Time-lapse (4D) seismic studies are becoming a useful tool for monitoring fluid movements in the subsurface. The technique is based upon the assumption that the only changes in the subsurface over time will be production related (e.g. saturation changes); therefore, with knowledge of the rock physics of the field, it may be possible to infer saturation changes from the difference between surveys shot at different times.
In the past, fields with steam injection have been considered the best targets for reservoir monitoring projects Lumley (1995) because of the sensitivity of velocity to temperature in common sedimentary rocks Wang and Nur (1989). However, there has been increasing interest in using 4-D seismic to monitor water-floods Johnstad et al. (1992), where the seismic response is less sensitive to the fluid parameters.
A universal problem in reservoir monitoring projects, is how to best compare surveys, and identify the differences caused by fluid movements. Simple differencing will only work if the surveys are fully repeatable, and the only differences between them are fluid related. However, this is never the case, as other differences always creep in.
There are ways to design surveys which maximize repeatability. For example, permanent geophone arrays can be used to reduce differences due to navigational errors. However, differences can appear from many sources, and so complete repeatability can never be achieved. Potential causes for differences include: environment problems such as weather conditions, cable feathering, sea-state, tides and seasonal temperature/salinity changes of the ocean; hardware problems such as equipment deterioration, source signature variability, misfires and geophone failure; and unavoidable survey design changes e.g. due to the position of a platform.
Given that unwanted changes do occur, it is natural to ask how they can be reduced. Cross-equalization is a catch-all term for methods that eliminate these acquisition and processing differences between surveys.
Cross-equalization is usually applied in the migrated-stack domain Ross et al. (1996), where the signal-to-noise ratio is higher, and changes due to fluids are focused. In this domain, cross-equalization consists of corrections for the following elements, which are often applied sequentially:
A common approach to cross-equalizing is to take a region of the survey to use as a design window. This window should be a subsection of the survey in which there are expected to be no changes over time. It is also important that stationarity can be assumed between the design window and the target regions. This means that the statistics of the systematic differences within the design window are the same as those within the zone of interest. Cross-equalization parameters are chosen that eliminate the differences within the design window, and then applied on the zone of interest.
Often a field had a 3-D survey shot in the 1980's, and is being reshot with 90's technology. In these circumstances, there is a question as to whether the two generations of survey can be cross-equalized, and used to locate areas of bypassed oil. These surveys will have completely different acquisition parameters. In general, the more recent survey will be of considerably higher bandwidth. Ideally the cross-equalization algorithm should try to use the statistics of the newer survey to increase the resolution of the older survey.
In this paper, I consider the bandwidth equalization and phase corrections elements of cross-equalization in both the time and frequency domains. I present methods that if the surveys have different frequency content, try to raise the bandwidth of the lower resolution survey, while taking care to avoid amplifying noise. Algorithms are tested on synthetic post-stack data. This paper does not consider the other parts of the cross-equalization process.