High Resolution Time-Frequency Analysis Method And Its Applications In Seismic Sequence Interface Detection

The oilfield industry in China has entered into the complicated stage of oiland gas field development, the accuracy requirement to seismic exploration isincreasing higher and higher, how to conduct the oil and gas exploration in theinterlaminations is a problem needed to be solved by the scientific workers.Seismic Sequence Interface Detection is to detect the sedimentary sequenceunderground using seismic signals which are the reflected complex signals fromeach layer underground, how to detect the underground sedimentary sequencefrom the seismic signals makes it urgent to seek after a time-frequency analysismethod with high resolution.With the time-frequency analysis theory being improved and perfectedcontinuously, the seismic sequence detection has experienced three importantsteps under the unremitting effort of the scientific workers.The short-time Fourier transform method is one of the most commontime-frequency analysis methods. However, the magnitude and shape of thewindow function in the short-time Fourier transform method are independent oftime and frequency and remain constant, which goes against analyzing timevariant signals, especially the break frequency can't be detected. Generally, thehigh frequency signals last for very short time, while the low frequency signalslast for fairly long time. So we hope to adopt the small time window for highfrequency signals, and large time window for low frequency signals to do theanalysis. While the signals are under analysis, this requirement of changingwindows is contradicted with the characteristics that the time window is fixed inthe short-time Fourier transform method.Wavelet transform method inherits and develops the localization idea in theshort-time Fourier transform method, in the meanwhile, it overcomes thefollowing shortcomings: the windows size doesn't change with frequency anddiscrete orthogonal basis is absent. With the characteristics of high resolution,wavelet transform is a kind of time-dimension (time-frequency) field analyzingmethod of the signals, possessing the capability to present the localizingcharacteristics of the signals in time and frequency fields, it is a local analysismethod for time field in which the shape of window function keeps constantwhile the windows width changes, so it is a rather ideal mathematical tool toprocess the signals. The window function of the continuous wavelet transformis changeable, which has obvious predominance to the Fourier transform for timevariant signals, but its defect is that, when the window function varies, theamplitude and phase will translate, which causes the lack of direct relationbetween the wavelet transform and Fourier transform.R.G. Stockwell, etc. brought forward S transform in 1966. S transformis a kind of extended idea of continuous wavelet transform, in which, the basicwavelet is made up of the product of monochromatic waves and Gaussianfunction, the monochromatic waves in the basic wavelet only make dilationtransform in time field, while Gaussian function makes dilation and translation.This point is different from the continuous wavelet transform. It can keepthe resolution relevant to frequency when it detects the non-stable signals.Compared with other time-frequency field analysis methods such as continuouswavelet transform and short time Fourier transform, etc., S transform has itsdistinguished advantages: the resolution of S transform of the signals is relatedto frequency (i.e. dimension);the result of S transform of the signals is directlyrelated with Fourier spectrum;basic wavelets needn't to be the admissible and soon.Because of the constancy of the basic wavelets in S transform, Stransform is confined at a certain degree in settling the practical problems, it isvery important to accurately locate the reflection interface (that is to locate theposition of reflectance)in processing the seismic data. The result of using Stransform to detect the interlaminations is not satisfactory. So it is necessary todevelop or improve S transform.Based on S transform, we further extended the basic wavelet. In practicalseism, the collected amplitude values in the seismic records vary with differenttimes and different areas, so do the energy delays of the seismic wavelets emittedfrom seismic source;besides, the energy and frequency attenuate with theincreasing propagation distance of the seismic waves. Aiming at these features ofseismic signals, we build a large category of basic wavelet functions that can beused in generalized S transform, and give out the corresponding inversetransform equation;S transform and generalized S transform are used inanalyzing interlaminated layers, and the advantages of generalized S transformare approved by comparing these two methods through numerical examples. Thispaper also presents the examples of applying the generalized S transformmethod in practical data processing in order to verify its validity. So the followingconclusions are drawn: Generalized S transform overcomes the shortcomingsof unchanged basic wavelets in S transform, it is a kind of space transform withhigh resolution. It can not only analyze large area of formation sedimentary cycle,locate the complicated sequence interfaces, but also detect the accurate positionof reflection plane which can't be differentiated by conventional seismic records.In addition, generalized S transform can remarkably reflect the distribution andthe interlayer contact situation of sand-shale interlaminations, the contactsituation between volcanic rock and enclosing rock, and the inner reflectionconfiguration. Generalized S transform can do high resolution formationsequence analysis to detect the thin layer thickness and identify the geologicphenomena such as micro-amplitude construction, lithologic pinchout andoverlap, etc. For the purpose of locating the lithologic trap of the interlaminatinglayers, it can also be used to identify the distribution area of volcanic rock andanalyze the inter construction of volcanic rock for further analyzing the phasestate volcanic rock, which can be used in the fine sequence formationinterpretation and lithology interpretation.In pratical applications, the generalized S transform analysis is made toevery seismic signal in seismic profile, the positions and energies of turningpoints are collected to get the generalized S transform sequence detected profileof the best frequency, this profile indicates refelectance, i.e. the position ofrefelction plane, so the underground sedimetary sequence interface can bedetected. The theoritical detection and appplication examples show that, thegeneralized S transform resolution is remarkably better than the conventionmethods such as short-time Fourie and wavelet transform and S transform, etc.,it is an effective tool for seismic sequence interface detection.