Elastic models of deformation in nature: why shouldn t we use the present day fault geometry?

Transcription

1 Elastic models of deformation in nature: why shouldn t we use the present day fault geometry? B. Freeman 1, G. Yielding, 1 S.J. Dee 1, 2, & P.G. Bretan 1 1 Badley Geoscience Limited, UK 2 BP Exploration Operating Co Ltd., Sunbury, UK

2 Introduction Justification of the Elastic Dislocation method Problems and solutions arising from the setup of ED/Boundary element methods as a forward modelling process Geological boundary conditions are observed in the deformed state

3 Many active faults slip by repeated earthquakes. The geodeticallymeasured deformation during the slip event can be well modelled by elastic dislocation methods. The accumulated deformation over many seismic cycles represents multiple elastic slip events, plus inter-seismic relaxation processes. From observations of earthquake events, we suggest that most subsidiary faulting/fracturing is generated during the slip event rather than during the inter-seismic relaxation. If so, then modelling the strain and stress changes associated with accumulated slip on large faults may provide a first-order prediction of the distribution and style of minor faults and fractures that are too small to map in the sub-surface.

4 Introduction to Elastic Dislocation methodology A fault panel is a rectangular dislocation with uniform slip, embedded in an elastic medium. Using the equations of Okada (1992), the resulting displacement and strain tensor can be computed at any observation point in the medium. The corresponding stress tensor and failure mode (if any) at the observation point can then be computed using appropriate material properties. Mapped faults in the subsurface can be approximated by an array of rectangular fault panels, each of uniform slip. A background bulk strain can also be superimposed.

5 Neotectonic example: El Asnam earthquake fault, Algeria 1980 earthquake fault zone: N- dipping thrust fault with hangingwall anticlinal ridge (topography reflects active structure) Europe-Africa plate boundary, showing seismic zone and slip vectors note NNW-SSE convergence direction

6 Neotectonic example: El Asnam earthquake fault, Algeria 1980 thrust earthquake: extensional surface breaks along hangingwall 5km Thrust break, 7m slip

7 Neotectonic example: El Asnam earthquake fault, Algeria (detailed surface-break mapping from Philip & Meghraoui, 1983) 5km 1980 earthquake: en echelon normal faulting on hangingwall of central fault segment: ~N-S trend, not parallel to main thrust fault

8 Neotectonic example: El Asnam earthquake fault, Algeria 8-panel fault model (based on geodetic net and earthquake source modelling); initial model dip-slip: Predicted surface deformation, x300: 0-8 m reverse slip dip-slip Predicted area where Coulomb shear stress exceeds failure, 50m depth

9 Neotectonic example: El Asnam earthquake fault, Algeria Change slip direction on underlying fault panel from dip-slip to minor oblique-slip results in rotation of failure planes in hangingwall, matching observed surface breaks. (detailed surface-break mapping from Philip & Meghraoui, 1983) 170 o Conclusion from neotectonic example: elastic dislocation model can give good prediction of subsidiary fractures associated with large faults.

10 Elastic dislocation methods are appropriate for modelling the coseismic deformation during earthquake slip events. Application to a neotectonic (seismic) example provides a good prediction of associated small-scale faulting (location and mode of failure, orientation of fracture planes). The method can potentially be used to predict fault/fracture distributions for input to reservoir modelling.

11 Review - ED workflow for fracture prediction Several authors have used an ED/Boundary element approach to predict subsurface strain, thence intensity and nature of brittle deformation in a reservoir interval (e.g. Bourne & Willemse 2001; Bourne et al. 2001; Maerten et al. 2002; Dee et al. 2007). Assumption: dominant control on small-scale faulting is the strain perturbation around larger (mappable) faults. ED solutions are required at Wells Horizon surfaces Observation grids Observation grid datum Subsidence Reverse Normal Strike-slip Uplift z x 3-D fault surface (Discontinuity) y Faulted framework defines the geological boundary conditions Geology combined with remote boundary conditions to model volume strain Strains used to calculate stresses and fracture characteristics

12 Essential problem Subseismic/small scale fracture prediction needs to minimize uncertainty Here is an obvious/serious problem arising from using observed geometry as the geological boundary conditions Well in vicinity of fault Forward modelling puts well in the wrong place Will this affect fracture prediction? We really need the forward model to end with the geologically observed state

13 Displacement field Dominantly fault-parallel close to fault Solutions inaccessible close to fault Dominantly horizontal away from fault. Effect increases with decrease in fault dip

14 Displacement field (A) No modelled observations (B) With small displacements and symmetrical fault arrays, lateral positional effects tend to cancel The combination of A and B makes the forward model look acceptable Positional error increases with higher displacement Modelled geometry is no longer acceptable

15 Problem 1 Using observed faults as boundary conditions we see that calculations meant to correspond with geological objects will be misplaced Solution: restore before forward modelling.

16 Restoration or Inversion? Displacement profile The deformation calculated at a point is uniquely dependent on the location of that point relative to the (variable) displacement boundary condition at the fault(s) p p` A point above the maximum, on the downthrown side is shifted downward to a location of HIGHER displacement relative to its starting point. This point will get over-restored q q` Conversely, a point below the maximum, on the downthrown side is shifted downward to a location of LOWER displacement relative to its starting point. This point will get under-restored Restoration is not simply a case of reversing the observed displacements Low High Red upthrown Blue downthron Restoration has to find the point in the undeformed state that maps to the observed point in the deformed state. This is a numerical inversion procedure

17 Problem 2(a) Hangingwall Large displacements Material points cross from one side of the fault to the other Footwall Material moves towards and through the fault In reality, because the material bounding a dislocation deforms, the shape of the dislocation itself should also change during deformation. The change in shape/orientation of the fault should also be considered as part of the modelling process

18 Effect of restoration on the fault surfaces When an ED model is run without restoring the fault (top left) material in the hangingwall ends up in the footwall. At first sight, the same can be said for the elastic model run with restoration (lower left). Un-restored elastic model However, when the restored and unrestored faults are viewed together we see that material starting in the FW stays in the FW and vice versa Restored elastic model

19 Problem 2b The faults are also observation surfaces

20 Practical solution Forward models must run with their boundary conditions (i.e. the faults) in the restored state Predictions that are to be compared with geological observations must have their observed locations mapped to the restored state In other words wells and horizon surfaces need to be restored prior to the forward model Observation grids/surfaces/volumes are implicitly defined in the restored state

21 Without pre-model restoration The deformed observation surface does not match the JD horizon. There is too much subsidence in the hangingwall. Material points move through faults, particularly in the hangingwall of the A fault. Distance (m) Pathfinder well Col Observation grid alligned with footwall regional A fault Depth (m) JD horizon Material points moving through fault Deformed observation surface

22 Without pre-model restoration JD depth surface Observation grid at 1500m Deformation grid moving through fault Too much hangingwall subsidence 1500 Depth (m) 2100

23 With pre-model restoration Deformed horizon grid surface JD depth surface Deformed observation grid is coincident with the horizon surface. The deformed horizon observation grid is now in its correct structural position. Compare this with the geometry with no pre-model restoration. Without pre-model restoration 1500 Depth (m) 2100

24 SW Pathfinder well NE Col Pathfinder well Conjugate shear planes S1 S3 Predicted fractures are of two types shear fractures parallel with the A, B or D faults or at a high angle to the faults high-angle tensile fractures. JD horizon High angle tensile fractures Fault parallel shear planes These orientations are broadly consistent with orientations from core (Losh, 1998) collected in the footwall of Fault A. All faults Fault A Fault D Fault B Fault F Predicted faults B D A Measured core High angle antithetic

25 Conclusions ED/Boundary element methods can be very effect predictors of small scale fractures and faults We show that using faults in their present day locations as boundary conditions for ED work lead to significant positional errors Critical for well location planning. Faults, horizons and wells need to have their geometry restored by applying the inverse (not the reverse) of the elastic deformation prior to the predictive forward model run. Forward modelling using the conventional Elastic Dislocation workflow for fracture prediction is then more likely to correctly predict the location of fracture sweet spots in the subsurface model.