Amplitude and AVO responses of a single thin bed

Abstract

The seismic reflection characterizations of a thin layer are important for reservoir geophysics. However, discussions on the reflection for a thin layer are usually restricted to precritical angle incidence. In this work, an exact analytical solution is derived to model the reflection amplitude and amplitude variation with offset (AVO) responses of a single thin bed for arbitrary incident angles. The results show that the influence of an ultra‐thin bed is great for opposite‐polarity reflections and is small for identical‐polarity reflections. Opposite‐polarity precritical reflection amplitudes first decrease in magnitude with the wavelength/thickness ratio to a local minimum, then increase to a maximum, and finally decrease gradually to zero as the layer vanishes. Opposite‐polarity postcritical reflections monotonically decrease from near unity to zero, proportional to the thickness of the layer. Identical‐polarity precritical reflection amplitudes first increase in magnitude with the wavelength/thickness ratio to a local maximum, then decrease to a minimum, and finally increase to the amplitude of a single bottom reflection when the layer vanishes. Identical‐polarity postcritical reflections have magnitudes near unity. The AVO responses for both opposite and identical‐polarity acoustic thin beds gradually increase with angle. The influence of the Poisson's ratio of the thin bed is small for either small incidence angles or thicknesses less than 7% of the seismic wavelength, but is large for high incidence angles or thicknesses greater than 13% of the wavelength. A decrease of Poisson's ratio causes a pronounced AVO response that reaches its maximum at the quarter‐wavelength tuning thickness.