Inversion in shallow-water using the WKB modal condition

Modal wave number tomography and bottom parameter dependence

“…It is known that the horizontal wave number of sound field in a shallow water environment is determined by the following WKB modal condition (Wang and Shang, 1981;Shang et al, 1996) :…”

“…It was proposed by Shang et al (1996) that one may estimate the environmental parameters by minimizing the modal wave number mismatch function defined by…”

“…In Shang et al (1996), the input data for the bottom parameter inversion is discrete modal wave numbers, the cost function measuring the differences between the measured values and the values calculated based on model. In this paper, we use a new cost function:…”

“…It is different from the input used by Shang (1996) that the reflection phase shift curve, instead of the discrete modal wave numbers, is chosen as the input for matching as a 'smooth constrain'. b) It should be emphasized that the inverted error induced by noise and mismatch of the SSP can be estimated analytically as discussed in Shang (1996). It is shown that the error of bottom reflection phase shift due to the uncertainty of the SSP is given by Shang, 1981).…”