Forward Modeling And Time Frequency Characteristic Analysis Of Thin Interbeds In Anelastic Media

As an important part of seismic data application research,forward modeling of thin interbeds is of great significance to studies of seismic response characteristics of typical oil and gas reservoir types.It is a bridge to realize the joint application of geological data and seismic data,and an effective means to reduce the uncertainty and multiple solutions of thin interbeds inversion.However,at present,the research of forward modeling of thin interbeds is mostly on the basis of the elastic medium,without considering the influence of formation viscous absorption,ignoring the time-varying characteristics and frequency dispersion characteristics of seismic data,which has an important impact on the time-frequency response characteristics of thin interbeds,and brings many uncertainties to thin interbeds inversion,attribute analysis and reservoir prediction,so it is necessary to further study.Based on the above considerations,this paper introduces the quality factor to describe the viscous absorption of the formation,establishes the complex velocity field,and derives the wave field extrapolation formula of the anelastic medium phase-shifting method.We have established the geological model of the isopachous thin interbeds with different layer numbers and single layer thickness of anelastic medium,and the geological model of orderly thickness-graded thin interbeds with different layer numbers and different thickness change gradients;Three kinds of quality factors are respectively assigned to sandstone and mudstone to describe the weak,medium and strong absorption characteristics of the formation,and the corresponding numerical models of thin interbeds are established.Based on the wave field extrapolation theory,the wave equation forward modeling of the above numerical model is completed by using the phase-shifting method in the depth domain of anelastic medium to obtain the reflection single shot record of thin interbeds;the zero offset seismic trace is extracted from the shot record and the spectrum is obtained by using the affine class time-frequency distribution;for the isopachous thin interbeds of anelastic medium,the time-domain characteristics such as amplitude,waveform and apparent time thickness and the frequency-domain characteristics such as peak frequency,peak amplitude,notch frequency and other frequency-domain parameters change with the formation viscosity and the layer numbers are investigated respectively;for the orderly thickness-graded thin interbeds of the anelastic medium,the time-domain waveform characteristics,the time-frequency spectrum change with the viscosity,the layer numbers and the thickness gradient are investigated respectively.The study found that,with the decreases of the formation quality factor,the viscous absorption of the formation increases,the time-domain amplitude of the reflection compound wave of thin interbeds decreases,the waveforms become smooth and fat,accompanied by a certain time shift,which results in the decrease of the resolution of thin interbeds and the deviation of the position of thin interbeds interface,and the methods of predicting the thickness of thin interbeds based on the amplitude of reflection wave have large errors.With the increase of viscous absorption,the high-frequency energy loss and the frequency bandwidth become narrow in the frequency domain,and the whole spectrum energy distribution moves to the low frequency direction,which leads to the decrease of the resolution of thin interbeds,and there are errors in the methods of predicting the thickness of thin interbeds based on the peak frequency.For the isopachous thin interbeds,when the layer numbers and the thickness of single layer are large,the peak frequency of high frequency direction and the total thickness of apparent time are less affected by the formation viscosity,and have certain stability.The peak frequency of high frequency direction can be used to predict the thickness of single layer,and the total thickness of apparent time can be used to predict the actual thickness of thin interbeds.When the thickness of thin interbeds is less than 1/8 wavelength,The first notch frequency is less affected by Q value and has strong stability.The first notch frequency can be used to quantitatively predict the thickness of thin interbeds.For the ordely thickness-graded thin interbeds,the law of time-frequency that “the frequency of thin beds increases while the frequency of thick beds decreases” is not affected by the viscous absorption of the formation,and the viscosity only affects the relative relationship of amplitude,the display of time-frequency distribution and the width of frequency band,This means that the thickness regulation mechanism of the thin interbeds is not affected by the viscosity of the formation,which has important theoretical guidance significance for the subsequent thin interbeds identification and reservoir prediction.