Lab 04: Seismic Deconvolution

Seismic deconvolution came after one had performed the frequency filtering on the seismic data via BPF’s. By performing the frequency filtering, the seismic data is smoothed. However, this event has affected the seismic data vertical resolution which is due to loss of some of its original wider frequency band. 

Therefore, this is where the seismic deconvolution came with an aim to increase the vertical resolution of the seismic data by compressing the source wavelet (also known as spiking deconvolution). Apart from that, the seismic deconvolution also can be used for noise attenuation procedures such as multiples attenuation and since we are dealing with land seismic data, it requires the enhancement of the vertical resolution to the data set. Before performing the spiking deconvolution to the seismic data set, there are few sets of parameters need to be considered and there are:

1.   Autocorrelation window (w): This sets up the part of seismic trace from which we will select the elements of the autocorrelation matrix in the equations.

2.   Filter length (N): This sets up the length of the spiking filter h(n).

3.  Percent pre-whitening (Ɛ): This sets up the amount of white random noise we want to include into our auto-correlation matrix to stabilize the solution of the normal equations.

To perform spiking deconvolution, there are two (2) MATLAB functions involve which are spiking_decon.m and auto_correlation_map.m. Both of these functions are used as per respected to the equation below.

(1)   The earth respond e(n) can safely be approximated as a white random series impulses. In this case, the amplitude spectrum of e(n) will be constant. That is

Equation 4.2

(2)   Using the Equation 4.1 to find the trace amplitude spectrum and substituting Equation 4.2 yields

Equation 4.1

Equation 4.2

Equation 4.3

(3)   Equation 4.2 means that the amplitude spectrum of the seismic trace is a scaled version of the amplitude spectrum of the source wavelet

Figure 1: MATLAB file

1.      Display all the parameters needed for applying the spiking deconvolution to the seismic data. Shot numbers from 4-6 has been chosen for the deconvolution model of the data.

2.      Parameter for showing the results before the spiking deconvolution (Figure 2a)

3.      Parameter for showing the auto-correlograms of shot gathers 4-6 (Figure 2b)

4.      Parameter for showing the results of the spiking deconvolution of the seismic data (Figure 2c)

Figure 2: (a) Shot gathers 4, 5 and 6 before applying spiking deconvolution, (b) Auto-correlograms of shot gathers 4, 5 and 6 and (c) Shot gathers 4, 5 and 6 after applying spiking deconvolution

Figure 3: PSD of the average trace of shot gathers 4, 5 and 6 before and after spiking deconvolution

Figure 3 above shows the overall data in the spectrum domain via the power spectral density of the average traces. In can conclude that the data has become more spiky after been applied the spiking decomposition in compare to before deconvolution. All in all, spiking deconvolution has created an alternative of having acceptable resolution without having noise in the data set in compare to have wide-frequency band, which contains noise.

Last but not least, to further enhance the spiking deconvolution results, an instantaneous AGC with window length of 0.5 s need to be apply to the deconvolved data and the results of the AGC is shown in the Figure 4. Note that, this AGC is applied in order to compensate for the lost amplitudes after applying the deconvolution.

Figure 4: Shot gathers 4, 5 and 6 after applying spiking deconvolution and instantaneous AGC