Compensating for attenuation by inverse Q filtering

Carlos A. Montaña and Gary F. Margrave

ABSTRACT

Three different approaches for inverse Q filtering are reviewed and assessed in terms of effectiveness in correcting amplitude and phase, computational efficiency and numerical instability. The starting point for the three methods is the linear, frequency-independent Q theory, in which an attenuated trace can be forward modeled as the product of a wavelet matrix, an attenuation matrix and the earth reflectivity series. In the first method the reflectivity series is solved by inverting a matrix similar to the attenuation matrix with minimized nearly-singular characteristics. The second approach is based on the downward continuation migration method and is a highly efficient and numerically stable method. The last assessed method uses the generalized nonstationary Fourier integrals to apply the inverse Q filter. The performance of the three kinds of filters is assessed by assuming that the exact value of Q is available. One synthetic trace is created with a pulse source to avoid introducing error by ignoring the conmutator term which is required when the Q filter is applied before a spiking deconvolution to remove the source signature. Several attenuated traces are forward modeled for different Q values, and used to test the filters. Two attributes are used to quantify the similarity between the expected and the real output: the L2 norm of the difference between the expected and the real output and the maximum crosscorrelation and its corresponding lag, computed for windowed fragments of the traces.

View full article as PDF (0.59 Mb)