Simplified seismic modelling of fractured rock - how effective is a locally effective medium (LEM) compared to explicit representation of individual fractures

Emmanouil Parastatidis, Mark W. Hildyard, Andy Nowacki

Research output: Contribution to conferenceAbstractpeer-review


It is vital in oil and gas, mining, nuclear waste disposal, and construction to have detailed knowledge of fractures in the rock mass, and particularly to understand the mechanical properties of the fractures which are linked with permeability and stability of infrastructure. Seismic waves can be an effective method to retrieve these properties particularly when measurements are coupled with forward and inverse modelling. These seismic models then need an appropriate representation of the fracturing. The fractures can be modelled either explicitly, considering zero thickness frictional slip surfaces (e.g., Schoenberg 1980, Pyrak-Nolte, et al., 1990, Hildyard 2007), or by considering an effective medium (e.g., Crampin, 1981, Hudson, 1981) which incorporates the effect of the fractures into the properties of the medium, creating anisotropy in the wave velocities. In this work, we use a third approach which is a hybrid of the previous two (e.g., Coates and Schoenberg 1995). The area close to the predefined fracture is treated as an effective medium and the rest of the medium is made homogeneous and isotropic, creating a Localised Effective Medium (LEM). We have shown (Parastatidis et al., 2017) that the LEM model can closely match an explicit model in reproducing waveforms recorded in a laboratory experiment. The LEM model performs close to the explicit model when the wavelength is much larger than the element size and relatively larger than the fracture spacing. By the definition of the LEM model, we expect that as the LEM layer becomes coarser the model will start approaching the effective medium result. However, what are the boundaries of the LEM and is there a balance between the stiffness, the frequency and the thickness, where the LEM performs close to an explicit model or approaches the effective medium model? To define the limits of the LEM we experiment varying fracture stiffness and source frequency. We then compare for each frequency and stiffness the explicit and effective medium with five models of LEM with different thickness. Finally, we conclude that the thick LEM layers with lower resolution perform the same with the thinner and finer resolution LEM layers for lower frequencies and higher fracture stiffness.
Original languageEnglish
Publication statusPublished - 3 Sept 2019
Event13th EURO-Conference on Rock Physics and Geomechanics: EURO 2019 - Potsdam, Germany
Duration: 2 Sept 20196 Sept 2019


Conference13th EURO-Conference on Rock Physics and Geomechanics
Internet address


  • fractured rock
  • seismic modelling


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