Inversion (Seismic)

Key Takeaways

• Seismic inversion converts reflection amplitude to absolute impedance — conventional seismic data records amplitude at reflection boundaries, which are proportional to the contrast in acoustic impedance (velocity × density) between adjacent layers; inversion mathematically integrates these contrasts through depth (or time) to reconstruct the absolute impedance profile at every trace location, transforming the "difference" data of reflection seismics into the "absolute" data of an impedance log; the result is a 3D volume of acoustic impedance values that can be directly compared to impedance logs at well locations and extended laterally between wells to map reservoir properties across the field.
• The low-frequency problem is the fundamental technical challenge in seismic inversion — seismic data is band-limited (typically 5-80 Hz), meaning it contains no information about the very low frequency trends in impedance (the broad ramps and gradients that control depth-to-velocity relationships and overall impedance levels); without the low-frequency component, inversion produces a "floating" result that may have the correct relative variations but wrong absolute values; model-based inversion addresses this by adding a low-frequency model derived from well log data and spatial interpolation between wells, which anchors the absolute impedance level while the seismic provides the resolution to capture detailed layer variations; the quality of the low-frequency model — which depends heavily on well control density and the interpolation methodology — is the most significant source of uncertainty in the inverted result away from well control.
• Pre-stack inversion simultaneously estimates compressional and shear impedance for fluid discrimination — reflectivity at a seismic boundary varies with the angle of incidence (AVO — amplitude variation with offset), and this variation encodes information about the ratio of compressional to shear velocity (Vp/Vs) in the reflecting layer; gas sands typically show a distinctive AVO response (increasing amplitude with offset, "AVO Class II or III anomaly") compared to brine sands of similar porosity; pre-stack inversion extracts both the compressional impedance (Zp) and shear impedance (Zs) from angle-stack or offset-stack seismic volumes, and the ratio Zp/Zs or the derived Lambda-Rho and Mu-Rho parameters (sensitive to fluid and mineralogy respectively) are used to discriminate gas-bearing from brine-bearing sands in the inter-well space.
• Simultaneous inversion combines multiple seismic datasets for the most robust property estimation — rather than inverting stacked or angle-stack volumes sequentially, simultaneous inversion jointly inverts near, mid, and far offset (or angle) stacks with a single consistent earth model, providing mutually consistent estimates of compressional impedance, shear impedance, and density that honor all the data simultaneously; simultaneous inversion is the current state of practice for quantitative seismic interpretation in reservoirs where fluid and lithology discrimination is the primary objective, and the simultaneous approach reduces the cross-talk between parameters that can affect sequential inversions.
• Rock physics is the bridge between elastic properties from inversion and petrophysical properties for reservoir characterization — acoustic impedance and Vp/Vs ratio from inversion must be transformed into porosity, clay content, and fluid saturation using rock physics relationships (empirical or theoretical models calibrated to core and log data from the reservoir); the rock physics transform adds uncertainty beyond the seismic inversion itself, because rock physics models have inherent variability and the transforms calibrated at well locations may not apply exactly in areas with different diagenetic history or clay type; Bayesian approaches that propagate uncertainty through both the inversion and the rock physics transform provide quantitative probability distributions for the resulting porosity and saturation estimates rather than single best-estimate values.