CN106842305A - A kind of seismic signal score field optimal order computational methods based on fuzzy field - Google Patents

Abstract

A kind of seismic signal score field optimal order computational methods based on fuzzy field, belong to seismic data processing field, it is intended to the optimal order of seismic signal score field is quickly determined using fuzzy field, simplify optimal order calculating process.Single-channel seismic signal is read in first, and blurring mapping is done to input signal；Then the time width and bandwidth of signal are calculated, signal is asked for and is based on the minimum window function of time-frequency bandwidth product, and blurring mapping is done to window function；LPF is done in blurring mapping using the ambiguity function of window function to signal；Calculate seismic signal from the direction gradient of the horizontally and vertically both direction of the ambiguity function of item；Singular value decomposition is carried out to direction gradient matrix, principal direction of the seismic signal from item ambiguity function is calculated；The score field optimal order of seismic signal is calculated finally by principal direction.

Description

A kind of seismic signal score field optimal order computational methods based on fuzzy field

Technical field

The invention belongs to seismic data processing field, and in particular to a kind of seismic signal score field based on fuzzy field is optimal Rank computational methods.

Background technology

Fourier Transform of Fractional Order (fractional Fourier transform, FrFT) is also referred to as angle Fourier change Change, be the generalized form of Fourier transformation.FrFT is to signal, that is, signal is transformed into score field.FrFT has multiple Conversion order, the Fourier transformation that different conversion orders has different transformation results, signal only has a kind of unique conversion knot Really.FrFT is introduced field of signal processing by Almeida (1994), gives the physical significance of FrFT, and its meaning is signal FrFT computings are rotation of the signal on time-frequency plane, and tentatively propose FrFT and traditional Time-Frequency Analysis Method is combined and divided The thought of number field Time-Frequency Analysis Method.FrFT is incorporated into traditional time frequency analysis, it is high to provide due to the conversion diversity of FrFT The time frequency analysis result of resolution ratio provides possibility.

In general, in numerous conversion orders, there is the time-frequency of the corresponding score field time frequency analysis result of order Resolution ratio highest, this order is referred to as the optimal order of score field time frequency analysis.The optimal order of score field Time-Frequency Analysis Method has Various computational methods.Capus and Brown (2003) propose global optimum and the fractional order Fourier in short-term of local optimum becomes Change, and optimal order is calculated by calculating the linear frequency modulation rate of signal；When Durak and Arikan (2003) is using score field minimum Bandwidth product calculates the optimal order of signal；Akan etc. (2007) is proposed using the spectral norm ratio most subtotal of time frequency analysis result The method for calculating optimal order.Shi Jun etc. (2010) removes white Gaussian noise with score field wavelet transformation, and denoising mean square error Minimum order is used as optimal order.

Because score field Time-Frequency Analysis Method has (2011) such as resolution ratio higher, Chen Hong first fractional order Gabor Conversion applies to seismic signal Spectral Imaging Technology, and using the minimum method search fractional order Gabor of broad sense time-frequency bandwidth product The optimal order of conversion.Research with score field Time-Frequency Analysis Method in seismic signal field deepens continuously, Chen Ying frequencies etc. (2011) score field Time-Frequency Analysis Method is applied into seismic data processing, earthquake is searched for using score field amplitude maximum method The optimal order of signal；Field beautiful jade etc. searches for the optimal order of seismic signal using score field coefficient of kurtosis maximization approach；Wang Yuqing etc. (2015) search seismic signal score field second order is defined as optimal order away from minimum order.

FrFT conversion is carried out to signal, is substantially that signal is decomposed with linear FM signal.Solve seismic signal Optimal order, different from other signals, seismic signal is multicomponent data processing, and is unaware that the linear frequency modulation that signal is included Rate, therefore linear frequency modulation rate can not directly be calculated by signal in itself.Therefore above-mentioned score field Time-Frequency Analysis Method is all employed The method of traversal search, it is impossible to directly calculate the optimal order of seismic signal, has research to search traversal from mathematical angle at present Rope is converted into calculating process, but operand is big, wordy.

The content of the invention

The invention provides a kind of seismic signal score field optimal order computational methods based on fuzzy field, it is intended to using fuzzy Domain quickly determines the optimal order of seismic signal score field, simplifies optimal order calculating process.

In order to solve the above-mentioned technical problem, above-mentioned purpose is reached, the present invention is adopted the following technical scheme that：

A kind of seismic signal score field optimal order computational methods based on fuzzy field, the described method comprises the following steps：

Step 1：Single-channel seismic signal s (t) is input into, blurring mapping is done to signal s (t), obtain the ambiguity function of signal A_s；

Step 2：Calculate the time width T of seismic signal s (t)_sAnd bandwidth B_s, ask for seismic signal s (t) and be based on time-frequency bandwidth product Minimum window function h_TBP(t), and to window function h_TBPT () does blurring mapping, obtain window function h_TBPThe ambiguity function A of (t)_g；

Step 3：Using ambiguity function A_gTo ambiguity function A_sLPF is done, ambiguity function A of the signal from item is obtained₀；

Step 4：Calculate ambiguity function A of the signal from item₀Direction gradient matrix G；

Step 5：Singular value decomposition is carried out to direction gradient matrix G, ambiguity function A of the signal from item is calculated₀Principal direction θ；

Step 6：Using signal from the ambiguity function A of item₀Principal direction θ calculate signal s (t) score field optimal order p_opt。

Further, the transformation for mula for being used to the blurring mapping that signal s (t) does in the step 1 is as follows：

In formula, τ is time delay, and θ is frequency displacement, and j is imaginary unit, and e is natural constant, and t is the time.

Further, in the step 2

To window function h_TBPT () does blurring mapping, obtain window function h_TBPThe ambiguity function A of (t)_g, transformation for mula is as follows：

Further, the filtering method in the step 3, computational methods are as follows：

A₀=A_sA_g (4)。

Further, ambiguity function A of the signal from item in the step 4₀It is the matrix signal of N × N, its direction gradient For：

Wherein g_x(k) representing matrix A₀In point (x_k, y_k) horizontal direction gradient, g_y(k) representing matrix A₀In point (x_k, y_k) The gradient of vertical direction.

Further, singular value decomposition is carried out to direction gradient matrix G in the step 5, it is specific theoretical as follows：

G=USV^T (6)

In formula, U is the matrix of N × 2, and V is 2 × 2 matrix, and S is 2 × 2 diagonal singular value matrixs, the first of matrix V Row vector is V₁=[V_1,1,V_1,2]

Ambiguity function A of the signal from item₀The computing formula of principal direction θ be：

Further, in the step 6

In sum, by adopting the above-described technical solution, the beneficial effects of the invention are as follows：

Seismic multi-component signal is transformed into the time delay of fuzzy field-frequency deviation plane, seismic signal is distributed in two from item The origin of dimensional plane, cross term is distributed in the position away from origin, is filtered using the minimum Gauss function of signal time-frequency bandwidth product Except the cross term of seismic signal, than using general window function filter effect more preferably, can preferably stick signal it is interior have Effect feature, improves the time frequency resolution of signal.

The method converts a signal into fuzzy field, and the optimal order of seismic signal can be directly calculated in fuzzy field, it is to avoid The drawbacks of traversal search of prior art, simplify calculating process, can effectively apply to seismic signal score field time frequency analysis.

Brief description of the drawings

Fig. 1 is method flow diagram；

Fig. 2 is single-channel seismic signal；

Fig. 3 is the ambiguity function of signal；

Fig. 4 is the ambiguity function of window function；

Ambiguity function of Fig. 5 signals from item.

Specific embodiment

All features disclosed in this specification, in addition to mutually exclusive feature and/or step, can be with any Mode is combined.

The present invention is elaborated below in conjunction with the accompanying drawings.

Step 1：It is input into single-channel seismic signal s (t) (as shown in Figure 2)；

Blurring mapping is done to signal s (t), the ambiguity function A of signal is obtained_s(as shown in Figure 3), the transformation for mula for being used It is as follows：

In formula, τ is time delay, and θ is frequency displacement, and j is imaginary unit, and e is natural constant

Step 2：Calculate the time width T of signal s (t)_sAnd bandwidth B_s, ask for signal s (t) and be based on the minimum window of time-frequency bandwidth product Function h_TBP(t)

To window function h_TBPT () does blurring mapping, obtain window function h_TBPThe ambiguity function A of (t)_g(as shown in Figure 4)

Step 3：Using ambiguity function A_gTo ambiguity function A_sLPF is done, ambiguity function A of the signal from item is obtained₀(such as Shown in Fig. 5)

A₀=A_sA_g (11)

Step 4：Calculate ambiguity function A of the signal from item₀Direction gradient matrix G, ambiguity function A of the signal from item₀It is N The matrix signal of × N, its direction gradient is：

Wherein g_x(k) representing matrix A₀In point (x_k, y_k) horizontal direction gradient, g_y(k) representing matrix A₀In point (x_k, y_k) The gradient of vertical direction.

Step 5：Singular value decomposition is carried out to direction gradient matrix G, decomposition formula is as follows：

G=USV^T (13)

In formula, U is the matrix of N × 2, and V is 2 × 2 matrix, and S is 2 × 2 diagonal singular value matrixs, the first of matrix V Row vector is V₁=[V_1,1,V_1,2]

Ambiguity function A of the signal from item₀The computing formula of principal direction θ be：

Step 6：Using signal from the ambiguity function A of item₀Principal direction θ calculate signal s (t) score field optimal order p_opt

Embodiments of the invention are as described above.The present invention is not limited to the above-described embodiments, and anyone should learn The structure change made under enlightenment of the invention, it is every with of the invention with same or like technical scheme, each fall within this Within the protection domain of invention.

Claims (7)

1. a kind of seismic signal score field optimal order computational methods based on fuzzy field, it is characterised in that methods described include with Lower step：

Step 1：Single-channel seismic signal s (t) is input into, blurring mapping is done to signal s (t), obtain the ambiguity function A of signal_s；

Step 2：Calculate the time width T of seismic signal s (t)_sAnd bandwidth B_s, ask for seismic signal s (t) and be based on time-frequency bandwidth product minimum Window function h_TBP(t), and to window function h_TBPT () does blurring mapping, obtain window function h_TBPThe ambiguity function A of (t)_g；

Step 3：Using ambiguity function A_gTo ambiguity function A_sLPF is done, ambiguity function A of the signal from item is obtained₀；

Step 4：Calculate ambiguity function A of the signal from item₀Direction gradient matrix G；

Step 5：Singular value decomposition is carried out to direction gradient matrix G, ambiguity function A of the signal from item is calculated₀Principal direction θ；

Step 6：Using signal from the ambiguity function A of item₀Principal direction θ calculate signal s (t) score field optimal order p_opt。

2. a kind of seismic signal score field optimal order computational methods based on fuzzy field according to claim 1, its feature It is that the transformation for mula used to the blurring mapping that signal s (t) does in the step 1 is as follows：

$A_s(\mathrm{\θ},\mathrm{\τ})={\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}s(t+\frac{\mathrm{\τ}}{2})s^{*}(t-\frac{\mathrm{\τ}}{2})e^{j2\mathrm{\π}\mathrm{\θ}t}dt---\left(1\right)$

In formula, τ is time delay, and θ is frequency displacement, and j is imaginary unit, and e is natural constant, and t is the time.

3. a kind of seismic signal score field optimal order computational methods based on fuzzy field according to claim 1, its feature It is, in the step 2

$h_{TBP}\left(t\right)=e^{-{\mathrm{\πt}}^2{B}_s/T_s}---\left(2\right)$

To window function h_TBPT () does blurring mapping, obtain window function h_TBPThe ambiguity function A of (t)_g, transformation for mula is as follows：

$A_g(\mathrm{\θ},\mathrm{\τ})={\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}{h}_{TBP}(t+\frac{\mathrm{\τ}}{2}){h_{TBP}}^{*}(t-\frac{\mathrm{\τ}}{2})e^{j2\mathrm{\π}\mathrm{\θ}t}dt---\left(3\right).$

4. a kind of seismic signal score field optimal order computational methods based on fuzzy field according to claim 1, its feature It is that the filtering method in the step 3, computational methods are as follows：

A₀=A_sA_g (4)。

5. a kind of seismic signal score field optimal order computational methods based on fuzzy field according to claim 1, its feature It is, ambiguity function A of the signal from item in the step 4₀It is the matrix signal of N × N, its direction gradient is：

$G=\left[\begin{array}{cc}.& .\\ .& .\\ .& .\\ g_x\left(k\right)& g_y\left(k\right)\\ .& .\\ .& .\\ .& .\end{array}\right],k\∈A_0---\left(5\right)$

Wherein g_x(k) representing matrix A₀In point (x_k, y_k) horizontal direction gradient, g_y(k) representing matrix A₀In point (x_k, y_k) vertically The gradient in direction.

6. a kind of seismic signal score field optimal order computational methods based on fuzzy field according to claim 1, its feature It is that singular value decomposition is carried out to direction gradient matrix G in the step 5, it is specific theoretical as follows：

G=USV^T (6)

In formula, U is the matrix of N × 2, and V is 2 × 2 matrix, and S is 2 × 2 diagonal singular value matrixs, the first row of matrix V to It is V to measure₁=[V_1,1,V_1,2]

Ambiguity function A of the signal from item₀The computing formula of principal direction θ be：

$\mathrm{\θ}=arctan\frac{V_{1,1}}{V_{1,2}}---\left(7\right).$

7. a kind of seismic signal score field optimal order computational methods based on fuzzy field according to claim 1, its feature It is, in the step 6

$p_{opt}=\frac{2\mathrm{\θ}}{\mathrm{\π}}---\left(8\right).$