Seismic time-frequency analysis method based on generalized Chirplet transform with time-synchronized extraction

Abstract

A seismic time-frequency analysis method based on generalized Chirplet transform with time-synchronized extraction, which has higher level of energy aggregation in the time direction and can better describe and characterize the local characteristics of seismic signals, and is applicable to the time-frequency characteristic representation of both harmonic signals and pulse signals, comprising the steps of processing generalized Chirplet transform with time-synchronized extraction for each seismic signal to obtain a time spectrum by: carrying out generalized Chirplet transform, calculating group delay operator and carrying out time-synchronized extraction on seismic signals, thereby the boundary and heterogeneity structure of the rock slice are more accurately and clearly shown and subsequence seismic analysis and interpretation are facilitated.

Claims

1. A seismic time-frequency analysis method based on generalized Chirplet transform with time-synchronized extraction for seismic data processing of an underground structure having a plurality of rock structures, comprising the steps, executed by a computer, of: (I) obtaining 3D seismic data of the underground structure; (II) performing seismic time-frequency analysis based on generalized Chirplet transform with time-synchronized extraction of the underground structure by the steps of: (a) presetting a set of 3D seismic data is S(T,M,N), where T is the duration of time, M is the total number of line numbers, and N is the total number of track numbers; (b) calculating an average Fourier spectrum of several seismic signals from the set of 3D seismic data in the step (a), and selecting a constant frequency value η.sub.0 for extraction; (c) processing generalized Chirplet transform with time-synchronized extraction for each seismic signal f(t)=S(T,m,n) of the set of 3D seismic data S(T,M,N) to obtain a time spectrum TGC.sub.f(η,t), where 1≤m≤M; 1≤n≤N and S.sub.TF(T,m,n)=TGC.sub.f(η.sub.0,T), which further comprises three sub-steps of: carrying out generalized Chirplet transform on the signals, calculating group delay operator and carrying out time-synchronized extraction, wherein the generalized Chirplet transform is carried out on the signal f(t) to obtain a time-frequency representation GC.sub.f(η,t), where $G{C}_f\left(\eta ,t\right)={{\int }_{ℝ}^{}}^{}f\left(\tau \right)g\left(\tau -t\right)e^{-i\frac{\hat{c}\left(t\right)}{2}{\left(\tau -t\right)}^2}{e}^{-\mathrm{i\eta \tau }}d\tau ,$ where R represents a set of real numbers, i represents an imaginary unit, g(t) is a window function, ĉ(t) is an optimized Chirp rate, η is a frequency variable, τ is a (integral) time variable, and t is the time variable, the group delay operator is calculated by: ${\tilde{t}}_f\left(\eta ,t\right)=-\left\{\frac{{\partial }_{\eta }G{C}_f\left(\eta ,t\right)}{G{C}_f\left(\eta ,t\right)}\right\},$ where {⋅} refers to an imaginary part, ∂.sub.η(⋅) refers to a partial derivative with respect to the frequency variable η, and the time-synchronized extraction is calculated by:
TGC.sub.f(η,t)=GC.sub.f(η,t)δ(t−{tilde over (t)}.sub.f(η,t)), where a definition of δ(t−{tilde over (t)}.sub.f(η,t)) is: $\delta \left(t-{\tilde{t}}_f\left(\eta ,t\right)\right)=\{\begin{array}{cc}1,& t={\tilde{t}}_f\left(\eta ,t\right)\\ 0,& \mathrm{otherwise}\end{array},$ (d) obtaining a constant frequency data volume as S.sub.TF(T,M,N), and (e) based on the generalized Chirplet transform, accurately locating a frequency of harmonic signals and a time when an impact signal occurs to obtain a time-frequency characteristic representation of both the harmonic signals and pulse signals for seismic data processing and for seismic time-frequency analysis of the rock structure of the underground structure, (III) applying the seismic time-frquency analysis based on the generalized Chirplet transform with time-synchronized extraction on the underground structure so as to present the time-frequency characteristic representation with both the harmonic signals and pulse signals of the rock structure of the underground structure in a form of an image.

2. The seismic time-frequency analysis method based on the generalized Chirplet transform with time-synchronized extraction according to claim 1, wherein in step (b), comprises the steps of: drawing the time spectrum, observing a main frequency interval of the signals, and selecting a frequency value for extraction in the main frequency interval.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of the time-frequency spectrum of impact signal f(t)=exp[2iπ(100t)] in different methods; wherein (a) is the generalized Chirplet transform; (b) is the generalized Chirplet transform with time-synchronized extraction.

(2) FIG. 2 is a schematic diagram of the time-frequency spectrum of harmonic signal f(t)=4.Math.δ(t−0.5) in different methods; wherein (a) is the generalized Chirplet transform; (b) is the generalized Chirplet transform with time-synchronized extraction.

(3) FIG. 3 is a schematic diagram of the time-frequency spectrum of synthetic signal f(t)=exp[2iπ(20t+10 sin(t))] in different methods; wherein (a) is the time-domain waveform of the real part of the signal; (b) is the short-time Fourier transform with time-synchronized extraction; (c) is the generalized Chirplet transform with time-synchronized extraction.

(4) FIG. 4 illustrates the rock slice at 40 Hz of a three-dimensional seismic data volume in an oil field which is processed with different time-frequency techniques, wherein (a) is the short-time Fourier transform with time-synchronized extraction; (b) is the generalized Chirplet transform with time-synchronized extraction.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(5) Embodiments of the present invention are described in detail below in connection with the accompanying drawings and embodiments.

(6) It should be noted that the terms “first” and “second” in the description, drawings and claims of the present invention are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in a sequence other than those illustrated or described herein. In addition, the terms “including”, “comprising” and “having” and any variations of them are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those identical as listed. Those steps or units may include other steps or units that are not clearly listed or are inherent to these processes, methods, products, or devices.

(7) I. According to the preferred embodiment of the present invention, a seismic time-frequency analysis method based on time-synchronized extraction of generalized Chirplet transform comprises the following steps of:

(8) (1) performing the time-synchronized extraction of generalized Chirplet transform, which comprises the following steps:

(9) (1.1) Carrying out the generalized Chirplet transform on the signal f(t) to obtain the time-frequency representation GC.sub.f(η,t), whose expression is as follow:

(10) $\begin{array}{cc}G{C}_f\left(\eta ,t\right)={\int }_{ℝ}^{}f\left(\tau \right)g\left(\tau -t\right)e^{-i\frac{\hat{c}\left(t\right)}{2}{\left(\tau -t\right)}^2}{e}^{-\mathrm{i\eta \tau }}d\tau & \left(i\right)\end{array}$

(11) where R represents the set of real numbers, i represents an imaginary unit, g(t) is the window function, ĉ(t) is the optimized Chirp rate, η is the frequency variable, τ is the (integral) time variable, and t is the integration time variable, then calculating by the following formula to obtain:
GS.sub.f(t,η)=C.sub.f(t,η,ĉ.sub.n),
here ĉ.sub.n=arg max.sub.c|C.sub.f(t,η,c.sub.i)|, i=1, . . . , K   (ii)

(12) where

(13) $\begin{array}{cc}{C}_f\left(t,\eta ,c\right)={\int }_{ℝ}^{}f\left(\tau \right)g\left(\tau -t\right)e^{-i\frac{c}{2}{\left(\tau -t\right)}^2}{e}^{-\mathrm{i\eta \tau }}d\tau & \left(\mathrm{iii}\right)\end{array}$

(14) (1.2) calculating the group delay operator {tilde over (t)}.sub.f(η,t):

(15) $\begin{array}{cc}{\tilde{t}}_f\left(\eta ,t\right)=-\left\{\frac{{\partial }_{\eta }G{C}_f\left(\eta ,t\right)}{G{C}_f\left(\eta ,t\right)}\right\}& \left(\mathrm{iv}\right)\\ & \end{array}$

(16) where {⋅} refers to the imaginary part, ∂.sub.η(⋅) refers to the partial derivative being find with respect to the frequency variable η.

(17) (1.3) calculating the time-synchronized extraction of the time-frequency spectrum of the generalized Chirplet transform:
TGC.sub.f(η,t)=GC.sub.f(η,t)δ(t−{tilde over (t)}.sub.f(η,t))   (v)

(18) where δ(t−{tilde over (t)}.sub.f(η,t)) is defined as:

(19) $\begin{array}{cc}\delta \left(t-{\tilde{t}}_f\left(\eta ,t\right)\right)=\{\begin{array}{cc}1,& t={\tilde{t}}_f\left(\eta ,t\right)\\ 0,& \mathrm{otherwise}\end{array}& \left(\mathrm{vi}\right)\end{array}$

(20) For the harmonic signal f.sub.h(t)=Ae.sup.iη.sup.0.sup.t, its generalized Chirplet transform result is:

(21) $\begin{array}{cc}G{C}_{f_{\delta }}\left(\eta ,t\right)={\int }_{ℝ}^{}{f}_h\left(\tau \right)g\left(\tau -t\right)e^{-i\frac{\hat{c}\left(t\right)}{2}{\left(\tau -t\right)}^2}{e}^{-\mathrm{i\eta \tau }}d\tau ={\int }_{ℝ}^{}{\mathrm{Ae}}^{{\mathrm{i\eta }}_0\tau }g\left(\tau -t\right)e^{-i\frac{\hat{c}\left(t\right)}{2}{\left(\tau -t\right)}^2}{e}^{-\mathrm{i\eta \tau }}d\tau =A\hat{g}\left(\eta -{\eta }_0\right)e^{-i\left(\eta -{\eta }_0\right)t}{e}^{i\frac{\hat{c}\left(t\right)}{2}{\left(\eta -{\eta }_0\right)}^2}& \left(\mathrm{vii}\right)\end{array}$

(22) According to formula (iv), the following can be obtained:

(23) $\begin{array}{cc}{\tilde{t}}_{f_h}\left(\eta ,t\right)=-\left\{\frac{{\partial }_{\eta }G{C}_{f_h}\left(\eta ,t\right)}{G{C}_{f_h}\left(\eta ,t\right)}\right\}=t+\hat{c}\left(t\right)\left({\eta }_0-\eta \right)& \left(\mathrm{viii}\right)\end{array}$

(24) From the definition (vi), the following equivalent can be derived:
{tilde over (t)}.sub.f.sub.h(η,t,)=t⇔ĉ(t)(η.sub.0−η)=0⇔η=η.sub.0   (ix)

(25) FIG. 1 verifies the conclusion of equation (ix). Time-synchronized extraction of generalized Chirplet transform can accurately locate the frequency of harmonic signals.

(26) For the impact signal f.sub.δ(t)=Aδ(t−t.sub.0), its generalized Chirplet transform obtained is:

(27) 0$\begin{array}{cc}G{S}_{f_{\delta }}\left(t,\eta \right)=A{\int }_{ℝ}^{}\delta \left(\tau -t_0\right)g\left(\tau -t\right)e^{-i\frac{\hat{c}\left(t\right)}{2}{\left(\tau -t\right)}^2}{e}^{-\mathrm{i\eta \tau }}d\tau =Ag\left(t_0-t\right)e^{-i\frac{\hat{c}\left(t\right)}{2}{\left(t_0-t\right)}^2}{e}_{{\mathrm{i\eta t}}_0}& \left(x\right)\end{array}$

(28) According to formula (iv), the following can be obtained:
{tilde over (t)}.sub.f(t,η)=t.sub.0   (xi)

(29) FIG. 2 verifies the conclusion of equation (xi). Time-synchronized extraction of generalized Chirplet transform can accurately locate the time when the impact signal occurs.

(30) 2. A seismic time-frequency analysis method based on time-synchronized extraction of generalized Chirplet transform comprises the following steps of:

(31) Suppose a set of 3D seismic data is S(T,M,N), and the constant frequency data volume required to be obtained is S.sub.TF(T,M,N).

(32) (2.1) Calculate the average Fourier spectrum of the seismic data, and select the constant frequency value η.sub.0 (assume the value is 30 Hz) to be extracted;

(33) (2.2) Process time-synchronized extraction of generalized Chirplet transform for each track S(T,m,n) (1≤m≤M; 1≤n≤N) of the 3D seismic data S(T,M,N) to obtain the time spectrum TF, and S.sub.TF(T,m,n)=TGC.sub.f(η.sub.0,T);

(34) (2.3) Obtain the constant frequency data volume as S.sub.TF(T,M,N), and process subsequent processing and interpretation of the rock slices according to the requirements.

(35) II. Numerical simulation results

(36) 1. Synthetic model data

(37) In order to verify the effectiveness of generalized Chirplet transform with time-synchronized extraction to improve time-spectrum, energy aggregation, a composite signal is selected, and as shown in FIG. 3(a), the mathematical expression is as follows:
f.sub.2(t)=exp[2iπ(20t+10 sin(t))]  (xii)

(38) Where the sampling time interval is 0.01 s.

(39) FIG. 3 shows the time-frequency results of the generalized Chirplet transform with time-synchronized extraction and the short-time Fourier transform with time-synchronized extraction. Comparing (b) and (c) of FIG. 3, it is found that the two different time-frequency analysis methods can accurately describe the rhythmic frequency change of the signal at the position of frequency changes with more rapid changes. However, at the position of frequency changes with slower changes, the time-frequency aggregation of the generalized Chirplet transform is better with time-synchronized extraction, making it capable of characterizing the time-frequency characteristics of the signal more accurately.

(40) 2. Actual seismic data

(41) Based on the theoretical analysis results, the generalized Chirplet transform with time-synchronized extraction is further applied to the seismic time-frequency analysis. FIG. 4 illustrates the results of rock slice at 40 Hz of a three-dimensional seismic data volume in an oil field. Since the generalized Chirplet transform with time-synchronized extraction can provide better time-frequency aggregation than the short-time Fourier transform with time-synchronized extraction, the method of the generalized Chirplet transform with time-synchronized extraction of the present invention can reflect the fine structure of the underground more accurately. As shown in FIG. 4(b), the boundary and heterogeneity structure are much more clearer.

(42) In summary, the method of the present invention introduces the group delay estimation operator to the generalized Chirplet transform for the first time. The method of the present invention performs time-frequency analysis on slow-changing and transient signals and the time-frequency representation of energy aggregation under both slow-changing and transient signal condition can both be obtained, thereby improving the adaptability of analyzed signals. Compared with the short-time Fourier transform with time-synchronized extraction, which is applied to seismic data processing, the present invention can characterize the fine underground structure and its heterogeneity more accurately.

(43) One skilled in the art will understand that the embodiment of the present invention as shown in the drawings and described above is exemplary only and not intended to be limiting.

(44) It will thus be seen that the objects of the present invention have been fully and effectively accomplished. Its embodiments have been shown and described for the purposes of illustrating the functional and structural principles of the present invention and is subject to change without departure from such principles. Therefore, this invention includes all modifications encompassed within the spirit and scope of the following claims.