Ray tracing through water
Initial OBS coordinates were determined by P-code GPS ship locations at the drop point. Ocean currents caused the instrument packages to drift during the ~45 minute descent to the seafloor. To ensure accurate positions, an OBS relocation procedure was developed. This inversion procedure used water wave traveltimes to find the optimum seafloor location of each instrument. The true location of an OBS was considered to be the position which minimized the error between the measured traveltimes and the traveltimes predicted by raytracing through a 1-D sea water velocity model.
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| Fig 1: True-scale ray paths through the layered sea water velocity model. (above) |
| Fig 2: Depth vs. velocity profile collect on-site during cruise. (right) |
| The model was based on a velocity vs. depth profile collected on the Ewing during the experiment (fig 2). Figure 1 shows ray paths of different offset through the model in true scale. The relatively small perturbations in water velocity (min to max km/s) allowed rays to travel nearly straight except at large offset. Assuming straight ray paths, the average velocity of the water between the surface and 1.6 km depths is 1.481 km/s. |
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Source distribution sensitivity
To determine the precision of the OBS relocation, diagnostics were run on synthetic data. Key questions were how the relocation was affected by the airgun source distribution and how noise in the traveltimes mapped into location errors.
Two source distributions were tested. The first distribution (fig 3) was a non-symetric layout similar to areas of the ship cruise lines. A single line passed close to, but not directly over, the OBS. Sources at distances of up to 8 km were included in the inversion. The second source distribution (fig 4) was a dense cross configuration centered on the OBS. The azimuthal coverage was good but the most distance source was just over 4 km from the OBS.
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| Fig 3: Distribution similar to ship cruise lines | Fig 4: Dense but spatially limited distribution |
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| Fig 5: Ship line distribution. blue=X, purple=Y, red=Z | Fig 6: Dense distribution. blue=X, purple=Y, red=Z |
Any starting position can be provided for the OBS. The postion affects the number of required iterations, but the inversion converges to the same coordinates because the error space lacks local minima for non-pathologic source distributions.
Noise sensitivity
The second diagnostic was to determine how sensitive the relocation procedure is to inevitable error in the traveltimes. To determine this sensitivity, two error distributions were compared. One used traveltimes with 0.05 seconds of random noise (fig. 7); the other used 0.005 seconds of noise (fig. 8). These statistics were derived using the source distribution in figure 4.
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| Fig 7: blue=X, purple=Y, red=Z. (Same as figure 5) | Fig 8: blue=X, purple=Y, red=Z |
OBS clock correction
The estimated clock correction is affected by noisy traveltimes as well. The error in the estimated clock correction is a fraction of the noise level. The majority of the time, the error will be less than 20% of the noise (fig. 9&10). An order of magnitude increase in the traveltime noise, resulted in an order of magnitude increase in the clock correction error.
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| Fig 9: clock correction error distribution | Fig 10: clock correction error distribution |
Depth and clock correction trade-off
There is some trade off between depth correction and OBS clock correction. No water wave ray paths can arrive from below the OBS. Moving an OBS deeper will increase traveltimes from all sources. This is difficult to distinguish from a shift in clock time. A wide array of sources will minimize this problem. Near-horizontal ray paths are sensitive to clock time but not to depth.
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| Fig 11: Trade-off for shipline source distribution | Fig 12: Trade-off for dense sources distribution |