Elastic Inversion of Seismic Amplitudes - the CRAVA Project

NR has developed elastic inversion software called CRAVA in collaboration with Statoil. CRAVA is an acronym for "Conditioning Reservoir variables to Amplitude Versus Angle data." CRAVA calculates elastic properties such as density, P- and, S-velocity from seismic amplitude cubes. Input data are amplitude cubes stacked at different angles and corresponding wavelets. Output are cubes of inverted elastic properties. CRAVA also offers the possibility to investigate the accuracy in the results by calculating uncertainties, or by simulating (Monte Carlo) cubes of possible elastic properties.

CRAVA has been tested on several oil fields.

Elastic Inversion

Prediction

Prediction gives "the most probable" elastic properties given the data. The prediction is unique given the seismic data and the assumptions on wavelet and physical models.

AVA data: Predictions:
Near seismic: Near seimsic cube Far seismic: Far seimsic cube Arrow Arrow CRAVA Arrow Arrow Arrow P-wave velocity cube S-wave velocity cube Density cube

Stochastic Simulation

Stochastic simulation (Monte Carlo) is an alternativ to prediction. There are two main reasons for using stochastic simulation:
  1. The uncertainty (variability) in the inversion is considered important.
  2. The small scale spatial structure below seismic resolution is considered important.
Stochastic simulated realizations are not unique and will span all possibilities within the constraints of seismic data and the assumptions on seismic wavelet and physical models. Note that the average of a large set of simulations (>50) will be identical to the prediction.

AVA data: Stochastic simulations:
Near seismic: Near seimsic cube Far seismic: Far seimsic cube Arrow Arrow CRAVA Arrow Arrow Arrow P-wave velocity cube 1 S-wave velocity cube 1 Density cube 1 P-wave velocity cube 2 S-wave velocity cube 2 Density cube 2

Properties

CRAVA is fast:
  • Ten million grid cells are processed in less than ten minutes.
  • The processing time increases proportional to the size of the problem.
CRAVA is based on standard physical approximations:
  • Seismic amplitudes are related to elastic parameters using convolution of wavelet with seismic reflection coefficients.
  • Angular dependent reflection coefficients are calculated from Zoeppritz equation.
CRAVA calculates any set of seismic parameters in an isotropic, inhomogeneous earth model:
  • P-wave velocity
  • S-wave velocity
  • Density
  • Vp/Vs ratio
  • Acoustic impedance
  • Shear impedance
  • Lamé coefficients
  • Poisson ratio
CRAVA can use zero-offset data:
  • Although CRAVA is intended for elastic inversion, it is possible to use a single zero-offset input cube. The inverted output will then be seismic impedance.
CRAVA account for spatial continuity:
  • Sedimentary rocks and their elastic properties have strong spatial continuity. This is taken care of by CRAVA by using spatial correlations (variograms) to model the elastic properties.
  • It is also known that seismic measurement errors are coloured, that is, the errors have spatial and temporal dependencies. This is caused by the processing techniques used for seismic data and by spatial averaging in the stacking process. CRAVA takes this effect into consideration.
CRAVA evaluates the uncertainty:
  • In addition to the inverted elastic properties, variance in the inverted elastic properties and their internal spatial correlation can be calculated. The latter is of importance when conditioning the elastic properties to well observations.
  • The uncertainty in the result can be evaluated using stochastic simulation (Monte Carlo) of cubes of elastic properties. The variability in these alternative cubes will depend on the accuracy in the inversion.
CRAVA can add spatial structure below seismic resolution:
  • Seismic data are band limited so small scale variations are invisible to seismic investigations. When using stochastic simulation, CRAVA adds small scale variations with correct spatial heterogeneity to the inverted cubes. This gives cubes with a realistic appearence. This is illustrated above; compare the predicted cubes to the simulated cubes.

References

The methods used by CRAVA are based on:

  • Arild Buland, Odd Kolbjørnsen and Henning Omre (2003) Rapid spatially coupled AVO inversion in the Fourier domain GEOPHYSICS,VOL.68 NO.3 (MAY-JUNE 2003) P.824-836

Scientific presentations about CRAVA

  • Geostatistical AVO Inversion on a Deep-water Oil Field presented at Petroleum Geostatistics 2007, Cascais, Portugal.
  • Geostatistical AVO inversion on Smørbukk Sør presented at SEG 2006 76th Annual Meeting
  • Bayesian AVO Inversion and Application to a Case Study presented at Production Geoscience 2005