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Frequency‐dependent PP and PS reflection coefficients in fractured media
Author(s) -
Pang Shuo,
Stovas Alexey
Publication year - 2020
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12880
Subject(s) - amplitude , amplitude versus offset , anisotropy , isotropy , anelastic attenuation factor , attenuation , mechanics , reflection (computer programming) , critical frequency , frequency domain , phase angle (astronomy) , geology , optics , physics , geophysics , ionosphere , mathematical analysis , mathematics , computer science , programming language
When a porous layer is permeated by mesoscale fractures, wave‐induced fluid flow between pores and fractures can cause significant attenuation and dispersion of velocities and anisotropy parameters in the seismic frequency band. This intrinsic dispersion due to fracturing can create frequency‐dependent reflection coefficients in the layered medium. In this study, we derive the frequency‐dependent PP and PS reflection coefficients versus incidence angle in the fractured medium. We consider a two‐layer vertical transverse isotropy model constituted by an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce the intrinsic dispersion due to fracturing in the sand layer. Based on the series coefficients that control the behaviour of velocity and anisotropy parameters in the fractured medium at low frequencies, we extend the conventional amplitude‐versus‐offset equations into frequency domain and derive frequency‐dependent amplitude‐versus‐offset equations at the elastic–anelastic surface. Increase in fracture length or fracture density can enlarge the frequency dependence of amplitude‐versus‐offset attributes of PP and PS waves. Also, the frequency dependence of magnitude and phase angle of PP and PS reflection coefficients increases as fracture length or fracture density increases. Amplitude‐versus‐offset type of PP and PS reflection varies with fracture parameters and frequency. What is more, fracture length shows little impact on the frequency‐dependent critical phase angle, while the frequency dependence of the critical phase angle increases with fracture density.