Seismic Inversion - Pre-stack Seismic Resolution Inversion

Pre-stack Seismic Resolution Inversion

Pre-stack inversion is often used when post-stack inversion fails to sufficiently differentiate geologic features with similar P-impedance signatures. Simultaneous inversion solves for S-impedance and density, in addition to P-impedance. While many geologic features can express similar P-impedance characteristics, few will share combined P-impedance and S-impedance traits (allowing improved separation and clarity). Often a feasibility study using the wells logs will indicate whether separation of the desired lithotype can be achieved with P-impedance alone or whether S-impedance is also required. This will dictate whether a pre- or post-stack inversion is needed.

Simultaneous Inversion (SI) is a pre-stack method that uses multiple offset or angle seismic sub-stacks and their associated wavelets as input; it generates P-impedance, S-impedance and density as outputs (although the density output resolution is rarely as high as the impedances). This helps improve discrimination between lithology, porosity and fluid effects. For each input partial stack, a unique wavelet is estimated. All models, partial stacks and wavelets are input to a single inversion algorithm —enabling inversion to effectively compensate for offset-dependent phase, bandwidth, tuning and NMO stretch effects.

The inversion algorithm works by first estimating angle-dependent P-wave reflectivities for the input-partial stacks. Next, these are used with the full Zoeppritz equations (or approximations, such as Aki-Richards, for some algorithms) to find band-limited elastic reflectivities. These are in turn merged with their low-frequency counterparts from the model and integrated to elastic properties. This approximate result is then improved in a final inversion for P-impedance, S-impedance and density, subject to various hard and soft constraints. One constraint can control the relation between density and compressional velocity; this is necessary when the range of angles is not great enough to be diagnostic of density.

An important part in the inversion procedure is the estimation of the seismic wavelets. This is accomplished by computing a filter that best shapes the angle-dependent well log reflection coefficients in the region of interest to the corresponding offset stack at the well locations. Reflection coefficients are calculated from P-sonic, S-sonic and density logs using the Zoeppritz equations. The wavelets, with amplitudes representative of each offset stack, are input directly into the inversion algorithm. Since a different wavelet is computed for each offset volume, compensation is automatically done for offset-dependent bandwidth, scaling and tuning effects. A near-stack wavelet can be used as the starting point for estimating the far-angle (or offset) wavelet.

No prior knowledge of the elastic parameters and density beyond the solution space defined by any hard constraints is provided at the well locations. This makes comparison of the filtered well logs and the inversion outputs at these locations a natural quality control. The lowest frequencies from the inversion are replaced with information from the geologic model since they are poorly constrained by the seismic data. When applied in global mode a spatial control term is added to the objective function and large subsets of traces are inverted simultaneously. The simultaneous inversion algorithm takes multiple angle-stacked seismic data sets and generates three elastic parameter volumes as output.

The resulting elastic parameters are real-rock properties that can be directly related to reservoir properties. The more advanced algorithms use the full Knott-Zoeppritz equations and there is full allowance for amplitude and phase variations with offset. This is done by deriving unique wavelets for each input-partial stack. The elastic parameters themselves can be directly constrained during the seismic inversion and rock-physics relationships can be applied, constraining pairs of elastic parameters to each other. Final elastic-parameter models optimally reproduce the input seismic, as this is part of the seismic inversion optimization.