[
    {
        "id": "authors:bmzv3-x8b22",
        "collection": "authors",
        "collection_id": "bmzv3-x8b22",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200113-110853879",
        "type": "article",
        "title": "Acoustic Wave Propagation in an Underwater Sound Channel 1. Qualitative Theory",
        "author": [
            {
                "family_name": "Blum",
                "given_name": "Joseph W.",
                "clpid": "Blum-J-W"
            },
            {
                "family_name": "Cohen",
                "given_name": "Donald S.",
                "clpid": "Cohen-D-S"
            }
        ],
        "abstract": "We give a qualitative study of wave propagation in an inhomogeneous medium principally by geometrical optics and ray theory. The inhomogeneity is represented by a sound-speed profile which is dependent upon one coordinate, namely the depth; and we discuss the general characteristics of wave propagation which result from a source placed on the sound channel axis. We show that our mathematical model of the sound-speed in the ocean actually predicts some of the behaviour of the observed physical phenomena in the underwater sound channel. Using ray theoretic techniques we investigate the implications of our profile on the following characteristics of SOFAR propagation: (i) the sound energy travelling further away from the axis takes less time to travel from source to receiver than sound energy travelling closer to the axis, (ii) the focusing of sound energy in the sound channel at certain ranges, (iii) the overall ray picture in the sound channel.",
        "doi": "10.1093/imamat/8.2.186",
        "issn": "0272-4960",
        "publisher": "Oxford University Press",
        "publication": "IMA Journal of Applied Mathematics",
        "publication_date": "1971-10",
        "series_number": "2",
        "volume": "8",
        "issue": "2",
        "pages": "186-198"
    },
    {
        "id": "authors:drn9c-qkj46",
        "collection": "authors",
        "collection_id": "drn9c-qkj46",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200110-142501972",
        "type": "article",
        "title": "Acoustic Wave Propagation in an Underwater Sound Channel 2. Quantitative Theory",
        "author": [
            {
                "family_name": "Blum",
                "given_name": "Joseph W.",
                "clpid": "Blum-J-W"
            },
            {
                "family_name": "Cohen",
                "given_name": "Donald S.",
                "clpid": "Cohen-D-S"
            }
        ],
        "abstract": "By using ray-theoretic-techniques we have developed in our previous paper, \"Acoustic Wave Propagation in an Underwater Sound Channel. 1. Qualitative Theory\" a certain qualitative understanding of several features of SOFAR propagation in an underwater sound channel. In the present paper a more penetrating quantitative study is done by means of analytical techniques on the governing equations. We study the transient problem for the Epstein profile by employing a double transform to formally derive an integral representation, and we obtain several alternative representations needed for asymptotic results which we also present. It is believed that several new and interesting asymptotic results have been derived.",
        "doi": "10.1093/imamat/8.2.199",
        "issn": "0272-4960",
        "publisher": "Oxford University Press",
        "publication": "IMA Journal of Applied Mathematics",
        "publication_date": "1971-10",
        "series_number": "2",
        "volume": "8",
        "issue": "2",
        "pages": "199-220"
    }
]