Analytic Studies of Seismic Waves in 3-D Structures
{'Code': '06030204', 'Directorate': {'Abbreviation': 'GEO', 'LongName': 'Directorate For Geosciences'}, 'Division': {'Abbreviation': 'EAR', 'LongName': 'Division Of Earth Sciences'}}
{'SignBlockName': 'Patricia Brooking'}
Wave propagation in layered media has been fruitfully studied for               several decades, with many applications in geophysics and other fields.         The fundamental limitation of this type of modelling, in most cases, is         its inability to handle lateral variations of structure.  A recent              discovery now indicates that analytical methods, developed and widely           used for layers with plane parallel interfaces, can be extended to the          case of plane interfaces that are not parallel.                                                                                                                 Consequently, it appears possible to develop a generalized ray theory           for wave propagation in a stack of wedge-shaped layers.  Layer                  interfaces can have arbitrary dip and strike, permitting the study of           waves in truly three-dimensional structures.  The methods that can be           so generalized, from parallel layering to non-parallel, are those that          derive from a fundamental and well-known relationship between travel-           time, range, and a sum over vertical slownesses (weighted by layer              thickness).  It is remarkable that this relationship, so familiar in            purely depth-dependent structures, is virtually unchanged in the three-         dimensional case.                                                                                                                                               We propose to explore the newly generalized methods to study wave               propagation associated with randomly dipping interfaces.
{'FirstName': 'Paul', 'LastName': 'Richards', 'EmailAddress': 'richards@ldeo.columbia.edu', 'StartDate': '07/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Columbia University Lamont Doherty Earth Observatory', 'CityName': 'Palisades', 'ZipCode': '10964', 'PhoneNumber': '9143592900', 'StreetAddress': 'Rt 9W', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY'}
{'Code': '1574', 'Text': 'Geophysics'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8708564.xml'}