Through_the_Looking_Glass_ESCI_444_6

# D a n b om g e op hy si cs on p 179 of his book

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D a n b om G e op hy si cs On P. 179 of his book, Yilmaz refers to Optimum Wiener filters  for the deconvolution of seismic data – let’s revisit this section.

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D a n b om G e op hy si cs Revisiting Table 2-7, let’s solve the problem Yilmaz posed and  solved with spiking deconvolution, this time using Wiener filters; here is the autocorrelation of the input wavelet.
D a n b om G e op hy si cs Revisiting Table 2-7, let’s solve the problem Yilmaz posed and  solved with spiking deconvolution, this time using Wiener filters; here is the crosscorrelation of input and desired functions.

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D a n b om G e op hy si cs Just a reminder about Cramer’s Rule to be used.
D a n b om G e op hy si cs Revisiting Table 2-7, let’s solve the problem Yilmaz posed and  solved with spiking deconvolution, this time using Wiener filters; here is formulation and solution (a0,a1) of the set of equations.

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D a n b om G e op hy si cs Revisiting Table 2-7, let’s solve the problem Yilmaz posed and  solved with spiking deconvolution, this time using Wiener filters; trying out the filter shows the results identical to spiking decon.
D a n b om G e op hy si cs Revisiting Table 2-7, let’s solve the problem Yilmaz posed and  solved with spiking deconvolution, this time using Wiener filters; trying out the filter shows the results identical to spiking decon.

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D a n b om G e op hy si cs Revisiting Table 2-7, let’s solve the problem Yilmaz posed and  solved with spiking deconvolution, this time using Wiener filters; trying out the filter shows the results identical to spiking decon.
D a n b om G e op hy si cs Revisiting Table 2-7, let’s solve the problem Yilmaz posed and  solved with spiking deconvolution, this time using Wiener filters; trying out the filter shows the results identical to spiking decon.

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D a n b om G e op hy si cs What to look for on seismic data that have not been deconvolved using field file, amplitude spectrum, and autocorrelation function.
D a n b om G e op hy si cs After deconvolution note the visible reflections, the broader amplitude spectrum, and more center-lobed autocorrelation.

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Deconvolution Assumptions Deterministic Flat Layers for Earth Model Source – Receiver Offset is Zero i.e., no converted waves Wavelet is Stationary W(t)   f(t) Noise is Zero  n(t) = 0 W(t) is Known
Deconvolution Assumptions Statistical Flat Layers for Earth Model Source – Receiver Offset is Zero i.e., no converted waves Wavelet is Stationary W(t)   f(t) Noise is Zero  n(t) = 0 R(t) is Random W(t) is Minimum Phase

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