Inversion parameterization
The inversion process begins with the low-frequency model, which is used to generate synthetic traces for the input partial stack. Zoeppritz equations or their approximations are used to estimate the band-limited elastic reflectivities. These model impedance values are then iteratively tweaked in such a manner that the mismatch between the modeled angle gather and the real angle gather is minimized in a least squares sense. The inversion process is based on three assumptions as stated below:
The linearized approximation for reflectivity holds.
PP and PS reflectivity as a function of angle can be given a set of linearized equations.
The back-ground trend can be described by a linear relationship between the logarithm of P- impedance and logarithm of both S-impedance and density.
Using these assumptions as well as Castagna’s and Gardner’s empirical equations, Fatti’s equation is used to invert multiple partial-offset or angle sub-stacks simultaneously without first estimating the P- and S-reflectivities from pre-stack seismic data and then transforming them to impedance.
Quite often when dealing with complex geology of unconventional shale resource plays where multi-zones need to be inverted simultaneously, the assumption mentioned above gets violated. A key question that needs to be answered is which back ground trend should be considered in the inversion. Would a trend be adequate for defining the background trend where multi trends exist in the zone of interest as shown below for a dataset from the Delaware Basin?
Lithological trend analysis in terms of crossplots to be used in impedance inversion in different litho-intervals, (a) Bell Canyon to Mississippian, (b) Bell Canyon to Bone Spring, (c) Bone Springs to Top Wolfcamp, and (d) Top Wolfcamp to Mississippian, (e) the different trends overlaid on one crossplot [purple line for trend in (d), red line for trend in a, blue for (c) and green for (b)].
This significant observation suggests us to not carry out simultaneous inversion in a large time window using a single average rock physics or facies trend. we therefore would recommend to carry out simultaneous impedance inversion in individual litho-units, comprising BoneSpring to Top Wolfcamp, Top Wolfcamp to Mississippian, and merge these impedance intervals into a composite volume. So, the simultaneous inversion may not be directly applicable. Consequently, it is essential to modify our simultaneous impedance inversion procedure.
References
Chopra, S., R. K. Sharma, and J. Keay, 2019, Efforts at effective reservoir characterization of Bone Spring and Wolfcamp formations in the Delaware Basin – a case study, presented at SEG Convention, held at San Antonio, in September.