Time-lapse (“4D”) seismic data obtained from areas with depleting reservoirs are often interpreted with a simple model utilizing the strain sensitivity of the seismic wave velocity, often denoted as the dilation parameter (R). This parameter can be assessed from seismic data, but it can also be measured in the laboratory. We present experimental data from various sediments and sedimentary rocks, and that demonstrate that R depends on stress path as well as stress itself and stress history. We also model the time shift expected in a 4D seismic survey, based on a rock physics and a geomechanical model. The result is that a simple constant R model, in spite of the complexities revealed in the laboratory, may give a reasonable good result. It is however pointed out that when lateral heterogeneity in the stress path is accounted for, the constant R approach is insufficient, and the pore pressure response of the rock surrounding the depleting reservoir needs to be accounted for.


Time-lapse (“4D”) seismic measurements permit detection of in situ stress changes and strains associated with subsurface pore pressure changes, for instance during petroleum reservoir depletion. Field data (by e.g. Hatchell and Bourne, 2005; Barkved and Kristiansen, 2005) demonstrate that stress changes in the overburden are the main source of the observed 4D response.

One prominent 4D attribute is the change in two-way travel time, ?TWT. A convenient way of interpreting the observed time-shift is by relating it to underground deformation through a dilation parameter R, defined as (Hatchell and Bourne, 2005; Røste et al., 2006):

Here vP is the velocity of vertically travelling seismic Pwaves, and ez is the vertical strain. With this definition, and assuming a homogeneous subsurface and homogeneous strain within it, the associated time shift can be written simply as

Hatchell and Bourne reported seismic R values of the order 1 - 5. Apparently, R was larger for unloading than for loading, and then also more significant for the overburden above a depleting zone (where the rock is being stretched as a result of the compacting reservoir below) than in the compacting reservoir itself.

The R parameter is according to its definition a rock physics parameter that can be obtained from laboratory measurements and rock physics models. Below we will show examples of laboratory measurements of stress and stress path dependent R for materials representative of reservoir and overburden sediments. Clearly, the laboratory data show a variety of behaviors, dependent on rock type and stress path. We will then model the seismic response associated with depth dependent strain sensitivity, and compare the result with the outcome of a commonly made assumption of constant R with depth. Finally we will discuss the relationship between strain and stress sensitivity, and how more information from 4D seismic around depleting reservoirs can be obtained by accounting for the undrained pore pressure response of shales surrounding the reservoir (bulding on Bauer et al., 2008).

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