183 7. Integrated seismic study location. The variogram model is used to compute the estimated variance of the stacked trace of the gather as the variance of the estimation error: unknown “true” stacked amplitude minus estimated stacked amplitude. The estimation variance is normalized and expressed as a percentage of the stacked amplitude called the Spatial Quality Index (SQI). Low SQI values mean good confidence in the stacked amplitude. The results shown here were obtained on the XL217 cross-line on the seismic cube (Figure 7.3). Figure 7.15 shows the instantaneous amplitude section (left) and its associated SQI factor (right). The sections are shown in depth. The time-to-depth conversion is discussed later. The quality of seismic instantaneous amplitudes is quantified by their attached SQI values. Blue SQI areas on the seismic section (low SQI values) indicate reliable amplitudes (80 to 90% reliability), green SQI areas indicate less reliable amplitudes (50 to 70% reliability). The more significant processes were analysed in greater detail, confirming that the amplitudes were not adversely affected by the processing. 7.5 Q factor We present here the methodology developed to estimate the Q factor per layer, using VSP data. It shows how the procedure has been extended to estimate the Q factor of seismic lines. A number of discussions in the literature use different approaches, which lead to a general form for the frequency dependence of the phase velocity. A synthesis has been carried out by Valera (1993). The resulting expression, which is valid for a relatively large and constant Q, is given by: V f V f Q f f 1 2 1 2 1 1 ( ) ( ) = +( )⋅ ( ) / / / π Ln (7.5) Where Q is the constant Q factor, V(f1) is the propagation velocity at frequency f1, V ( f2) is the propagation velocity at frequency f2. Equation (7.5) can be written as follows: Q V V f f =( )⋅( )⋅ ( ) 1 1 2 / / / π ∆ Ln (7.6) Where ∆ ∆ ∆ ∆ ∆ ∆ V V f V f z t z t d t = ( ) − ( ) = − + ( ) 1 2 / / and V z t d t V f = + ( ) = ( ) ∆ ∆ ∆ / 2 z t d t V f + ( ) = ( ) ∆ ∆ / 2 Equation (7.5) shows that the high frequency components of a wave train propagate faster than the low frequency components. For a VSP, Q is computed from equation (7.6). For 2 geophone positions (Δz apart), ΔV is estimated from the variation Δt of the arrival times of the down-going wave over a distance Δz and from dΔt the residual variation of Δt due to the variation of frequency between f1 and f2.
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