Data Self-Driven Bandpass Filtering Method without Boundary Effect

Abstract

The present invention discloses a method for eliminating the boundary effect of band-pass filtering based on data self-driving. First, the original data is extended, the top and bottom boundaries are self-driven and edged with data, and the edged data is assigned values to ensure that the boundary and the data change continuously, and there will be no artificial reflection interface at the position where the boundary is connected to the original data. Then, the band-pass filtering is performed on the data with the edge, and the edge data is removed to obtain the band-pass filtering result without boundary effect. Compared with the traditional band-pass filtering algorithm, this solution obtains a high-precision filtering result by increasing a small amount of calculation, has a simple implementation process, high precision, is applicable to most seismic reflection data, and has high practical application and popularization value.

Description

Technical Field

[0001] The invention belongs to the field of seismic data processing, and in particular relates to a bandpass filtering method without boundary effect based on data self-driving. Background Art

[0002] Affected by the acquisition environment, marine seismic data often have serious low-frequency background noise, mainly caused by swells. It is characterized by low frequency and large amplitude, and appears as background noise covering the entire record. The conventional processing method is 3-4Hz low-cut filtering, but in the actual processing process, due to the existence of boundary effects, the bandpass filter operator usually cannot achieve the ideal accuracy ( Figure 1 ).

[0003] The bandpass filter boundary effect is caused by the change in length of the signal source after passing through the filter operator ( Figure 2 ), this is because the result of bandpass filtering is the result of the convolution of the input seismic signal and the bandpass filter. The larger the length of the bandpass filter operator, the greater the change in length. The length of the bandpass filter operator depends on the low-frequency end of the filter. In the practice of bandpass filtering of seismic data, it is known that the low-cut filter of 3-4Hz has a greater impact on the boundary, and the bandpass filter above 50Hz has a smaller impact on the boundary, which can generally be ignored. The shallower the water depth, the more obvious the shallow impact. Generally, when the water depth is greater than 500ms, the shallow impact can be ignored (related to the length of the filter operator); while the deep impact is unavoidable. When there is an effective reflection layer near the bottom boundary of the data record, its impact must be considered. The significance of eliminating the filter boundary effect is reflected in three points: 1. Shallow water seismic data may be encountered in the project to improve seafloor imaging; 2. To maximize the availability of deep seismic reflection signals; 3. To prevent data pollution caused by filtering in offset imaging, which reduces the imaging quality.

[0004] At present, the main method for suppressing 3-4Hz low-frequency noise is still using conventional bandpass filtering algorithms, which have negligible effects on marine seismic data with greater water depth and longer recording time. At the same time, the filtering method based on the Infinite Impulse Response filter uses a more complex edge processing algorithm, which can prevent the generation of false frequencies while completely suppressing noise. However, the above method still has certain defects: the design of the IIR filter needs to solve a multi-parameter and multi-objective optimization problem. Whether it is local optimization or global optimization, complex calculations are required to convert the filtering indicators into the designed filter parameters, while the conventional bandpass filtering algorithm only requires the filtering frequency and empirical slope to obtain the filter operator, so the efficiency of the IIR algorithm is much lower than that of the conventional bandpass filtering algorithm. Summary of the invention

[0005] In order to solve the boundary problem existing in conventional bandpass filtering algorithms, the present invention proposes a bandpass filtering method without boundary effect based on data self-driving, performs extension and edging operations on seismic data, and then obtains a filtering result with boundary truncation effect by bandpass filtering the edged data, thereby solving the boundary problem existing in conventional bandpass filtering algorithms.

[0006] The present invention is implemented by adopting the following technical solution: a data self-driven bandpass filtering method without boundary effect, comprising the following steps:

[0007] Step A, edge the original data in the time domain: add N sampling points to the upper and lower ends of the original data, where N is the edge width;

[0008] Step B, performing data self-driven assignment on the edged data: using the data of the length of the first and last N sampling points of the original data, a smooth boundary value is obtained by establishing a continuous function;

[0009] Step C: band-pass filter the data after edge trimming, remove the border after filtering, and restore the length of the original data, so as to realize a band-pass filter without border anomalies.

[0010] Furthermore, in step A, assuming that the original data length is T+1 sampling points, the original data length is first extended by 2N sampling points, and then N sampling points are corrected downward to obtain a boundary with N sampling points added above and below. At this time, the length of the data after the border becomes T+2N+1 sampling points, where the values ​​of sampling points 0 to N-1 are 0, and the values ​​of sampling points T+N+1 to T+2N are also 0, which is expressed as:

[0011]

[0012] Where N is the border width, x 1 (k) represents the edged data, x(k) represents the original data, and k represents the number of sampling points.

[0013] Furthermore, the automatic assignment in step B is specifically implemented in the following manner:

[0014] Step B1, assigning a border value to obtain the first part of data;

[0015] x 1 The value of the Nth sampling point of (k) is assigned to sampling points 0 to N-1, and x 1 The value of the T+Nth sampling point (k) is assigned to the T+N+1 to T+2N sampling points, and the upper and lower boundary values ​​of the newly assigned values ​​are multiplied by the coefficient a; the values ​​of the data of the Nth to T+Nth sampling points remain unchanged, and the obtained data is used as the first part of the data x 1p1 (k), expressed as:

[0016]

[0017] Step B2, mirroring the original data boundary to obtain the second part of data;

[0018] x 1 The values ​​of the N+1th to 2Nth sampling points of (k) are mirrored upward to obtain the values ​​of the 0th to N-1th sampling points; x 1 The values ​​of the Tth to T+N-1th sampling points of (k) are mirrored downward to obtain the values ​​of the T+N+1th to T+2Nth sampling points; the values ​​of the Nth to T+Nth sampling points are assigned 0, and the obtained data is used as the second part of the data x 1p2 (k) namely:

[0019]

[0020] Step B3, realizing the assignment of the data after bordering;

[0021] The first part of data x obtained in step B1 1p1 (k) Subtract the second part of data x obtained in step B2 1p2 (k), get the data x after the data self-driven edge assignment b (k):

[0022] x b (k) = x 1p1 (k)-x 1p2 (k)

[0023]

[0024] Furthermore, a is 2 or 3.

[0025] Furthermore, in step A, the border width depends on the length of the filter operator. Assuming the length of the filter operator is M+1, the border width N is greater than or equal to M.

[0026] Compared with the prior art, the advantages and positive effects of the present invention are:

[0027] This scheme first extends the original data, performs data self-driven edging on the top and bottom boundaries, and assigns values ​​to the edging data to ensure that the boundary and data change continuously, and no artificial reflection interface appears at the position where the boundary and the original data are connected; then, the data with edging is band-pass filtered to remove the edging data to obtain a band-pass filtering result without boundary effect. Compared with the traditional band-pass filtering algorithm, the method of the present invention obtains high-precision filtering results by increasing the amount of calculation very little, and the implementation process is simple and efficient. It is suitable for most seismic reflection data, especially shallow water seismic data (especially when the water depth is less than 500ms) and when there is an effective reflection layer near the deep boundary, the band-pass filtering algorithm of this patent must be used to avoid the amplification effect and offset arc effect caused by the large boundary value. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a schematic diagram of the large value abnormal noise at the boundary of conventional bandpass filtering (low-cut 3Hz filtering);

[0029] Figure 2 This is a schematic diagram of the change in waveform length caused by bandpass filtering;

[0030] Figure 3 This is a schematic diagram of the principle of the method described in an embodiment of the present invention;

[0031] Figure 4 This is a schematic diagram of data before filtering according to an embodiment of the present invention;

[0032] Figure 5 This is a schematic diagram of data after bordering according to an embodiment of the present invention;

[0033] Figure 6 This is a schematic diagram of data subjected to bandpass filtering (5 Hz filtering) after edging according to an embodiment of the present invention;

[0034] Figure 7 Schematic diagram of the final filtering result of the embodiment of the present invention;

[0035] Figure 8 It is a schematic diagram of the filtering result of the conventional bandpass filtering method;

[0036] Fig. 9 This is a schematic diagram of the result of self-driven bandpass filtering without boundary effect of data in an embodiment of the present invention;

[0037] Fig.10 The figure is a flow chart of the method described in the embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described below in conjunction with the accompanying drawings and embodiments. In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention can also be implemented in other ways different from those described herein, and therefore, the present invention is not limited to the specific embodiments disclosed below.

[0039] For the low-frequency background noise of marine seismic data, after designing the low cutoff frequency, the conventional bandpass filtering algorithm and IIR algorithm only affect the data whether there is a boundary problem. This embodiment proposes a bandpass filtering method without boundary effect based on data self-driving. Its basic principle is as follows Figure 3 As shown in the figure, by increasing a small amount of convolution calculation, the boundary problem of the conventional bandpass filtering algorithm is solved. The implementation process is simple and applicable to most seismic reflection data. Its calculation efficiency is higher than that of the IIR algorithm. It includes the following steps:

[0040] Step A, edge the original data in the time domain: first extend the original data by 2N sampling points, and then move the original data downward by N sampling points, that is, add N sampling points of boundaries above and below the original data, the size of N depends on the filtering parameters, generally not more than 500ms;

[0041] Step B, self-driven data assignment of the border area: using the original data of the length of the first and last N sampling points, a smooth boundary value is obtained by establishing a continuous function;

[0042] Step C: band-pass filter the data after edge trimming, remove the border after filtering, and restore the length of the original data, so as to realize a band-pass filter without border anomalies.

[0043] Specifically, the following is combined Figure 3 and Fig.10 The method of the present invention is described in detail:

[0044] Step A: Edge the original data in the time domain:

[0045] Assume that the original data length is T+1 sampling points and the sampling rate is 1ms; first, the original data length is lengthened by 2N sampling points, and then corrected downward by N sampling points. At this time, the data length becomes T+2N+1 sampling points, where the values ​​of sampling points 0 to N-1 are 0, and the values ​​of sampling points T+N+1 to T+2N are also 0.

[0046] (1) Assume that the input signal is x(k) with a length of T+1 sampling points, and the filter operator is h(k) with a length of M+1 sampling points, then the convolution result y(k) is:

[0047]

[0048] That is, after the data with the original length of T+1 sampling points passes through the bandpass filter with the length of M+1 sampling points, the output length becomes T+M+1 sampling points, then the edge width N is greater than or equal to M sampling points, that is, the edge width depends on the length of the filter operator;

[0049] (2) The length of the bandpass filter depends on its frequency at the low-frequency end. That is, the operator length of the low-cut filter is large, which has a great impact on the data boundary. Taking the zero-phase filter as an example, the slope length is calculated under the condition of stable filtering (in dB / octave):

[0050] max[(round(6*sqrt(LOW_FREQ),18.0))] (2)

[0051] Here, round means rounding the result (6*sqrt(LOW_FREQ)) to the nearest integer.

[0052] The larger the slope length, the larger the filter length, the more stable the filtering, and the more leakage frequency. At present, the lowest frequency that can be received by the offshore streamer detector is generally 3Hz. Taking 3Hz as the boundary, it can be seen from formula (2) that in order to achieve stability, a slope of 18dB / octave is required for the 3Hz low-cut filter. By filtering the original data at 3Hz low-cut, it can be seen that the upper boundary influence width is about 300ms.

[0053] (3) The length of the rim width N can be determined by the following method: first, perform bandpass filtering on the original data to obtain the filtering result with boundary effect. The boundary effect will appear at the top and bottom boundaries of the data, and the length of the impact on the top and bottom is the same. Determine the length of the impact on the top boundary (or bottom boundary), and the top rim width N can be greater than this value. Generally, it can be taken as a whole hundred milliseconds greater than this value. The rim width of the bottom boundary can also be taken as N. That is, if the determined top boundary impact length is 420ms, then N can be taken as 500ms. Through the filtering example, it can be seen that for a 3Hz low-cut filter, the upper boundary impact width is about 300ms, and the lower boundary impact width is the same; for a 2Hz low-cut filter, the upper boundary impact width is about 500ms; for a 1Hz low-cut filter, the upper boundary impact width is about 800ms. Since the filter impact width is independent of the sampling rate, in practical applications, when the lowest filter is greater than or equal to 2Hz, the rim width N can be selected to be the number of sampling points corresponding to 500ms.

[0054] After determining the border width N, the top and bottom borders are initialized. The original data x(k) becomes x after bordering. 1 (k), the length changes from T+1 sampling points to T+2N+1 sampling points, and the corresponding relationship is:

[0055]

[0056] For example, assuming the original data is 5000ms and the sampling rate is 1ms, first increase the data length by 1000ms and then correct it downward by 500ms. At this time, the data length becomes 6000ms, where the amplitude value from 0ms to 499ms is 0, and the amplitude value from 5501ms to 6000ms is also 0.

[0057] Step B, performing data self-driven assignment on the border area;

[0058] Formula (3) is the data without value after edging. 1 (k) Perform boundary self-driving assignment, which is specifically achieved through the following steps:

[0059] Step B1: Boundary assignment step 1

[0060] (1) x 1 The value of the Nth sampling point of (k) is assigned to sampling points 0 to N-1, and x 1 The value of the T+Nth sampling point of (k) is assigned to the T+N+1 to T+2N sampling points, and the upper and lower boundary values ​​of the newly assigned values ​​are multiplied by a; the value of the data in the middle part (N to T+N sampling points) remains unchanged, and the obtained data is used as the first part of the data x 1p1 (k), can be expressed as:

[0061]

[0062] Step B2: Boundary assignment step 2

[0063] x 1 The values ​​of the N+1th to 2Nth sampling points of (k) are mirrored upward to obtain the values ​​of the 0th to N-1th sampling points; x 1 The values ​​of the Tth to T+N-1th sampling points of (k) are mirrored downward to obtain the values ​​of the T+N+1th to T+2Nth sampling points; the values ​​of the Nth to T+Nth sampling points are assigned 0, and the obtained data is used as the second part of the data x 1p2 (k) namely:

[0064]

[0065] Step B3: Boundary assignment step 3

[0066] Using the data x from the first part 1p1 (k) Subtract the second part of the data x 1p2 (k), get the data x after the data self-driven edge assignment b (k), that is: x b (k) = x 1p1 (k)-x 1p2 (k), specifically expressed as:

[0067]

[0068] Formula (6) can be expressed as: when the input data is: A = {A 0 , A 1 , ... A T-1 , A T}, the data after edging is P = {2A 0 -A N , 2A 0 -A N-1 , ... 2A 0 -A 1}∪{A 0 , A 1 , ... A T-1 , A T}∪{2A T -A T-1 , 2A T -A T-2 , ... 2A T -A T-N}. After experiments, the value of a in formula (6) can be set to 2 or 3 to obtain an ideal boundary. The boundary obtained in this way changes continuously with the data, and there is no artificially given wave impedance interface.

[0069] For example, in step A, it is assumed that the original data is 5000ms. Based on the edging and initialization in step A, the amplitude value at 500ms is assigned to the amplitude value from 0ms to 499ms, the amplitude value at 5500ms is assigned to the amplitude value from 5501ms to 6000ms, and then the amplitude values ​​from 0ms to 499ms and from 5501ms to 6000ms are multiplied by 2 (in this embodiment, a takes the value 2), and the amplitude value at 500-5500 remains unchanged to obtain the first part of the data. Then, based on the data in step A, with 500ms as the center axis, the amplitude values ​​from 501ms to 1000ms are mirrored upwards to obtain the corresponding amplitude values ​​from 499ms to 0ms; with 5500ms as the center axis, the amplitude values ​​from 5000ms to 5499ms are mirrored downwards to obtain the corresponding amplitude values ​​from 5501ms to 6000ms; the amplitude values ​​from 500ms to 5500ms are assigned a zero value to obtain the second part of the data. Finally, the data from the first part is subtracted from the data from the second part to obtain the final data after edging.

[0070] Step C: Remove the border data:

[0071] The data after bandpass filtering of equation (6) is x bt (k), the length is T+2N+1 sampling points, then the result of removing the edge data is:

[0072] x f(k) = x bf (k+N), 0≤k≤T (7)

[0073] In order to verify the effectiveness and practicality of the present invention, some actual seismic data is selected for filtering application. Specific processing process: for the actual seismic data, data self-driven edging is performed based on the original data. Figure 4 is the original data, Figure 5 The data after edging is shown in Figure 1. It can be seen that the data after edging is smooth and has no abnormal boundary values. Figure 6 For Figure 5 The result after 3Hz low-cut filtering shows that the bandpass filter cutoff effect occurs at the edge position. Figure 7 This is the final filtered result after removing the rimmed border, showing no bandpass filter truncation effect. Figure 8 and Fig. 9 The figures are schematic diagrams of filtering results obtained by conventional bandpass filtering and the data self-driven edge bandpass filtering algorithm of the present invention. It can be seen that after using the conventional bandpass filtering algorithm, abnormal truncation effect noise will appear at the top and bottom of the data, while the bandpass filtering results of the present invention completely suppress such noise, avoiding the influence of such noise on shallow water offset imaging and deep effective reflection imaging.

[0074] The above description is only a preferred embodiment of the present invention and does not limit the present invention in other forms. Any technician familiar with the profession may use the technical content disclosed above to change or modify it into an equivalent embodiment with equivalent changes and apply it to other fields. However, any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. Data self-driven borderless effect band-pass filtering method, Characterized in that, Comprising the following steps: Step A: Frame the original data in the time domain: Add a border of N sampling points to both the upper and lower ends of the original data, where N is the framing width; Assume the original data has T + 1 sampling points. First, increase the length of the original data by 2N sampling points, and then correct it downward by N sampling points to obtain a border with N sampling points added to both the upper and lower ends. At this time, the length of the framed data becomes T + 2N + 1 sampling points, where the values of the sampling points from 0 to N - 1 are 0, and the values of the sampling points from T + N + 1 to T + 2N are also 0, expressed as: ； Where N is the width of the border, x 1 (k) represents the data after bordering, x(k) represents the original data, k represents the number of sampling points; Step B: Perform data self-driven assignment on the framed data: Use the data with a length of N sampling points at the beginning and end of the original data to obtain smooth boundary values by establishing a continuous function; The automatic assignment is specifically implemented through the following methods: Step B1: Assign values to the framed border to obtain the first part of the data; Assign the value of the Nth sampling point of x 1 ( k ) to the 0th to (N - 1)th sampling points, and assign the value of the (T + N)th sampling point of x 1 ( k ) to the (T + N + 1)th to (T + 2N)th sampling points, and multiply the upper and lower boundary values of the newly assigned values by the coefficient a; the values of the sampling points from the Nth to the (T + N)th remain unchanged, and the obtained data is used as the first part of the data x 1p1 ( k ), expressed as: ； Step B2: Mirror the original data border to obtain the second part of the data; Shift x 1 ( k ) values of the N+1 to 2Nth sampling points upward to mirror, obtaining values of the 0 to N-1th sampling points; Shift x 1 ( k ) values of the T to T+N-1th sampling points downward to mirror, obtaining values of the T+N+1 to T+2Nth sampling points; Assign 0 to values of the N to T+Nth sampling points, and use the obtained data as the second part of data x 1p2 ( k ), that is: ； Step B3: Realize the assignment of the framed data; The first part of the data obtained in step B1 x 1p1 ( k ) subtract the second part of the data obtained in step B2 x 1p2 ( k ), to obtain the data after self-driven edge assignment of the data x b ( k ): x b ( k )= x 1p1 ( k )- x 1p2 ( k )； ； Step C: Perform band-pass filtering on the framed data, remove the border after filtering, and restore it to the length of the original data.

2. The data self-driven borderless effect band-pass filtering method according to claim 1, Characterized in that: a takes 2 or 3.

3. The data self-driven borderless effect band-pass filtering method according to claim 1, Characterized in that: In step A, assume the length of the filtering operator is M + 1, and the framing width N is greater than or equal to M.

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