Mode decomposition for a three‐dimensional sparse array

Matched‐mode processing determines the source location (range, depth, and bearing) by matching the mode replica function with the mode amplitude decomposed from data. Mode decomposition has been successfully demonstrated for a vertical array or multi‐vertical arrays that constitute a (three‐dimensional) filled volumetric array. For these cases, the intrinsic difference of the matched‐field and matched‐mode processing lies in how the normal modes are processed (decomposed) by each method. For a sparse three‐dimensional array such as a slanted vertical array, a slack array, or a horizontal line array, mode decomposition is not a straightforward process. A brute force and an approximate mode decomposition method are presented here; the latter has the simplicity of requiring only one mode decomposition for matched mode processing for all bearings. It is also shown that the performance of a sparse array is related to the accuracy of mode decomposition as previously demonstrated for a vertical array.