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The Fourier pseudospectral method has been widely accepted for seismic forward modelling because of its high accuracy compared to other numerical techniques. Conventionally, the modelling is performed on Cartesian grids. This means that curved interfaces are represented in a ' staircase fashion ' causing spurious diffractions. It is the aim of this work to eliminate these non-physical diffractions by using curved grids that generally follow the interfaces.A furthei advantage of using curved grids is that the local grid density can be adjusted according to the velocity of the individual layers, i.e. the overall grid density is not restricted by the lowest velocity in the subsurface. This means that considerable savings in computer storage can be obtained and thus larger computational models can be handled.One of the major problems in using the curved grid approach has been the generation of a suitable grid that fits all the interfaces. However, as a new approach, we adopt techniques originally developed for computational fluid dynamics (CFD) applications. This allows us to put the curved grid technique into a general framework, enabling the grid to follow all interfaces. In principle, a separate grid is generated for each geological layer, patching the grid lines across the interfaces to obtain a globally continuous grid (the so-called multiblock strategy).The curved grid is taken to constitute a generalised curvilinear coordinate system, where each grid line corresponds to a constant value of one of the curvilinear coordinates. That means that the forward modelling equations have to be written in curvilinear coordinates, resulting in additional terms in the equations. However, the subsurface geometry is much simpler in the curvilinear space.The advantages of the curved grid technique are demonstrated for the 2D acoustic wave equation. This includes a verification of the method against an analytic ' Paper presented at the 54th EAEG meeting, Paris, June 1992. 32 1 322 P . Nielsen et al.reference solution for wedge diffraction and a comparison with the pseudospectral method on Cartesian grids. The results demonstrate that high accuracies are obtained with few grid points and without extra computational costs as compared with Cartesian methods.

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At South Arne a highly repeatable time-lapse seismic survey (normalized root-mean-square error or NRMS of less than 0.1) allowed us to reliably monitor reservoir production processes during five years of reservoir depletion. Time-lapse AVO (amplitude v. offset) inversion and rock-physics analysis enables accurate monitoring of fluid pathways. On the crest of the field, water injection results in a heterogeneous sweep of the reservoir, whereby the majority of the injected water intrudes into a highly porous body. This is in contrast to a pre-existing reservoir simulation model predicting a homogeneous sweep. On the SW flank, time-lapse AVO inversion to changes in water saturation DS w reveals that the drainage pattern is fault controlled. Time-lapse seismic data furthermore explain the lack of production from the far end of a horizontal producer (as observed by production logging), by showing that the injected water does not result in the expected pressure support. On the highly porous crest of the reservoir compaction occurs. Time-lapse time shifts in the overburden are used as a measure for compaction and are compared with predictions of reservoir compaction from reservoir geomechanical modelling. In areas where compaction observations and predictions disagree, time-lapse seismic data give the necessary insight to validate, calibrate and update the reservoir geomechanical model. The information contained in time-lapse seismic data can only be fully extracted and used when the reservoir simulation model, the reservoir geomechanical model and the time-lapse seismic inversion models are co-visualized and available in the same software application with one set of coordinates. This allows for easy and reliable investigation of reservoir depletion and gives deeper insight than using reservoir simulation or time-lapse seismic individually.

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