Logging Data Errors and their Propagation in Fluid Substitution
The sensitivity of the Gassmann fluid substitution technique to uncertainty in the input wireline measurements data has not been adequately studied (as per commonly available literature). This study describes the methodology to quantify errors present in the fluid substituted velocity by initially calculating the errors for petrophysical and the linearly elastic input parameters and then propagating the calculated input data errors throughout the fluid substitution process. The synthetic pore fluid modeling technique commonly utilizes data from the wireline log measurements to model various pore fluid mixture scenarios that may give rise to the observed amplitude variation with offset (AVO) response. Each input parameter, whether directly measured or derived using a combination of measured parameters, is bound within an uncertainty range due to the inherent limitations of the measuring instrument or resulting from uncertainty in the empirical parameter estimation. By applying the theory of error propagation, the uncertainty is calculated at each step of the Gassmann fluid substitution process flow and the resultant uncertainty in the fluid substituted velocity is determined. The uncertainty in the fluid substituted velocity can affect both the phase and the amplitude of synthetic traces generated for different offset angles and therefore, can produce anomalous AVO response in synthetic fluid substitution models. This uncertainty in the synthetic models can impact any direct comparisons with observations in order to determine the effect of different fluid scenarios. Additionally, the observed AVO data may be imprecise due to the anomalous AVO response resulting either from geologic uncertainty, data processing artifacts, or a combination of both thus increasing uncertainty in lithologic AVO interpretation.