| Summary: | When a hydrophone is deployed under the critical depth in deep ocean, the interference pattern will be complex and variable. The waveguide invariant is no longer constant and is treated as a distribution. The interference pattern is impacted by refracted and surface reflected (RSR) modes, as well as surface reflected and bottom reflected (SRBR) modes together. This phenomenon is illustrated by numerical simulation and explained by the waveguide invariant theory in this paper. The theory demonstrates: (1) The interference pattern in zone-b corresponds to the waveguide invariant <inline-formula><math display="inline"><semantics><mrow><msub><mi>β</mi><mrow><mi>R</mi><mi>S</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula> that varies quickly and leads to the slope change, which is contributed by RSR modes whose phase velocity is less than the sound velocity at seafloor; (2) The interference pattern in zone-a1 and zone-c1 is corresponding to the <inline-formula><math display="inline"><semantics><mrow><msub><mi>β</mi><mrow><mi>S</mi><mi>R</mi><mi>B</mi><mi>R</mi><mi>W</mi><mi>S</mi></mrow></msub></mrow></semantics></math></inline-formula> that is the approximately 0.7 and leads to the stable slope, which is contributed by SRBR modes whose phase velocity is between the sound velocity at seafloor and sediment velocity; (3) The interference pattern in zone-a2 and zone-c2 is corresponding to the <inline-formula><math display="inline"><semantics><mrow><msub><mi>β</mi><mrow><mi>S</mi><mi>R</mi><mi>B</mi><mi>R</mi><mi>S</mi><mi>H</mi></mrow></msub></mrow></semantics></math></inline-formula> which hardly varies at low frequency but varies fiercely with source frequency increasing, so the striations are complex with high frequency, which is contributed by SRBR modes whose phase speed is between sediment speed and half space speed.
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