Post-stack seismic inversion is a processing technique that aims to extract the acoustic impedance of the subsurface from surface measurements (stacked seismic data) (Hampson and Russell, 1991). The inputs of post-stack inversion usually include stacked seismic data, well log data, and a set of geological constraints in the form of a model. The manner in which these inputs are combined depends on the inversion algorithms. Hampson and Russell (1991) described three post-stack seismic inversion methods: band-limited (BLI), sparse-spike (SSI), and model-based (MBI) inversion. Band-limited inversion tends to produce limited frequency results. Sparse-spike inversion produces lower resolution models compare to model-based inversion. Model-based inversion produces the most robust results. Therefore, a model-based inversion approach was used to estimate P-impedance volumes. The first step in the model-based inversion is building an initial impedance model of the earth. The initial model is then perturbed until the derived synthetic seismic best fits the real seismic data (Maurya and Sarkar, 2016; Figure 7). Some of the advantages of interpreting seismic data in acoustic impedance rather than seismic amplitude domain can be summarized as (Maurya and Sarkar, 2016):(1) Inversion increases the vertical resolution of seismic data by extending the frequency bandwidth. Increased resolution simplifies the stratigraphic definition.(2) Acoustic impedance is a product of sonic velocity and bulk density; therefore, impedance results can be directly compared to well log measurements. The MBI uses a generalized linear inversion (GLI) algorithm that assumes the seismic trace and the wavelet are known and modifies the initial model until the input seismic trace matches the synthetic trace (Cooke and Schneider, 1983). GLI produces a model that best fits the measured data using a least squares method. Figure 7 illustrates the workflow of post-stack seismic inversion. Inputs include post-stack seismic data, well logs, and geological constraints (interpreted horizons and faults). The output is the estimated P-impedance. Well log data and geological constraints are used to build the initial impedance model. GLI iterates updating the model parameters until the error between synthetic derived from P-impedance and seismic data is smaller than a user-defined threshold value.

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