In time-lapse seismics a dilation parameter (R) is used to link the change in two-way travel time to subsurface strain (compaction/subsidence). R is a measure of strain sensitivity of the vertical seismic P-wave velocity. Ultrasonic laboratory measurements of R are presented using unconsolidated glass beads and sands, compacted clay, artificial and natural sandstone, and shale. It is shown that R depends strongly on stress path, implying that in situ stress paths should be applied in laboratory investigations. R may also vary across a formation due to heterogeneities (lithology/stress field). Moreover, data on artificially cemented sandstones indicate that R as deduced from core data should be corrected for effects of coring - induced rock alteration.


Time-lapse ("4D") seismic measurements permit direct observations of seismic velocity changes caused by pore pressure and stress changes within and around producing petroleum reservoirs. In addition, changes in fluid saturation will influence the seismic response. However, in cases of no fluid injection to enhance production or weak water drive, the stress alteration is the main source of time-lapse response [1]. 4D seismics thus represents a tool for identification of depleted and non-depleted reservoir zones. It also has the potential to assess in a quantitative way the underlying stress changes and associated deformations (compaction and subsidence). The change in two-way seismic travel time (TWT) can in a simple manner be directly linked to underground deformation (vertical strain ez; defined as positive for compaction) and strain sensitivity of the vertical P-wave velocity (vPz), through the dilation parameter1 R [1, 2], defined as:

(mathematical equation available in full paper)

With this definition, assuming a homogeneous subsurface and homogeneous strain within it, the relative change in TWT can be written simply as:

(mathematical equation available in full paper)

A main justification for introducing the dilation parameter is that it can be considered as a characteristic property of the rock. If the P-wave velocity were sensitive to changes in the normal strain in the direction of propagation, and only that, this would indeed be the case. Clearly, this assumption has some relevance: vertical stretching of a rock tends to create horizontal cracks (or weaken grain contacts in the vertical direction), and vertical P-waves are primarily sensitive to cracks (and grain contacts) with that orientation. However, as will be illustrated below, the P-wave velocity is not only sensitive to the strain parallel to its propagation direction. This complicates the situation and questions the validity of the dilation parameter concept. Field observations, according to Hatchell and Bourne [1], give values of R of the order 1 - 5. The observed seismic R is reported to be larger for unloading (inflation of a reservoir, or stretching of the overburden above a depleting reservoir) than for loading (depletion of a reservoir) Strain sensitivity can also be measured directly in the laboratory on rock cores. Conventionally, only stress sensitivity has been reported in the literature, and laboratory data are most often limited to hydrostatic stress paths. However, in the Earth, be it in a depleting reservoir or in the surrounding rock masses, the stress (and strain) path deviates from hydrostatic.

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