Research On The Methods Of High-resolution Full Spectrum Decomposition

Seismic signals are typically of non-stationary, which require time-frequencyrepresentations, known as spectral decomposition techniques in geophysics, todescribe its frequency characteristics varying with time. With the increased degree ofChina’s onshore oil and gas exploration, exploration targets are gradually shifting tothe complex oil and gas reservoirs such as stratigraphy or lithology reservoirs. In thiscase, common spectral decomposition methods have become increasingly unable tomeet the accuracy and resolution requirements of seismic interpretation. For thisreason, this paper is committed to research on spectral decomposition methods andtechniques to obtain high-resolution and concentrated time-frequency distributions.The research seeks to improve the interpretation power and provide technical supportfor the production and development, thereby reducing the risk of reservoir explorationand development.Common time-frequency representations will play a basic role in the explorationof high-resolution methods. This paper first reviews several common time-frequencyrepresentations, including the STFT, Gabor transform, CWT, S transform andWigner-Ville distribution. These representations are compared particularly focus onthe resolution and phase characteristics. To provide forward and inverse operators forthe following-up high-resolution methods, utilizing the concept of basis function, theforward processes of linear time-frequency transformations are derived tocross-correlations and inverse transformations are derived to convolutions. Thecross-correlation and convolutions are adjoint operators and their frequencyimplementation increases the computational efficiency.Two high-resolution spectral decomposition methods are developed in this paper,the first of which is the Gabor transform based reassignment method. The theory andderivation of reassignment are well stated, as well as some synthetic and real dataexamples. The test results show that, the reassigned spectrum are much moreconcentrated than the Gabor spectrum with only2~3times more computational cost.However, the frequency resolution of the reassigned spectrum is affected by theparameter sigma of Gaussian windows. Large sigma value leads to wider windowlength in the time domain, which is good for low frequency components and viceversa. To solve this problem, this paper propose to use a time varying sigma, since thefrequency components of seismic data are usually damped with time. The proposedapproach is called variable window parameter reassignment.For seismic data contaminated by the random noise, thresholding in the time-frequency domain can help to attenuate the noise. However, it is hard toattenuate the noise without losing effective energy in the Gabor spectrum domain,since the signal energy spreads in the transformed domain, leading to a low disparityof the energy level with the noise. In the reassigned spectrum domain, the effectivesignal energy is strongly concentrated to points, while random noise spreads in thewhole time-frequency map with a much lower energy level. Consequently, a randomnoise attenuation method is proposed in this paper through thresholding in thereassigned Gabor domain. Time-frequency de-noising in the reassigned domain needsan inverse reassignment operator to go back to the time domain. Then, a weightingfactor is created during the forward reassignment process to save the information ofhow many components are transferred from a point to the desired point. In this way,after thresholding (or masking) the reassigned spectrum to attenuate the random noise,the Gabor spectrum can be reconstructed with this pre-computed weighting factor.Synthetic examples demonstrate the effectiveness of the proposed method. Thereassignment method is mainly demonstrated to work on1D signals in the timedomain. For2D seismic signals, events with varying dips in the time-space domainwill turn to be Chirp or chirp-like signals in the frequency-spacial domain. So, analternative choice is to perform the reassignment along the lateral spacial direction inthe space-wavenumber domain to preserve the lateral continuity of the seismic events,which is referred to as the space-wavenumber reassignment. The synthetic and realdata examples show that the reassignment method is a feasible option for spectraldecomposition and incoherent noise attenuation.Another high-resolution decomposition method developed in this paper is thesparse inversion based method, also referred to as inverse spectral decompositionmethod. The inversion problem of spectral decomposition can be described throughtwo different approaches, one of which is using the concept of non-stationary seismicconvolutional model, expressing that the signal is composed from the sum of theconvolutions of wavelets of different frequencies and corresponding reflectivity. Thefrequency dependent reflectivity are referred to as the time-frequency distribution.Another approach states that the frequency dependent reflectivity are generated fromsignal decomposition by special basis functions. The first approach is shown to be thesame as the CWT, which is a special case of the second approach of statement. Thetheory of linear inversion is introduced to solve the inversion problems. To generatesparse spectra, L1norm regularization methods are used, such as the fast iterativesoft-thresholding algorithm (FISTA) and the In-Crowd algorithm. The FISTA ispopular due to its simply implement and the ability to deal with complex numbers.The In-Crowd algorithm is more like a flow or an idea rather than an algorithm. Thispaper integrate FISTA with In-Crowd algorithm, using FISTA to solve sub-problem ateach In-Crowd update. Synthetic examples show that the integrated method is nearly3times faster than FISTA used singly. Seismic data contains many traces with high spatial correlation. There is usually only a little time delay and some random noisedifference between two adjacent traces. Most of characteristic of the two traces aresimilar. Utilizing this property, the result of previous trace after a time-delaycorrection can be as a initial solution to warm start inversion of current trace. In thisway,6times of the computational cost are reduced. The sparse property in thespectrum is also used for the random noise attenuation, the robust ability of which isshown in a synthetic example.The concept of time-frequency phase spectrum is introduced for the hydrocarbonreservoir detection and horizons identification. Due to the low-resolution, the phasespectra of common time-frequency distributions are difficult utilized for seismicinterpretation. While the phase spectrum from inversion method, carring theinformation of local phase, has the same high-resolution level with the time-frequencyenergy spectrum. The real data example show that horizons are more easily identifiedwith the help of the phase information than using the energy information only. As animportant complement to the time-frequency energy spectrum, the time-frequencyphase spectrum has the potential to become a new seismic interpretation tool.The two high-resolution spectral decomposition methods both show good resultsin the synthetic and real examples. However, they are now still in the exploratorystage, so that before extensive applications, there are some related problems to solve.Two of them are investigated in this paper. The residual between the estimatedwavelet and the real wavelet will affect the result of the inversion spectrum. In orderto solve this problem, a wavelet correction technique is presented based on the L2norm constraint of the wavelet error. The sparse inversion spectral decompositionmethod pursues a high time-frequency resolution distribution and improves he abilityof interpretation of thin-layers. However, on the opposite side, the high resolutiondecomposition leads to under-sampled in the time slices and horizon slices of thespectra of3D seismic data. To overcome this drawback, we propose a discrete Cosinetransform based sparse recovery method which increases the visualization ofunder-sampled spectrum slices. A real data example is used to demonstrate theeffectiveness of the proposed method. The new techniques of high-resolution spectraldecomposition will promote the development of some related new techniques, one ofwhich is presented in this paper. Frequency-dependent AVO contains additionalattributes of the reservoir, which can enhance the accuracy of the seismicinterpretation. However, one difficult of extracting the additional attributes from thinlayers is that the tuning effects affect seismic amplitudes which can mask or at leastalter the features associated with permeability and fluid content. Therefore, this paperpresents one approach to remove the effects of thin-beds on frequency-dependentAVO analysis via spectral inversion.