Deconvolution and least-squares filtering


Deconvolution is applied to enhance the vertical resolution of the data; at the same time the phase of the data should be equalized and preferably made zero. This process requires a proper description of the “wavelet”. As such the airgun signal, correlated vibroseis signal, geophone response, instrument response, reverberation mechanism, ghost mechanism, absorption mechanism etc. can be used. Some of these mechanisms can be measured (deterministic deconvolution) and others have to be estimated from the data (data adaptive deconvolution). Once the “wavelet” is known we can deconvolve for it in various ways taking into account the fact that the deconvolution filters have a finite length and the trade-off between enhancement of the resolution and deterioration of the signal-to-noise ratio. The physical processes and associated mathematical expressions of the various mechanisms will be treated.




Geophysicists who deal with seismic data processing and who especially want to familiarize themselves with the theoretical and practical aspects of deconvolution and least-squares filtering.




Participants will be able to apply deconvolution judiciously to the data. Based on a thorough understanding the theory and choice of diagnostics, before and after, the appropriate method with optimum parameter choice will be selected. Questions like amplitude preservation and phase integrity can be handled correctly.



Continuing Professional Development






Deconvolution and least-squares filtering


1.   The convolutional seismic trace model

2.   Deconvolution: definition of inverse-, spiking- or whitening filter

3.   Examples: - reverberation - dereverberation

                        - ghost - deghosting

                        - absorption - deabsorption

4.   Resolution: signal dispersion as a function of amplitude and phase spectrum

5.   The Z-transform, polynomials and factorization

6.   Minimum-phase, mixed-phase and maximum-phase wavelets

7.   The inverse filter of a two-point wavelet

8.   The inverse filter of an arbitrary wavelet

9.   Minimum-phase wavelets: properties in the different domains

10. Least-squares (ls) filters: - the normal equations

                                               - ls inverse filters

                                               - ls prediction- and ls prediction error filters

11. Least-squares filters in the frequency domain: design and properties

12. Two-sided filters: design and properties

13. Filtering in the presence of noise

14. Special topics: - tuning - detuning

                              - vibroseis deconvolution

                              - inverse array filtering = directional deconvolution

                              - surface consistent deconvolution

                              - deterministic deconvolution with measured or modeled wavelet

                              - homomorphic deconvolution




2 days






Houston, Texas, United States



14-15 September 2017


Dubai, United Arab Emirates



5-6 November 2017






Register now