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Special reservoir or fluid has an abnormal response to some certain frequencies, so that seismic decomposition and reconstruction are used to highlight the seismic reflection at certain frequencies useful to identify special geological bodies. Because seismic wavelets are time-varying and spatial-variable in the propagation, synthetic traces based on single wavelet make some weak but useful information lost, and make artifacts form. However, Morlet wavelet aggregation with mathematical analytical expression is able to fully and correctly reflect the variations of wavelet in the propagation of underground medium. The matching pursuit algorithm on the basis of Morlet wavelet improves the calculating efficiency in decomposition and reconstruction greatly. This method is applied to the actual study area to do conjoint analysis of single well and well-tie multi-wavelet decomposition. It is found that frequencies sensitive to interest reservoirs range from 8 to 34 Hz. Reconstructing the wavelets at those special frequencies and analyzing the reconstructed seismic data, it is pointed out that interest reservoirs have abnormal characteristics with respectively strong RMS amplitude in the reconstructed data. Crossplot of gamma value at wells and reconstructed RMS amplitude suggests that anomalies caused by interest reservoirs are well separated from the background anomalies when the reconstructed RMS amplitude is greater than 3650. Quantitative prediction results of interest reservoirs distribution in the study area reveal that interest reservoirs of western and northern study area are distributed annularly and bandedly, while most contiguous sandstone in eastern regions appears sporadically.

With the objects of seismic exploration and development transiting form the conventional structural reservoirs to the subtle reservoirs including low relief structure, thin interbedded reservoirs, upward dipping formation and lithological pinch out, the conventional post-stack seismic data cannot meticulously describe various geological anomalies [

Multi-wavelet concept was first proposed by Geronimo, Hardin and Massopust, et al. [

Since that the reservoir in the research area is tight thin sandstone with low porosity and low permeability and that the sandstones vary quickly in lateral direction, the general reservoir prediction method cannot identify the distribution of interest reservoirs. Therefore, this paper intends to use matching pursuit decomposition based on Morlet wavelet to decompose the seismic data volume into data at single frequencies, and pick out the frequencies at which the interest reservoirs have an obvious abnormality combined with well data analysis. The data at interest frequencies are planned to be reconstructed to obtain a new seismic data volume at which the seismic attributes and well data analysis are applied to predict the distribution of interest reservoirs.

The convolution model of common seismic interpretation has an assumption that the wavelet is unique and constant [

where

tiple reflection, interference and other aspects, the wavelet morphology is time-varying and spatial-variable in the propagation. Above assumption differs significantly from the actual situation, which may lead to the loss of some weak effective information and generating several artifacts. Thus, the wavelets with different frequencies and amplitudes are used in convolution respectively and superimposed finally, and the convolution results are much closer to the real seismic data [

where

theoretical model analysis, while it has a definite morphology after exciting the source wavelet in fact. Although various factors in the propagation make the wavelet morphology change, the performance of this change is mostly a relatively high frequency component attenuation increasing and a relatively low frequency attenuation decreasing. The basic shape of those wavelets with different morphologies are similar, so that it is considered to use a mathematical analytical expression to describe those wavelets aggregation. For example, Morlet wavelet function has a clear mathematical analytical form in time and frequency domains, and it is able to characterize the energy attenuation and velocity dispersion of seismic waves in the propagation of underground medium [

and

where f is frequency,

functions to modulate the wavelet morphology. The higher k value is, the more serious wave compression is, the less side lobe gets, and the narrower wavelets becomes.

The basic principle of multi-wavelet decompositionand reconstruction is decomposing the seismic traces into various wavelets with different frequencies and amplitudes in mathematical methods, which is shown in

During various mathematical algorithms of wavelet decomposition and reconstruction such as shot-term Fourier transform (STFT), wavelet transform (WT), matching pursuit (MP) and so on [

tional efficiency greatly [

where

where

and

and

respectively. Wherein instantaneous frequency is the derivative of instantaneous phase versus time.

The H area is located on a faulted anticline structure of Turpan-Hami basin, China. It’s almost 10 km^{2} (_{2}s_{2} member, the lithological associations of H area are classified into three categories which is shown in

Using different lithology and fluid having various responses to different frequencies, multi-wavelet decomposition and reconstruction are applied to J_{2}s_{2} member of the study area on reservoir prediction. Analysis are from point to line and then to surface.

Transforming multi-wavelet decomposition results of seismic trace near wells into the amplitude spectrum shown in

where O and f is the oblateness and main frequency of energy group respectively, and R represents the correlation coefficient between fitting formula and scatter data. The closer to 1 the

The original seismic records are decomposed into plenty of data at single frequency ranging from 0 to 90 Hz via multi-wavelet matching pursuit decomposition method. Seismic well-tie sessions of

tered. Thus, responses of different lithological associations to particular frequencies varies greatly. Observing the characteristic responses of different lithological associations at frequencies ranging from lower frequency of 10 Hz to higher one of 50 Hz, it is found that sandstone in the second class is characterized by enhanced energy at low frequencies which is less than 20 Hz, and that sandstone of the third class performs enhanced energy at middle frequencies from 20 to 34 Hz, and that sandstone of the first class has stronger energy at high frequencies more than 35 Hz. From the above analysis, it shows that frequencies of energy anomalies reflected by the interest second and third classes is both low and medium frequency bands which is less than 35 Hz.

Considering the analysis results of single well and well-tie multi-wavelet decomposition, it is suggested that the interest frequencies of the study area in interest reservoirs range from 8 to 34 Hz. Then wavelets of those frequencies are linearly superimposed by multi-wavelet matching pursuit reconstruction to obtain new reconstructed seismic data which is shown in

During all 36 wells in the study area, there are only a quarter having lithological data. For this, comparing the gamma value of wells without lithology data in interest reservoirs with gamma value of wells with lithology data, and combining with gamma characteristics of different lithological associations, the wells without lithology information are classified according to lithological associations. The crossplot of mean gamma values in interest reservoirs and RMS amplitude at wells extracting from reconstruction data is shown in

In summary, multi-wavelet decomposition and reconstruction technology break through the limitations caused by the single wavelet assumption in conventional seismic convolution, and Morlet wavelet function greatly describes frequency attenuation and velocity dispersion of seismic wavelet in the propagation. Matching pursuit decomposition and reconstruction technology based on Morlet wavelets decomposes the original seismic traces into multiple Morlet wavelet linearly superimposing. By analyzing the sensitive frequencies where geological bodies generate anomalies, wavelets at those frequencies are picked out and linearly reconstructed to obtain new seismic data where reservoir predictions are well done. Application of this method to H area in Turpan-Hami basin shows that multi-wavelet decomposition and reconstruction technology greatly describes the lateral discontinuity of reservoirs, provides strong support for reservoir geology and geophysical interpretation.

Lifang Cheng,Yanchun Wang,Zhiguo Li,Fuxiu Gong, (2016) Prediction of Tight Sand Reservoir with Multi-Wavelet Decomposition and Reconstructing Method. International Journal of Geosciences,07,529-538. doi: 10.4236/ijg.2016.74040