An analytical comparison of seismic inversion with several multivariate predictive techniques is made. Statistical data reduction techniques are examined that incorporate various machine learning algorithms, such as linear regression, alternating conditional expectation regression, random forest, and neural network. Seismic and well-log data are combined to estimate petrophysical or petroelastic properties, like bulk density. Currently, spatial distribution and estimation of reservoir properties is leveraged by inverting 3D seismic data calibrated to elastic properties (VP, VS, and bulk density) obtained from well-log data. Most commercial seismic inversions are based on linear convolution, i.e., one-dimensional models that involve a simplified plane-parallel medium. However, in cases that are geophysically more complex, such as fractured and/or fluid-rich layers, the conventional straightforward prediction relationship breaks down. This is because linear convolution operators no longer adequately describe seismic wavefield propagation due to nonlinear energy absorption. Such nonlinearity is also suggested by the seismic nonstationarity phenomenon, expressed by vertical and horizontal changes in the shape of the seismic wavelet (amplitude and frequency variations). The nonlinear predictive operator, extracted by machine learning algorithms, makes it possible in certain cases to estimate petrophysical reservoir properties more accurately and with less influence of interpretational bias.

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