Interpretation & inversion
We interpret data for subsurface anomalies and changes, we match data to the response from models and invert for reservoir density and density changes and for subsurface compaction.
Gravity and depth changes (subsidence) above a gas accumulation. Values are proportional to the area of the circles. Blue means increase and red decrease. To the right is a cross-plot of gravity change and subsidence. Below is a sketch of the gas accumulation, gas production from a nearby gas reservoir and likely movements of fluid contacts. From (Eiken et al. 2023).
Time-lapse gravity data can be more straightforward to interpret than most other geophysical data. This is because the signal is proportional to mass changes, which are fundamental to understand the dynamics of the subsurface. It does not rely on complex rock physics relations, as seismic and CSEM data do. Microgravity can be powerful when flowing fluids have large density contrasts, such as gas–water and air–water. Also, injection or extraction with the related pressure changes cause expansion or compression in a reservoir, which can result in measurable surface gravity changes.
Height changes may have many different causes and can be interpreted in terms of subsurface rock strain. This again is the result of pressure changes and rock compressibilities.
A further stage of data analysis is to compare observations with models of changes in gravity or height. This is a way of identifying surprises, and may initiate model updates. Model matching can be done in Attrack‘s time-lapse module.
The Chi squared sum (Χ2) statistic is useful for parameter fitting and history matching of observed vs. modelled changes (following Vevatne et al., 2012):
where N is the number of seafloor stations, ΔzR is the measured relative depth change, c1 is a data offset (to be fitted), c2 is a scale factor (to be fitted), Sm is modelled subsidence, and σ is the estimated error of a measured difference.
The figure below show in (B) seafloor subsidence of up to 4 cm over 3 years at the Midgard field (Eiken et al. 2022). Panel C shows the mismatch with the subsidence predicted from the reservoir flow model coupled with a Geertsma geomechanical model, for each station. The red circles in the south (the Delta-segment) show that the seafloor has subsided less than expected. A well was drilled into the Delta-segment and received water breakthrough already after two years of production. The subsidence mis-match suggested faults acted as barriers. A new well was drilled and confirmed the lack of depletion.
A: Depth map of the Midgard field with warm colors as shallow and green as deeper, showing the main fault segments, B: 2009-2006 subsidence shown as circles with radius proportional to the value C: Difference between observed and modelled subsidence. Backdrop colors show modelled compaction (in cm), and the circle radius is proportional to the subsidence mismatch. Red circles mean the observed subsidence is less than modelled. D: Inversion for reservoir compaction (in cm) using a Geertsma geomechanical model of the overburden. From Eiken et al. (2022).
Surface time-lapse gravity or height data can be inverted for reservoir changes. Gravity data are inverted for density or mass changes per area and subsidence or uplift data for strain (compaction or extension). When changes are restricted to a reservoir with known outer boundaries, inversions become much better constrained than e.g. in exploration.
We have in Attrack implemented 3 solvers of Tikhonov regularization with different constraints, and term them standard, sparse and bounded. The choice of smoothing parameter values is a compromise between a stable solution and high resolution. Prior knowledge, such as fault locations or limits to density contrasts, can help to constrain the problem. The sparse solution emphasizes dominant features while suppressing the weaker. The bounded solution ensures than density changes stay within realistic limits. Residuals at the observation points (for example RMS misfit) should not be larger than the uncertainty in the data. The total mass or volume change provides another valuable parameter.
Subsidence maps can be inverted further for lateral variation in reservoir pressure and rock compressibility (e.g. Fokker et al. 2012), which again can identify undrained compartments in a producing oil or gas field. During QC of data processing, inversions can help identify erroneous values at single stations.
Tikhonov linear inversion of the subsidence data at Midgard (D in the figure above) clearly indicated the location of a sealing fault.