## Decomposition by Prony method and its components filtering

A distinctive feature of the Prony decomposition, in comparison with other decompositions, is that the Prony decomposition is based on attenuated sinusoid, and therefore, is the closest to the nature of seismic trace. Moreover, while wavelet based and other transformations are depended on frequency, time and/or window, the Prony transform takes into account Q-factor and phase, and does not depend on the chosen window (Mitrofanov, 2011). Thus, the Prony Decomposition or Transform has an advantage.

The decomposition establishes a discrete spectrum associated with a set of shot-time intervals located along the analysed trace, and can be expressed as

When data is decomposed, some of these parameters can filter it. Filleting data by e.g. frequency only, could be considered as an analogue of the well-known band-pass filtering with a better resolution both in time and space domains, providing an opportunity to analyse a wave field in more detail (G. Mitrofanov, 2011). The output will be traces with one or more parameters. It is used widely, e.g., in power systems (Hauer J.F., 1990) and radar signatures characterisation (Moses, 1989).

In geo exploration, the decomposition can be used to solve various geological, and production tasks. It can involve an analysis of target horizons characteristics and a prediction of possible prospects. While other seismic frequency decomposition methods allows to analysis structural elements only, the Prony method helps to identify areas with frequency-dependent effects: the anomalous values of seismic energy scattering (dispersion). Such effect can be deep and lateral variations in reservoir properties, in particular, the anomalies of high pore pressure (Helle H. B, 1993).

Prony Filtering allows to obtain a better resolution both in time and space domains, providing an opportunity to analyze a wave field in more detail. The spectrum contains calculated values of the four parameters, (1) amplitude, (2) frequency, (3) damping factor (Q) and (4) phase. As a result it provides a stable estimation of damping sinusoidal components of short signals. The images built from the selected damping sinusoidal components represent the final results in the form of common time sections. Thus, a medium response on different frequencies can be determined and its variations depending on the time frequency. The procedure improves the resolution of short seismic signals and an analysis of the corresponding sections constructed for different frequencies. It consequently helps to identify areas with anomalous values of seismic energy scattering (dispersion) caused by frequency-dependent effect.

Prony Filtering tests have been performed on a large number of mathematical and physical models. Extensive research was required due to non-linearity of the procedure. During the research, the several aspects were analyzed: seismic signal form influence, stability of the procedure for noise, signals resolution, etc. The investigations confirmed that technique was effective in analyzing reservoir structure, contouring of oil/gas production areas, and in determining productive reservoir properties. To some extent, these results were expected because the seismic signal is similar to the damping sinusoid, and the damping coefficient is related to the Q factor, which plays a significant role in the description of lithology, fluid content and pressure variations.

PSS-Geo performed statistician analysis of techniques in comparison with classical exploration methods for more than 30 000 km 2D seismic lines, and about 60 000 km2 3D. Particular, for the Barents Sea anomalies maps were constructed down to Carboniferous-Devon age.

Learn also, how Prony Decomposition

can help to define Sealing & Leaking Faults and fluid migration paths

Wisting

Oil

Data courtesy of TGS

The new advances in the Reservoir Characterisation from Pre Stacks Solutions-Geo: Prony and Phase Decompositions had been presented at SEG/DGS 4-5 March 2018 | Manama, Bahrain

###### Q-factor expressed from Prony transformed signal.

###### It indicated zones of damped amplitudes, particular fluid accumulation zones, reservoirs.

Data courtesy of Spectrum AS

Data courtesy of Exploro AS & PSS-Geo AS

Data courtesy of TGS

###### Frequency Decomposition - Prony filtered data

24,36,45 Hz in RGB color blend, 3D analysis, for structural elements.

Data courtesy of Exploro AS & PSS-Geo AS

Data courtesy of MultiClient Geophysical ASA

## 25 Hz

Wisting

Oil

**Mercury**

**Gas**

## 25 Hz

**Skrugard**

Oil

Geophysical interpretation based on Seismic inversion and Rock Physic templates. Predicted reservoir layers are in yellow, possible hydrocarbons rocks are in green. See more...