Exploring self-affine properties in seismograms

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Self-affine properties have been observed in a large variety of rough profiles and time series from natural data sets. In this work, seismograms used for oil prospecting, which contain information of distinct subsurface features collected by seismic waves reflected or scattered at their interfaces, are taken into consideration. It is expected that any self-affine property, measured by the Hurst exponent H, depends on the depth. For each seismic trace, H is evaluated locally within a moving window, which is chosen narrow enough to reveal space dependency but also wide enough to display scale invariance. With the use of color code diagrams, it is possible to draw two-dimensional diagrams that show the local dependence of H for the analyzed seismogram. The reliability of the method is tested by the investigation of seismograms that contain ground roll components, as well as multiple reflections. The effect of different kinds of filter in the scaling properties is also investigated. In this case, comparisons are drawn among the diagrams obtained from original seismograms and those subjected to appropriate filter to eliminate spurious components.

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