recommended for 400 Hz simulations.

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Last updated: 990914 Comments/Questions: pmd@mit.edu