Scattering of seismic waves simulated by finite difference modelling in random media: Application to the Gravberg-1 well, Sweden

Abstract

We generate surface and VSP synthetic seismograms using finite difference modelling of the elastic wave equation in self-similar media. The elastic model is determined by analyses of the sonic log from the deep Gravberg-1 borehole in central Sweden. The upper 1200 m is highly fractured and the velocities are best described by a log-normal distribution rather than a Gaussian distribution. Analyses of this interval after removing the deterministic trend and assuming a self-similar Gaussian distribution of the random component give a standard deviation of 370 m/s, a correlation distance of 45 m and a Hurst number of 0.18. These values and others from deeper levels are used to generate the 2-D elastic model and the synthetic seismograms are compared with real data. Synthetic surface seismic data show a poor qualitative match when compared to real data. Synthetic VSP data match the real VSP better qualitatively. In general, the synthetic data show considerably more scattering effects than the real data. Possible explanations for this discrepancy include: (1) intrinsic attenuation has been ignored; (2) a Gaussian distribution of the random component was assumed; or (3) the heterogeneities have a preferred orientation. The poor match implies that the method for extracting the 2-D or 3-D velocity variations in the uppermost crust from 1-D sonic log data need to be studied further.