Review Paper: A semi‐empirical model of strain sensitivity for 4D seismic interpretation

Abstract

We reformulate the original model of Hatchell and Bourne and Røste, Stovas and Landrø that couples fractional velocity change to subsurface strain via a fundamental constant R. The new model combines elastic compressibility of a dual‐porosity system for a sand–shale mixture with horizontal planes of inter‐granular weakness. The majority of observed R‐factor magnitudes from post‐stack 4D seismic data in both the reservoir and overburden can thus be explained. R is predicted to depend strongly on lithology and also initial strain state. The model is also extended to predict the observed angle‐dependence of time‐lapse time‐shifts from pre‐stack data. An expression for the gradient of time‐shift with incidence angle is obtained in terms of the background VP/VS, and also the ratio of tangential to normal compliances BT/BN representing loss or creation of inter‐granular coupling. If accurately estimated from data, this compliance ratio can be used as an additional parameter to assess the post‐production state of the overburden. It is concluded that whilst R remains the over‐arching parameter controlling the magnitude of time‐shifts measured from 4D seismic data, BT/BN is a subtler parameter that may also prove of future value.

Review Paper: Post‐stack 4D seismic time‐shifts: Interpretation and evaluation

“…In practice, an overburden extension-reservoir compression polarity reversal is not commonly observed at top reservoir or in the immediate underburden (Hatchell and Bourne 2005b). This observation supports the growing conclusion that R-factors in the overburden must be large -it is observed that they must be around 5 or greater (MacBeth et al 2018). Indeed recent work by Røste and Ke (2017) has suggested that overburden factors of up to 17 may be possible.…”

“…This observation supports the growing conclusion that R‐factors in the overburden must be large – it is observed that they must be around 5 or greater (MacBeth et al . ). Indeed recent work by Røste and Ke () has suggested that overburden factors of up to 17 may be possible.…”

“…R is held constant, despite the understanding that it must vary with lithology and stress path, as the precise nature of the variation is not yet clearly established (MacBeth et al . ).…”

“…To solve this issue, Hatchell and Bourne () and Røste, Stovas and Landrø () simultaneously proposed a linear relation that connects the fractional velocity change to the vertical strain change ε zz where R is the Hatchell–Bourne–Røste (HBR) factor that is a constant for a particular lithology, and stress path. Although has proven to be very useful in practice, the fundamental origin, applicability and lithological variation of the R factor are still under investigation (MacBeth, Kudarova and Hatchell ). Inserting into and re‐arranging yields a simple relation for the time‐shift …”

“…where R is the Hatchell-Bourne-Røste (HBR) factor that is a constant for a particular lithology, and stress path. Although (4) has proven to be very useful in practice, the fundamental origin, applicability and lithological variation of the R factor are still under investigation (MacBeth, Kudarova and Hatchell 2018). Inserting (4) into (2) and re-arranging yields a simple relation for the time-shift…”