Additional pre-processing steps

The results shown in Figure demonstrate that the basic algorithm can be effective. However, the low amplitude of the added interface response events relative to the remaining coseismic noise suggests that additional pre-processing steps should be explored in order to improve the final result. In this vein, we tested the use of a second time derivative as a means of balancing the amplitudes of the interface response relative to the coseismic energy. This spectral balancing enhances the generally higher-frequency interface response. This step sharpens the image (Figure a), and improves the ability of the PEF to precisely locate the signal amidst the noise. Applying the same processing steps as used for Figure and using the same parameters, we find that the end result (Figure d) is markedly improved over Figure d, with greater clarity of the added events.

 

nice2D
Figure 8 (a) Data file (second time derivative of file in a). (b) Window for determination of signal PEF 332#332. (c) Window for determination of noise PEF 338#338. (d) Output of processing, 357#357. Note that added horizontal events 0.045 s and 0.065 s are visible.

Still present is the dipping coseismic energy between 0.025 and 0.04 seconds. Because this energy is so strong, and so close to horizontal, it leaks through the PEF, corrupting a portion of the record. This problem is the focus of on-going investigation and is being addressed with waveform separation.

Waveform separation is a standard technique in VSP and cross-well seismic processing, used to remove high-amplitude early arrivals in records by capitalizing on the different move-outs of different arrivals. We employ the method as follows: (1) picks are manually made along the arrival targetted for removal, (2) the gather is moved out such that the arrival (as defined by the picks) is horizontal and then stacked, and (3) the resulting trace is normalized by the number of traces in the gather and then subtracted from each of the moved-out traces. (4) After the subtraction, the gather is moved back to its original alignment. By repeating this process, it is possible to remove more than one coherent arrival from the record. Figure shows a series of images as various arrivals are removed from the record (a). Figure d shows the result after three iterations through the process, and shows that although the process has effectively removed much of the energy of the strong coseismic first arrivals, it has also partially removed the interface response (0.01 to 0.02 seconds). This is a result of the chance line-up of waveforms during the second iteration. We chose to use the data shown in Figure c for the PEF processing sequence.

 

xwell
Figure 9 (a) Data file (same as a). (b) Result after one iteration through waveform separation process. (c) Result after second iteration. This is the file that we use in the PEF processing sequence. (d) Result after three iterations through the waveform separation process. Note that the interface response (0.01 to 0.02 seconds) event has been partially removed.

We apply the second derivative after waveform separation since it has proven successful. Because the coherence of the coseismic noise has been disturbed by the waveform separation technique, we opt to determine the PEF's 332#332 and 338#338 with the data shown in the windows of Figure b and c. The starting datafile (after waveform separation and second derivative) is shown in Figure a, with the final result in Figure b. Here we see that the clarity of the added events is improved, but that some of the coseismic energy remains. In this case, the remaining coseismic energy is closer to horizontal than that in Figure d. Thus, if we were to stack this gather, the resulting trace would definitely include unwanted coseismic energy. We continue to pursue solutions to this problem.

 

nicexwell
Figure 10 (a) Data file (Second derivative applied to data from Figure c). (b) Result after PEF processing sequence. Note that added horizontal events 0.045 s and 0.065 s are clearly visible.