Theoretical analysis of bottom reflected broadband waveforms

Abstract

Bottom reflection of broadband waveforms from explosive sources leads to pulse distortion, including the presence of a precursor to the main pulse, a topic that goes back to the 1950s [Arons and Yennie, JASA 22, 231–237 (1950)). A theoretical analysis of broadband bottom reflection can provide valuable insights into observed waveform distortion and its dependence on the grazing angle and sediment properties. When the attenuation in the bottom can be approximated as varying linearly with frequency, the magnitude of the reflection coefficient is independent of frequency, but with a common phase shift over positive frequencies (and with the opposite phase shift over negative frequencies). Combining these contributions leads to the pulse distortion . Variations of the sediment properties that cause the same phase shift at a given grazing angle produce the same pulse distortion. Conversely, inferring a phase shift from the pulse distortion can be used to place constraints on the inversion of sediment properties. Examples will be discussed. [Work supported by ONR.]Bottom reflection of broadband waveforms from explosive sources leads to pulse distortion, including the presence of a precursor to the main pulse, a topic that goes back to the 1950s [Arons and Yennie, JASA 22, 231–237 (1950)). A theoretical analysis of broadband bottom reflection can provide valuable insights into observed waveform distortion and its dependence on the grazing angle and sediment properties. When the attenuation in the bottom can be approximated as varying linearly with frequency, the magnitude of the reflection coefficient is independent of frequency, but with a common phase shift over positive frequencies (and with the opposite phase shift over negative frequencies). Combining these contributions leads to the pulse distortion . Variations of the sediment properties that cause the same phase shift at a given grazing angle produce the same pulse distortion. Conversely, inferring a phase shift from the pulse distortion can be used to place constraints on the inversion of sediment propertie...