The previous two blog posts looked at 'standard' frequency decomposition techniques which applied convolution of the trace with bandpass filters in a traditional manner. This post focuses on the High Definition Frequency Decomposition or HDFD.
Link to Part 1 - Constant Bandwidth
Link to Part 2 - Constant Q
Part 3 – High Definition Frequency Decomposition (HDFD)
The High Definition Frequency Decomposition (HDFD) algorithm uses a different approach to the ‘standard’ frequency decomposition filters. The application of a modified matching pursuit algorithm allows trace reconstruction with precise vertical localisation.
Matching pursuit is a trace-based form of frequency analysis and decomposition. It uses a dictionary of Gabor wavelets which are correlated to each event in the seismic data individually. Once an event has been matched to a wavelet, it is extracted from the trace and the next event is matched. This iterative process continues until 99% of the trace energy has been matched and a synthetic trace has been generated.
Reconstruction of a particular frequency response is achieved by summation of the response of all wavelets that intersect the desired frequency. The relative proportion of the response included from each wavelet is determined by the degree of overlap of the bandwidth of each wavelet with the desired frequency. This is why the bandwidth of HDFD responses is so wide (and why the vertical resolution is so good).
First optimisation pass. a) Atoms matched during the first matching pass (red, blue and green) have been co-optimised to find the best combination of amplitudes to fit the seismic trace (black) over the region of the atoms’ overlap. b) The effect of co-optimising multiple atoms at once is to provide a better approximation (orange) to the seismic trace in regions of constructive or destructive interference between the atoms.
Two options of HDFD are available, one producing the best possible vertical resolution and one with an improved colour resolution.
When using the colour resolution option, the data is split into three band-limited versions of the input data using a modified FFT. Then the modified matching pursuit algorithm is applied separately to each of the three components and the results are combined to produce the final outputs.
When using the vertical resolution option, no splitting is carried out and the modified matching pursuit algorithm is applied directly to the input data.