Frequency-independent centroid frequency shift Q factor calculation method and device, equipment and medium

Abstract

The invention discloses a frequency-independent centroid frequency shift Q factor method, device and equipment and a medium. The method comprises the following steps: calculating the centroid frequency of a source wavelet; the centroid frequency of the geometric mean wavelet is calculated, and then the variance of the geometric mean wavelet is calculated; and calculating a frequency-independent Q factor based on the centroid frequency of the source wavelet, the centroid frequency of the geometric mean wavelet and the variance. According to the invention, the influence of frequency on Q factor calculation is eliminated.

Description

Technical Field

[0001] The present invention relates to the field of seismic exploration data processing, and more specifically, to a frequency-independent centroid frequency shift Q-factor method, apparatus, device, and medium. Background Art

[0002] The centroid frequency shift (CFS) method is a commonly used method in Q-factor estimation. This method utilizes the characteristic that the pulse width is affected by the distance during signal propagation. It is usually based on the assumption of special wavelets with full-band characteristics, such as Gaussian wavelets, BOX wavelets, triangular wavelets, or frequency-weighted exponential (FWE) source wavelets. Generally, the shapes of the amplitude spectra received by different source wavelets will be different due to attenuation. Even in the case of the same medium and travel time, it will cause inaccurate estimation. Since the initial equation calculates the centroid frequency based on the full frequency band, in practical data applications, a frequency band with a higher signal-to-noise ratio than the main frequency is usually selected for Q-value estimation, so the above approach is not rigorous.

[0003] Therefore, it is necessary to develop a frequency-independent centroid frequency shift Q-factor method, apparatus, device, and medium.

[0004] The information disclosed in the background art part of the present invention is only intended to deepen the understanding of the general background art of the present invention, and should not be regarded as an admission or any form of suggestion that this information constitutes the prior art known to those skilled in the art. Summary of the Invention

[0005] The present invention proposes a frequency-independent centroid frequency shift Q-factor method, apparatus, device, and medium, which eliminates the influence of frequency on Q-factor calculation.

[0006] In a first aspect, an embodiment of the present disclosure provides a frequency-independent centroid frequency shift Q-factor method, including:

[0007] Calculating the centroid frequency of the source wavelet;

[0008] Calculating the centroid frequency of the geometric mean wavelet, and then calculating the variance of the geometric mean wavelet;

[0009] Calculating a frequency-independent Q-factor based on the centroid frequency of the source wavelet, the centroid frequency of the geometric mean wavelet, and the variance.

[0010] As a specific implementation manner of the embodiment of the present disclosure, calculating the centroid frequency of the source wavelet includes:

[0011] Extending the centroid frequency to an arbitrary frequency band [a, b], and determining the recurrence relation of the incomplete gamma function;

[0012] Performing integral transformation and expansion derivation on the centroid frequency after recurrence to obtain the transformed centroid frequency;

[0013] Simplify the calculation for the transformed centroid frequency to obtain the centroid frequency of the source wavelet.

[0014] As a specific implementation manner of the embodiments of the present disclosure, the transformed centroid frequency is:

[0015]

[0016] where f 0 is the reference frequency.

[0017] As a specific implementation manner of the embodiments of the present disclosure, the centroid frequency of the source wavelet is:

[0018]

[0019] where f 0 is the reference frequency and the definition of n.

[0020] As a specific implementation manner of the embodiments of the present disclosure, the centroid frequency of the geometric mean wavelet is:

[0021]

[0022] where

[0023] As a specific implementation manner of the embodiments of the present disclosure, the variance of the geometric mean wavelet is:

[0024]

[0025] As a specific implementation manner of the embodiments of the present disclosure, the Q factor is:

[0026]

[0027] where and are the centroid frequencies of the source wavelet and the detector point wavelet respectively, is the centroid frequency of the geometric mean wavelet, is the variance of the geometric mean wavelet, and Δt is the wavelet time sampling interval.

[0028] In a second aspect, the embodiments of the present disclosure further provide a frequency-independent centroid frequency shift Q factor device, including:

[0029] A first calculation module for calculating the centroid frequency of the source wavelet;

[0030] A second calculation module for calculating the centroid frequency of the geometric mean wavelet and further calculating the variance of the geometric mean wavelet;

[0031] The third calculation module calculates a frequency-independent Q factor based on the centroid frequency of the source wavelet, the centroid frequency of the geometric mean wavelet, and the variance.

[0032] As a specific implementation manner of an embodiment of the present disclosure, calculating the centroid frequency of the source wavelet includes:

[0033] Extend the centroid frequency to an arbitrary frequency band [a, b], and determine the recurrence relation of the incomplete gamma function;

[0034] Perform integral transformation and expansion derivation on the centroid frequency after recurrence to obtain the transformed centroid frequency;

[0035] Perform simplified calculation on the transformed centroid frequency to obtain the centroid frequency of the source wavelet.

[0036] As a specific implementation manner of an embodiment of the present disclosure, the transformed centroid frequency is:

[0037]

[0038] where f 0 is the reference frequency.

[0039] As a specific implementation manner of an embodiment of the present disclosure, the centroid frequency of the source wavelet is:

[0040]

[0041] where f 0 is the reference frequency and the definition of n.

[0042] As a specific implementation manner of an embodiment of the present disclosure, the centroid frequency of the geometric mean wavelet is:

[0043]

[0044] where

[0045] As a specific implementation manner of an embodiment of the present disclosure, the variance of the geometric mean wavelet is:

[0046]

[0047] As a specific implementation manner of an embodiment of the present disclosure, the Q factor is:

[0048]

[0049] where and are the centroid frequencies of the source wavelet and the geophone wavelet respectively, is the centroid frequency of the geometric mean wavelet, is the variance of the geometric mean wavelet, and Δt is the wavelet time sampling interval.

[0050] In a third aspect, an embodiment of the present disclosure further provides an electronic device, which includes:

[0051] a memory storing executable instructions;

[0052] a processor, the processor runs the executable instructions in the memory to implement the frequency-independent centroid frequency shift Q-factor method.

[0053] In a fourth aspect, an embodiment of the present disclosure further provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, it implements the frequency-independent centroid frequency shift Q-factor method.

[0054] The methods and apparatuses of the present invention have other characteristics and advantages, which will be apparent from or will be described in detail in the accompanying drawings and subsequent specific embodiments incorporated herein. These drawings and specific embodiments together are used to explain the specific principles of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] By describing the exemplary embodiments of the present invention in more detail in conjunction with the accompanying drawings, the above and other objects, features, and advantages of the present invention will become more apparent. Among them, in the exemplary embodiments of the present invention, the same reference numerals generally represent the same components.

[0056] Figure 1 A flowchart showing the steps of a frequency-independent centroid frequency shift Q-factor method according to an embodiment of the present invention is shown.

[0057] Figure 2 A schematic diagram showing the simulated spectra of FWE with a slip bandwidth and a decaying wavelet at different starting frequencies according to an embodiment of the present invention is shown.

[0058] Figure 3 A schematic diagram showing the relative error of a traditional CFS according to an embodiment of the present invention is shown.

[0059] Figure 4 A schematic diagram showing the relative error according to an embodiment of the present invention is shown.

[0060] Figure 5 A block diagram showing a frequency-independent centroid frequency shift Q-factor apparatus according to an embodiment of the present invention is shown.

[0061] Description of the reference numerals:

[0062] 201. First calculation module; 202. Second calculation module; 203. Third calculation module. Detailed implementation manner

[0063] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein.

[0064] To facilitate understanding of the solutions and effects of the embodiments of the present invention, six specific application examples are given below. Those skilled in the art should understand that this example is only for facilitating the understanding of the present invention, and any specific details are not intended to limit the present invention in any way.

[0065] Example 1

[0066] Figure 1 A flowchart showing the steps of a frequency-independent centroid frequency shift Q-factor method according to an embodiment of the present invention is shown.

[0067] As Figure 1 shown, the frequency-independent centroid frequency shift Q-factor method includes: Step 101, calculating the centroid frequency of the source wavelet; Step 102, calculating the centroid frequency of the geometric mean wavelet, and then calculating the variance of the geometric mean wavelet; Step 103, calculating a frequency-independent Q-factor based on the centroid frequency of the source wavelet, the centroid frequency of the geometric mean wavelet, and the variance.

[0068] In one example, calculating the centroid frequency of the source wavelet includes:

[0069] Expanding the centroid frequency to an arbitrary frequency band [a, b], and determining the recurrence relation of the incomplete gamma function;

[0070] Performing integral transformation and expansion derivation on the centroid frequency after recurrence to obtain the transformed centroid frequency;

[0071] Performing simplified calculation on the transformed centroid frequency to obtain the centroid frequency of the source wavelet.

[0072] In one example, the transformed centroid frequency is:

[0073]

[0074] where f 0 is the reference frequency.

[0075] In one example, the centroid frequency of the source wavelet is:

[0076]

[0077] where f 0For the reference frequency, the definition of n.

[0078] In one example, the centroid frequency of the geometric mean wavelet is:

[0079]

[0080] Where,

[0081] In one example, the variance of the geometric mean wavelet is:

[0082]

[0083] In one example, the Q factor is:

[0084]

[0085] Where, and are the centroid frequencies of the source wavelet and the detector point wavelet respectively, is the centroid frequency of the geometric mean wavelet, is the variance of the geometric mean wavelet, and Δt is the wavelet time sampling interval.

[0086] Specifically, the Q factor formula of the traditional CFS method is:

[0087]

[0088] Where, f S and f R are the centroid frequencies of the source wavelet and the detector point wavelet respectively, f G and are the geometric mean centroid frequency and variance of the source wavelet and the detector point wavelet respectively, and Δt is the wavelet time sampling interval. Expanding it to an arbitrary frequency band [a, b], the centroid frequency of the source wavelet is:

[0089]

[0090] f 0 is the reference frequency, is the incomplete gamma function, so the recurrence relation of the incomplete gamma function is:

[0091]

[0092] Substituting formula (3) into formula (2), we get:

[0093]

[0094] For the second term of formula (4), it can be transformed into an integral form:

[0095]

[0096] Expand and derive formula (5) and substitute it into formula (4) to obtain:

[0097]

[0098] It can be simplified to:

[0099]

[0100] Furthermore, we obtain

[0101]

[0102] The centroid frequency of the source wavelet of formula (7) is the same as the centroid frequency of the full frequency band of formula (1). Therefore, the centroid frequency of the FWE source wavelet is independent of frequency. Similarly, the centroid frequency of the FWE detection point wavelet is independent of frequency. Similarly, the variance of the geometric mean wavelet is

[0103]

[0104] where, is the centroid frequency of the geometric mean wavelet, Therefore, formula (8) shows that the variance and the centroid frequency of the geometric mean wavelet are both independent of frequency. Therefore, the factor of the centroid frequency shift method independent of frequency is

[0105]

[0106] where, and are the centroid frequencies of the source wavelet and the detection point wavelet respectively, and it can be seen from formula (7) that they are independent of frequency; is the centroid frequency of the geometric mean wavelet, is the variance of the geometric mean wavelet, and it can be seen from formula (8) that they are independent of frequency. Therefore, the factor estimation of the centroid frequency shift method in formula (9) is not affected by the frequency band, even for a single frequency. Therefore, the method of the present invention can be extended to the field where it is not assumed that the wavelet is independent of frequency. Compared with the traditional CFS method, this method can be more widely applied to Q-factor estimation.

[0107] Example 2

[0108] The present invention also provides a centroid frequency shift Q-factor device independent of frequency, including:

[0109] The first calculation module calculates the centroid frequency of the source wavelet;

[0110] The second calculation module calculates the centroid frequency of the geometric mean wavelet, and further calculates the variance of the geometric mean wavelet;

[0111] The third calculation module calculates a frequency-independent Q factor based on the centroid frequency of the source wavelet, the centroid frequency of the geometric mean wavelet, and the variance.

[0112] In one example, calculating the centroid frequency of the source wavelet includes:

[0113] Expanding the centroid frequency to an arbitrary frequency band [a, b] and determining the recurrence relation of the incomplete gamma function;

[0114] Performing integral transformation and expansion derivation on the recursively obtained centroid frequency to obtain the transformed centroid frequency;

[0115] Performing simplified calculation on the transformed centroid frequency to obtain the centroid frequency of the source wavelet.

[0116] In one example, the transformed centroid frequency is:

[0117]

[0118] where f 0 is the reference frequency.

[0119] In one example, the centroid frequency of the source wavelet is:

[0120]

[0121] where f 0 is the reference frequency and the definition of n.

[0122] In one example, the centroid frequency of the geometric mean wavelet is:

[0123]

[0124] where

[0125] In one example, the variance of the geometric mean wavelet is:

[0126]

[0127] In one example, the Q factor is:

[0128]

[0129] where and are the centroid frequencies of the source wavelet and the detector point wavelet respectively, is the centroid frequency of the geometric mean wavelet, is the variance of the geometric mean wavelet, and Δt is the wavelet time sampling interval.

[0130] Specifically, the Q - factor formula of the traditional CFS method is:

[0131]

[0132] where f S and f R are the centroid frequencies of the source wavelet and the geophone - point wavelet respectively, f G and are the geometric mean centroid frequency and variance of the source wavelet and the geophone - point wavelet respectively, and Δt is the wavelet time sampling interval. Expanding it to any frequency band [a, b], the centroid frequency of the source wavelet is:

[0133]

[0134] f 0 is the reference frequency, is the incomplete gamma function, so the recurrence relation of the incomplete gamma function is:

[0135]

[0136] Substituting formula (3) into formula (2), we get:

[0137]

[0138] For the second term of formula (4), it can be transformed into an integral form:

[0139]

[0140] Expanding and deriving formula (5) and substituting it into formula (4), we get:

[0141]

[0142] It can be simplified to:

[0143]

[0144] Furthermore, we get

[0145]

[0146] The centroid frequency of the source wavelet in formula (7) is the same as the centroid frequency of the full frequency band in formula (1). Therefore, the centroid frequency of the FWE source wavelet is independent of frequency. Similarly, the centroid frequency of the FWE geophone - point wavelet is independent of frequency. Similarly, the variance of the geometric mean wavelet is

[0147]

[0148] where is the centroid frequency of the geometric mean wavelet, so formula (8) shows that the variance and the centroid frequency of the geometric mean wavelet are both independent of frequency. Therefore, the factor of the frequency-independent centroid frequency shift method is

[0149]

[0150] where and are the centroid frequencies of the source wavelet and the geophone wavelet respectively, and it can be seen from formula (7) that they are independent of frequency; is the centroid frequency of the geometric mean wavelet, is the variance of the geometric mean wavelet, and it can be seen from formula (8) that they are independent of frequency. Therefore, the factor estimation of the centroid frequency shift method in formula (9) is not affected by the frequency band, even for a single frequency. Therefore, the method of the present invention can be extended to fields where the wavelet is not assumed to be independent of frequency. Compared with the traditional CFS method, this method can be more widely applied to Q factor estimation.

[0151] Example 3

[0152] Figure 2 shows a schematic diagram of the simulated spectra of FWE with a slip bandwidth and the decaying wavelet at different starting frequencies according to an embodiment of the present invention.

[0153] Figure 3 shows a schematic diagram of the relative error of the traditional CFS according to an embodiment of the present invention.

[0154] Figure 4 shows a schematic diagram of the relative error according to an embodiment of the present invention.

[0155] To verify the effectiveness of the method, simple model data is used for accuracy and adaptability analysis. The model is based on the constant Q model, uses the FWE wavelet, the propagation time is 0.1 s, and the reference frequency is f 0 = 40 Hz, as Figure 2 shown. It can be seen that the traditional CFS method will be more inaccurate when the bandwidth increases, showing its frequency dependence, as Figure 3 shown. Regardless of how the bandwidth and the sliding frequency change, the accuracy of the method of the present invention can always keep the relative error below 1%, asFigure 4 As shown, these illustrate the wide applicability and accuracy of the present method.

[0156] Based on the FWE wavelet hypothesis, the present invention derives the centroid frequency equation for any frequency band by using the incomplete gamma function and proves its frequency independence based on the constant Q model. Then, the present invention analyzes the relative error of this method under any bandwidth and compares it with the traditional CFS method. Finally, a simple model data is used for accuracy and adaptability analysis to verify the wide applicability and accuracy of the method of the present invention.

[0157] Example 4

[0158] Figure 5 The block diagram of a frequency-independent centroid frequency shift Q-factor device according to an embodiment of the present invention is shown.

[0159] As Figure 5 shown, the frequency-independent centroid frequency shift Q-factor device includes:

[0160] A first calculation module 201 that calculates the centroid frequency of the source wavelet;

[0161] A second calculation module 202 that calculates the centroid frequency of the geometric mean wavelet and further calculates the variance of the geometric mean wavelet;

[0162] A third calculation module 203 that calculates a frequency-independent Q-factor based on the centroid frequency of the source wavelet, the centroid frequency of the geometric mean wavelet, and the variance.

[0163] As an alternative, calculating the centroid frequency of the source wavelet includes:

[0164] Extending the centroid frequency to any frequency band [a, b] and determining the recurrence relation of the incomplete gamma function;

[0165] Performing integral transformation and expansion derivation on the centroid frequency after recurrence to obtain the transformed centroid frequency;

[0166] Performing simplified calculation on the transformed centroid frequency to obtain the centroid frequency of the source wavelet.

[0167] As an alternative, the transformed centroid frequency is:

[0168]

[0169] where f 0 is the reference frequency.

[0170] As an alternative, the centroid frequency of the source wavelet is:

[0171]

[0172] Among them, f 0 is the reference frequency, the definition of n.

[0173] As an alternative, the centroid frequency of the geometric mean wavelet is:

[0174]

[0175] Among them,

[0176] As an alternative, the variance of the geometric mean wavelet is:

[0177]

[0178] As an alternative, the Q factor is:

[0179]

[0180] Among them, and are the centroid frequencies of the source wavelet and the detector point wavelet respectively, is the centroid frequency of the geometric mean wavelet, is the variance of the geometric mean wavelet, and Δt is the wavelet time sampling interval.

[0181] Example 5

[0182] The present disclosure provides an electronic device, which includes: a memory storing executable instructions; a processor that runs the executable instructions in the memory to implement the above frequency-independent centroid frequency shift Q factor method.

[0183] The electronic device according to an embodiment of the present disclosure includes a memory and a processor.

[0184] The memory is used to store non-temporary computer-readable instructions. Specifically, the memory may include one or more computer program products, and the computer program products may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory, etc. The non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc.

[0185] The processor may be a central processing unit (CPU) or other forms of processing units with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In an embodiment of the present disclosure, the processor is used to run the computer-readable instructions stored in the memory.

[0186] Those skilled in the art should understand that, in order to solve the technical problem of how to obtain a good user experience effect, this embodiment may also include well-known structures such as communication buses and interfaces, and these well-known structures should also be included in the protection scope of this disclosure.

[0187] For the detailed description of this embodiment, reference may be made to the corresponding descriptions in the foregoing embodiments, and details will not be repeated here.

[0188] Example 6

[0189] The embodiments of the present disclosure provide a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the frequency-independent centroid frequency shift Q-factor method described above is implemented.

[0190] According to the computer-readable storage medium of the embodiments of the present disclosure, non-transitory computer-readable instructions are stored thereon. When the non-transitory computer-readable instructions are run by a processor, all or part of the steps of the methods of the foregoing embodiments of the present disclosure are executed.

[0191] The above-mentioned computer-readable storage medium includes but is not limited to: optical storage media (such as CD-ROMs and DVDs), magneto-optical storage media (such as MOs), magnetic storage media (such as magnetic tapes or external hard drives), media with built-in rewritable non-volatile memories (such as memory cards), and media with built-in ROMs (such as ROM cartridges).

[0192] Those skilled in the art should understand that the purpose of the above description of the embodiments of the present invention is only to exemplarily illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any of the examples given.

[0193] The above has described the embodiments of the present invention. The above description is exemplary and not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A frequency-independent centroid frequency shift Q-factor method, characterized in that, it includes: Calculating the centroid frequency of the source wavelet; Calculating the centroid frequency of the geometric mean wavelet, and then calculating the variance of the geometric mean wavelet; Based on the centroid frequency of the source wavelet, the centroid frequency of the geometric mean wavelet, and the variance, calculating the frequency-independent Q-factor.

2. The frequency-independent centroid frequency shift Q-factor method according to claim 1, wherein, Calculating the centroid frequency of the source wavelet includes: Expanding the centroid frequency to an arbitrary frequency band [a, b], and determining the recurrence relation of the incomplete gamma function; Performing integral transformation and expansion derivation on the centroid frequency after recurrence to obtain the transformed centroid frequency; Performing simplified calculation on the transformed centroid frequency to obtain the centroid frequency of the source wavelet.

3. The frequency-independent centroid frequency shift Q-factor method according to claim 2, wherein, The transformed centroid frequency is: where f 0 is the reference frequency.

4. The frequency-independent centroid frequency shift Q-factor method according to claim 2, wherein, The centroid frequency of the source wavelet is: where f 0 is the reference frequency.

5. The frequency-independent centroid frequency shift Q-factor method according to claim 1, wherein, The centroid frequency of the geometric mean wavelet is: Among them, 6. The frequency-independent centroid frequency shift Q-factor method according to claim 5, wherein, The variance of the geometric mean wavelet is:

7. The frequency-independent centroid frequency shift Q-factor method according to claim 1, wherein, The Q-factor is: Among them, and are the centroid frequencies of the source wavelet and the detector point wavelet respectively, is the centroid frequency of the geometric mean wavelet, is the variance of the geometric mean wavelet, and Δt is the wavelet time sampling interval.

8. A frequency-independent centroid frequency shift Q-factor device, characterized in that, it includes: A first calculation module for calculating the centroid frequency of the source wavelet; A second calculation module for calculating the centroid frequency of the geometric mean wavelet and then calculating the variance of the geometric mean wavelet; A third calculation module for calculating the frequency-independent Q-factor based on the centroid frequency of the source wavelet, the centroid frequency of the geometric mean wavelet, and the variance.

9. An electronic device, characterized in that, the electronic device includes: A memory storing executable instructions; A processor that runs the executable instructions in the memory to implement the frequency-independent centroid frequency shift Q-factor method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the frequency-independent centroid frequency shift Q-factor method according to any one of claims 1-7.

Images