An AVO inversion method in the frequency domain based on a layered model—a Bakken Shale case study

Conventional AVO techniques are based on the linear approximation of Zoeppritz equations for the inversion of elastic properties across a subsurface interface. However, for a layered model consisting of internal multiple layers beyond seismic resolution, it can be difficult to use the traditional AVO inversion methods due to the practicalities of picking amplitudes, resolution problems, and thin-layer effects. We propose an improved AVO inversion method applied to a layered model for inversion of layer thickness and properties by incorporating the frequency content of the wavelet. The proposed method uses the propagator matrix method as a theoretical description of the frequency-dependent reflection coefficients for the layered model in an inversion scheme. We test the proposed method on a single layered model with synthetic data to produce an inversion for layer thickness and porosity, and then investigate the feasibility of the method for the characterization of the fracture zone in the Bakken formation. For the inversion of the reference crack density and layer thickness of the fracture zone in the Bakken formation, the minima of the objective functions generate inversion results that indicate a reasonable fit with the true model parameters. The inversion error may result from the intrinsic complexity of reflections from a layered model, in which several different combinations of layer thicknesses and associated properties may produce similar frequency-dependent coefficients. By contrast, in the multicomponent model data example, the inversion of converted PS-wave data seems to be less stable compared to PP-wave data. The potential of the proposed AVO inversion method may include applications to complex models, such as a sandstone/shale interbedded system, or a formation that presents internal heterogeneity