Hampson-Russell Software & Services, a CGGVeritas company, has developed StratiSI 4-D, a global 4-D inversion scheme. It is one of a new range of algorithms from CGGVeritas designed to simultaneously utilize all of the available 4-D data to produce results that are globally consistent and well constrained. 

In the global 4-D inversion, joint perturbations of Vp, Vs and ρ values are introduced for the base and all monitor surveys and are accepted or rejected as a whole to find the best fit for all the vintages. To incorporate 4-D constraints, the inversion uses a simulated annealing procedure adapted to the multi-vintage setting. It allows user control over the level of 4-D coupling which can be expressed in terms of simple rock physics rules restricting the range of variations between consecutive surveys.

For example, if water injection takes place between the base and monitor survey times, we may expect a large increase in Vp but only a small decrease in Vs due to the density change and can set appropriate limits on the variation of these parameters. Outside of the reservoir zone further constraints can be applied. In areas where no 4-D effect is expected or observed, a model optimization is performed across all vintages, which reduces the impact of non-repeatable noise on the inversion results.

The 4-D coupling introduced in the global inversion identifies solutions consistent with observed production data and a priori knowledge of the reservoir. This is a vital step in reducing the non-uniqueness of 4-D inversion and it results in more accurate, quantitative estimates of changes in reservoir properties.

The interpretation of elastic attributes from inversion can be aided by lithology or fluid classification. The principle is to determine the ranges of elastic attributes corresponding to particular lithology and fluid combinations. Hampson-Russell uses a Bayesian classification scheme involving multivariate probability distribution functions. This recognizes that elastic attributes from different lithologies can overlap and the inversion results should therefore be described in terms of percentage probability of belonging to one or more of the defined litho-classes.

Cascading global 4-D inversion with 4-D Bayesian lithology classification allows reservoir properties, in particular fluid saturation, to be derived from the elastic attributes. It facilitates interpretation by clearly showing the evolution in the fluid distribution over time and quantifying the uncertainty in the inversion results.

This approach for the time-lapse monitoring of reservoir fluids has been applied to the Brage Field in the Norwegian North Sea, a mature field which has been in production since 1993. The objective of the study was to identify undrained oil sands with the aim of extending the life of the field. The 4-D processing of the 1992 base and 2003 monitor surveys was performed by CGGVeritas. It included anisotropic (TTI) pre-stack depth migration to achieve accurate positioning of the reservoir’s bounding faults and optimum focusing of events in the migrated gathers.

A “4-D mask” was defined using an energy attribute cube, computed from 2003-1992 amplitude differences. For the cells outside the mask (i.e. with minimal 4-D difference) a time-invariant solution was sought so that the model had the same values at base and monitor survey times. Inside the 4-D mask, the allowed ranges of Vp, Vs and ρ variations between base and monitor surveys were determined from fluid substitution analysis: water injection is expected to increase Vp and ρ by a maximum of 5% and decrease Vs by up to 2%.  Pressure effects on the 4-D response are expected to be very small and were therefore not included in the definition of the 4-D constraints.

This new approach provides an intuitive framework to monitor production-induced fluid movements with 4-D seismic. The use of smart 4-D constraints reduces the inherent non-uniqueness of 4-D inversion and produces quantitative results which are more accurate and more consistent with the expected production effects.