Incorporating estimates of data covariance in elastic FWI to combat noise based on auto-regressive process
Luping Qu, Scott Keating, He Liu, Xin Fu, Kristopher A. Innanen
An important step in seismic data processing is noise attenuation, which typically improves the subsurface seismic image and signal-to-noise ratio (SNR). In seismic records,coherent noise, which correlates spatially or temporally, are more difficult to attenuate or process as it can interfere with signals and be mistakenly recognized as signals. Through incorporating data covariance matrix into the misfit function, both the model parameters and noise can be estimated. When implementing this, the data covariance matrix with random noise can be simplified to be a vector. However, the data covariance matrix with coherent noise still need to be completely computed and stored. We find the serial data-error correlations can be characterized by adding the forward model with a autoregressive error model. As autoregressive error models do not estimate error with point estimates, the inverse of data-error covariance matrix does not need to be computed. The order of the autoregressive process required to fit the data is determined by the residual data-fitting examination. To avoid overfitting, estimates with several different orders were conducted and adopted in the following rounds of FWI.