Seismic Inversion

Seismic Inversion for Rock Properties

The use of inversion methods allows for 1D borehole measurements to be parameterized into 3D space by integrating the well and the seismic data. To some degree, the inversion output simulates wireline measurements being recorded at each trace in a seismic survey without the need to drill expensive wells. This is possible by analyzing the variation of seismic amplitude with incident angle (AVO and/or azimuth) at a geological interface, which contains information about the rock and fluid properties within the layers. The AVO information is used to convert the seismic data from amplitudes to properties within the layer. The process is controlled and calibrated by available well log data and by structural interpretation. Our preferred inversion engine is able to handle the following data types to invert for acoustic and elastic properties:

1. Fullstack
2. Partial angle stacks
3. Azimuthal partial angle stacks
4. 4D partial angle stacks
5. Multi-component (PP and PS) partial angle stacks

The inversion algorithm specifications include:

1. Globally optimized, full bandwidth algorithm
2. Inverts all input seismic stacks simultaneously to handle noise better and obtain the best fitting earth model
3. Uses simulated annealing to locate the global minimum of a given function
4. Can be performed using Aki & Richards and Fatti AVO models
5. Wavelets can be varied vertically to compensate for temporal variations in the seismic

The table below shows various types of inversion processes and applications, the input data requirements, and the output volumes (directly from the inversion or after algebraic manipulation).

Multicomponent Seismic Inversion

When well data analysis detects small changes in density at the reservoir level, multicomponent seismic data can be used to estimate more reliable density in 3D compared to conventional PP data. This is possible because PS reflectivity is more susceptible to density changes at longer offsets. Figure P1 shows the main inputs and outputs from multi-component seismic inversion.

Figure P1: Main inputs for prestack multicomponent seismic inversion with 3 partial angle stacks.

Figure P2 compares conventional PP (left) inversion approach for density versus PP PS inversion (right). The inversion method uses PP and PS seismic data to jointly invert for elastic properties. The PS mode adds additional information to the inversion problem related to density. (Right) Shear impedance and density from PP PS seismic inversion have less uncertainty than seismic inversion using PP seismic only.

Figure P2: Comparison of seismic inversion for density using PP seismic (left) versus PP PS (right).
(Leiceaga et al., 2010)

Azimuthal Seismic Inversion

In rocks affected by fractures, the azimuthal variation of properties is measurable. In azimuthal seismic inversion studies, the amplitude variations are used as a function of azimuth and angle of incidence to obtain elastic and anisotropic properties. These properties can be used to better understand the subsurface, identifying areas with strong anisotropic behavior induced by fractures. This information may be used to accurately map the productive areas in the study area and refine the prediction of future drilling objectives.

Fractures and Anisotropy

The subsurface is considered anisotropic when elastic properties vary with direction of propagation. Figure A1 shows a medium with azimuthal anisotropy induced by fractures, showing the birefringence of the shear wave (S fast and S slow). The fast S wave indicates that the shear energy is vibrating in the direction parallel to the fractures. The slow S indicates that the shear wave is vibrating in the direction perpendicular to the fractures. The fast S / slow S ratio indicates the degree of anisotropy. Higher concentration of fractures induces greater anisotropy and the difference between fast S and slow S. This information is used to estimate the degree of fracture as an expression of the degree of anisotropy.

Anisotropy and Azimuthal Seismic Inversion - Figure 1

Figure A1: Azimuthal anisotropy induced by fractures.
(Chopra and Castagna, 2014)

Inversion of Azimuthal Seismic Data

Azimuthal seismic data acquisition and processing can be used to determine subsurface properties that correspond to anisotropy. Seismic waves are sensitive to anisotropy, but in a more complex way when compared to resistivity and permeability. The propagation of a wave depends on the direction of propagation and polarization direction relative to the axis of symmetry. Using the mathematical equation of Psencik and Martins, 2001, reflectivity can be estimated in an anisotropic media.

Anisotropy and Azimuthal Seismic Inversion - Equations

Properties of weak contrast PP reflection/transmission coefficients for weakly anisotropic elastic media.
(Pšenčík and Martins, 2001)

Figure A2 shows the effects of anisotropy with varying angle of incidence and azimuth. It is important to note that the measurable changes do not occur until the angle of incidence is above 15 degrees.

Anisotropy and Azimuthal Seismic Inversion - Figure 2

Figure A2: Effects of anisotropy with varying angle of incidence.
(Chopra and Castagna, 2014)

Figure A3 illustrates the main inputs to a prestack azimuthal inversion with four sectors and three partial angles stacks as well as the output properties. The algorithm inverts simultaneously the partial stacks for each azimuth and the corresponding wavelets. The final step is identifying zones with high anisotropy induced by fractures by analyzing the attributes obtained in the azimuthal seismic inversion.

Figure A3: Main inputs for prestack azimuthal seismic inversion with 4 azimuthal sectors and 3 partial angle stacks.

The attributes obtained from azimuthal inversion, especially the volumes that indicate the preferential directions of polarization of the fast shear wave, show the orientation and azimuth of the fracture systems, as well as the directions of the maximum and minimum stresses. These directions may be used, together with geometric attributes at a meso-scale, to construct a robust Discrete Fracture Network (DFN) with less a priori assumptions that are commonly made due to the lack of information. In this sense, the results of azimuthal inversion help reduce uncertainty in the DFN.