SEISMIC RESPONSE OF A VISCOELASTIC LAYER

Abstract

In seismic prospecting, the reflected seismic wavelets yield valuable information about the reflector and properties of the path traversed by seismic waves. Their arrival times give information about its location of the reflector in the earth and their amplitudes provide an estimate of the acoustic impedance contrast at the reflector. Shape of a seismic wavelet is also its very important attribute. It is the result of frequency dependent attenuation and dispersion of seismic waves, which in turn are caused by anelasticity of the propagating medium and solid - fluid interaction in the fluid saturated porous medium. A careful analysis of shape of wavelets should yield important information about the pore fluids. For this purpose, important factors affecting the shape of wavelets need to be identified and a quantitative estimate of their influence on the shape of wavelets obtained. In the present work, an attempt has been made to achieve this objective. Plane wave synthetic seismograms have been generated at a number of offsets at the surface of a three layered earth model. These seismograms simulate a CMP (Common Mid Point) gather just before AVO (Amplitude Variation with Offset) analysis. A 50 Hz Ricker pulse has been used as the source wavelet. The second layer of the three layered earth model is porous and viscoelastic; the other two layers are elastic. Standard Linear Solid (SLS) model has been used to represent the visoelastic behaviour of the solid matrix of the second layer. Biot's theory has been used to compute complex and frequency dependent velocities of P- and S-waves in the porous viscoelastic layer saturated with gas and water or oil and water or only water. In all computations the frequency range is 1 - 100 Hz, the most commonly accepted frequency range in seismic prospecting Equations similar to Zoeppritz equations have been derived to compute complex and frequency dependent reflection coefficients. Vertical component of displacement of reflected P waves at the surface of the earth model have been computed including transmission losses and in free surface effect accounted for. The synthetically generated reflected seismic wavelets have been analyzed to quantify the effect of viscoelasticity and type and amount of pore fluids on the shape of seismic wavelets. The results obtained in this work indicate that porosity, type and amount of the pore fluids and solid - fluid interaction in the porous viscoelastic layer influence the frequency dependence of seismic wave velocities, quality factor, attenuation coefficients and reflection coefficients. Seismic wave velocities are influenced by variations of porosity to a greater extent than to variations in water saturation. Variation of peak amplitude of seismic wavelets with offset is dominated by the type of pore fluid. The shapes of seismic wavelets show a marked variation with porosity, becoming broader at high porosity and also undergoing change of polarity. Greater changes are observed with gas in the pores. Distinguishing different fluids on the basis of wavelet shapes becomes more noticeable at larger offsets. AVO analysis carried on synthetic data indicates that attributes A and B are also sensitive to porosity and water saturation.