Summary
We present a method for recovering time-lapse velocity changes using full waveform inversion (FWI). In a preprocessing step we invert for a single intermediate model by simultaneously minimizing the data misfit in the baseline and the monitor surveys. We record the individual FWI gradients corresponding to the baseline and the monitor datasets at each iteration of the inversion. Regions where these gradients consistently have opposing sign are likely to correspond to locations of time-lapse change. This insight is used to generate a spatially varying confidence map for time-lapse change. In a subsequent joint inversion we invert for baseline and monitor models while regularizing the difference between the models with this spatially varying confidence map. Unlike double difference full waveform inversion (DDFWI) we do not require identical source and receiver positions in the baseline and monitor surveys.
Introduction
FWI (Lailly, 1983; Tarantola, 1984; Pratt, 1999) uses the entire seismic record to invert for subsurface material properties such as seismic velocity and density. When monitoring a reservoir, the primary objective is to recover changes in the material properties due to production changes. A straight-forward application of FWI to this time-lapse problem is to invert for the baseline (i.e., initial) state and the monitor (i.e., new) state independently. Subtracting these models intuitively approximates the time-lapse change in material parameters. However, artifacts are also present due to the nonlinear nature and illposedness of the uncoupled inverse problems for the baseline and monitor models.
In an attempt to overcome some of these problems Watanabe et al. (2004) and Denli et al. (2009) introduced DDFWI for monitoring production related changes. In DDFWI the baseline data residual from an initial baseline inversion is subtracted from the monitor dataset. Conceptually this can be seen as removing a part of the data that the initial model could not explain. After the monitor model is inverted from this modified data and the baseline model is subtracted a better timelapse estimate is obtained. The data subtraction in DDFWI imposes constraints on the seismic acquisition. Both the source and receiver locations have to be the same in the baseline and monitor surveys. Differences are not uncommon in marine surveys as is illustrated for instance by Eggenberger et al. (2014). These differences will result in artifacts in the velocity change estimate.
Several methods have been introduced that avoid the requirement of identical acquisition. Zamanian et al. (2014) invert for the time-lapse change by casting the inverse problem in a hierarchical Bayesian framework. Maharramov et al. (2014)
circumvent some of the problems of subtracting independent baseline and monitor inversions by swapping baseline and monitor datasets a fixed number of times. In a different approach Maharramov and Biondi (2014) introduce a joint inversion in which Total Variation (TV) regularization suppresses the oscillatory model-difference artifacts that arise in joint FWI with noisy datasets. Another approach is to iteratively swap baseline and monitor datasets in FWI and record which regions change consistently as a result. This information can be used to generate a confidence map, which can regularize the modeldifference in a subsequent time-lapse inversion. This was done by Yang (2014) in a method called Alternating FWI (AFWI). The idea we introduce in this study is similar to Yang’s approach. Instead of performing a potentially long sequence of expensive full waveform inversions for the confidence map, we perform a single joint inversion with a single model. In this joint inversion we minimize both the baseline and monitor data residuals with this single intermediate model. Regions where the gradient of the baseline data term consistently has a different sign than the gradient of the monitor data term are considered to be potential regions of time-lapse change. We quantify this principle and construct a confidence map from the gradient history. Similar to the work of Yang (2014) we use this (different) confidence map to regularize the model difference in a final joint inversion.
