A new bidirectional deconvolution method that overcomes the minimum phase assumption

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## Inverting a single wavelet

To verify the bidirectional deconvolution's ability to handle mixed-phase wavelets, we first set the input data to be a single wavelet, to see whether the data can be compressed to a single spike. We choose three types of wavelets as inputs:
1. a minimum-phase wavelet used in the previous report (Zhang and Claerbout, 2010), referred to as wavelet 1.
2. a wavelet that deviates slightly from minimum-phase: it models a simple marine ghost - a low frequency function passing through a time derivative at the source and another at the receiver. The low frequency function chosen is the convolution of two one-sided triangles.
3. a zero-phase wavelet created by convolving the minimum-phase with its own time-reverse wavelet. Such wavelet has identical and components, referred to as wavelet 3.

minwavlet,mod-minwavlet,jonwavlet,mod-jonwavlet,symwavlet,mod-symwavlet
Figure 1.
(a) Input wavelet 1 and (b) its deconvolution result. (c) Input wavelet 2 and (b) its deconvolution result. (e) Input wavelet 3 and (f) its deconvolution result.

fita-symwavlet,fitb-symwavlet
Figure 2.
For the wavelet 3 inversion, (a) filter ; (b) filter .

Figure 1(a) 1(b), figure 1(c) 1(d) and figure 1(e) 1(f) show wavelets 1,2,3, and the results of reflectivity models respectively. In all 3 cases, our bidirectional deconvolution method is able to compress the wavelet into a spike.

Figure 2 shows the retrieved filters and from wavelet 3's inversion. Notice that and given by the inversion are different from each other, while ideally they should be the same, since and are the same when we create wavelet 3. This observation indicates that the solutions and of this method do not necessarily converge to the inverse of the initial and .

 A new bidirectional deconvolution method that overcomes the minimum phase assumption

Next: Inverting a synthetic trace Up: Data Examples Previous: Data Examples

2010-11-26