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. Identicalpolarity 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.

Seismic Reflectivity in Carbon Dioxide Accumulations: A Review

“…Also, a common measure for the vertical seismic resolution is given by a quarter of the dominant wavelength [53]. As explained in [6], [8] and [54], the CO 2 accumulations within the Utsira sandstone in the Sleipner field can be regarded as thin layers.…”

“…In particular, the curves for the thicknesses h = 5 m and h = 10 m show a periodic behavior; meaning that the different frequency components of a seismic signal are reflected with different amplitudes. To understand this periodicity on a theoretical basis, it is useful to consider the analytical result for the reflectivity of an acoustic layer embedded between two halfspaces, treated in [52] and [53]. From that solution it can be shown that the function R pp (f , θ) has multiple maxima or peaks at frequencies f n max and minima or notches located at frequencies f n min , given respectively by [15] …”

Reflection and transmission coefficients of a thin bed

“…However, these reflection coefficient formulas are either too complex for application (Brekhovskikh, 1960;Meissner and Meixner, 1969) or only suitable to some extreme hypothetical conditions without considering multiples (Widess, 1973;Chung and Lawton, 1995;Liu and Schmitt, 2003;Pan and Kristopher 2013). In this paper, we initially give the propagator matrix equations for a thin-bed model with displacement functions, different from Brekhovskikh's derivation with displacement potential functions.…”

“…Chung and Lawton (1995) extend Widess (1973) study into a thin bed, which has equal amplitudes and identical polarities in the bottom and top interfaces and analyze the influence of different wavelets on thin-bed reflections. Liu and Schmitt (2003) present an acoustic reflectance spectrum formula of a thin bed in the frequency domain and discuss the impact of thickness and Poisson's ratio on thin-bed seismic AVO responses. Pan and Kristopher (2013) compare thin-bed elastic AVO responses with Liu and Schmitt's (2003) acoustic AVO responses, and they investigate the influence of quality factor Q to examine attenuation effects.…”

“…Liu and Schmitt (2003) present an acoustic reflectance spectrum formula of a thin bed in the frequency domain and discuss the impact of thickness and Poisson's ratio on thin-bed seismic AVO responses. Pan and Kristopher (2013) compare thin-bed elastic AVO responses with Liu and Schmitt's (2003) acoustic AVO responses, and they investigate the influence of quality factor Q to examine attenuation effects.…”