Quantitative 4D warping inversion
Authors: Grandi Andrea , Wauquier Severine , Cummiing Hannah , Deplante Christian , Hubans Christian 
Published: March 2015

Abstract
Born nearly thirty years ago, time lapse (4D) seismic monitoring has proven to monitor fluid movement and to distinguish between drained and undrained portions of a reservoir. Its ultimate aim is to quantitatively contribute to improving reservoir models, to the benefit of their predictive capability. Now, the benefits of time-lapse seismic for reservoir characterisation do not depend only on the quality of 4D acquisition and processing; they also greatly depend on the particular 4D inversion scheme used.
Timing is also crucial: correct although sub-optimal results delivered in a few months may have a more direct operational impact (such as moving a well location) than optimal results arriving too late. Therefore long and complex full inversion schemes, often considered the preferred route to achieving optimal results, might be too slow (requiring months to be completed) to sanction immediate actions. On the other hand, other inversion techniques sharing the denomination of 'warping' can provide a quick answer (generally in few weeks).
Warping is quite a generic name, covering a broad collection of techniques, including correlation-based methods, time-shift non-linear inversions and relative velocity (or time-strain) non linear inversions. Initially, warping algorithms were developed in order to produce relevant 4D difference volumes by means of an estimate of local time-shift between base and monitor. Standard correlation-based methods and non-linear time-shift inversion are mainly used to align base and monitor surveys and generate time-shifts which may sometimes be used interpretatively but in general have insufficient resolution and stability to be of interest as 4D reservoir attributes.
Conversely, when formulated as a non-linear inversion to retrieve interval quantities such as relative velocity changes or time strain, warping can provide more accurate and reliable 4D attributes that can be easily integrated in the reservoir models.
As an application of the in-house methodology along these general considerations, three examples are discussed. Case A is a HPHT reservoir with low signal to noise ratio and problematic repeatability close to the platform; in this case dedicated warping facilitates obtaining a stable 4D signal at the reservoir level as well as in the overburden. Case B is a turbiditic reservoir where 4D signal due to gas either injected or coming out of solution under depletion is measured. Case C is a stress-sensitive reservoir where stable 4D signal inverted at the reservoir level correlates very well with production data.

Introduction
The first repeated 3D seismic surveys were acquired in North Texas at the in 1982/1983 to monitor a combustion process around an injection well (Greaves and Fulp, 1987). The results clearly indicated the combustion progress that was seen as a bright spot due to the increase in gas saturation. Despite some other examples that appeared afterwards, the 4D seismic was mainly confined to monitor shallow heavy oil in northern Canada. It was only when time-lapse recordings shifted to offshore fields, where seismic is cheaper and wells more expensive, that the technique started to spread and developed fast. The pioneering studies of this phase are Magnus field from BP and Gullfaks from Statoil. Since then huge efforts have been made in the improvement of seismic acquisitions and processing techniques allowing increased repeatability of seismic surveys; thus, 4D seismic has now become standard practice in the monitoring of reservoirs.
Although an extensive use of time-lapse seismic has been made in a qualitative sense, just recently it has been used in a more quantitative approach where flow simulation and 4D seismic are merged in an attempt to provide largely improved forecasts of reservoir behaviour. When this goal is reached and time-lapse proven to be as successful as expected, it will have a major impact on the future of the industry having a significant impact also in fields that exhibit only small 4D effects.