Optimal phase matching wave source estimation method based on head wave statistics and norm constraint

Abstract

The invention discloses an optimal phase matching wave source estimation method based on head wave statistics and norm constraint, and belongs to the field of signal processing. On the basis of statistical method wave source estimation, a Hilbert orthogonal component and a constant phase rotation mechanism are introduced to realize RMS energy retention type all-phase scanning wave source extraction, and the method specifically comprises the following steps: carrying out dynamic correction, first arrival alignment and interception on a fluctuation signal observation data set to obtain an initial time domain wave source under a minimum phase assumption; generating an adjoint component through Hilbert transformation, carrying out phase rotation at a step length of 1 degree, carrying out L2 norm energy maintenance after each rotation, and constructing a candidate wave source library with consistent energy; and keeping the amplitude of each candidate wave source consistent with the original wave source, then carrying out convolution with the measured reflection coefficient to generate a synthetic record, and carrying out cross-correlation analysis on the synthetic record and the actually measured signal record to determine the optimal phase and wave source. The method has the obvious advantages of keeping lower inversion residual error, better fitting of profile waveform and measurement data, higher inversion resolution and the like.

Description

Technical Field

[0001] This invention relates to the field of signal processing, and in particular to a source estimation method based on optimal phase matching with first-wave statistics and norm constraints. Background Technology

[0002] In signal processing, source extraction is a crucial prerequisite for impedance inversion and parameter prediction, and its accuracy directly affects the reliability and resolution of the inversion results. Existing source extraction methods can be broadly categorized into deterministic and statistical methods. Deterministic methods rely on well logging data to calculate reflection coefficient sequences and combine them with well-side signal channels to invert the source signal using convolution theory, such as least-squares Wiener filtering and spectral division. These methods do not require assumptions about the statistical characteristics of reflection coefficients and offer high accuracy, but they typically only utilize a single reference channel at a time and struggle to simultaneously fuse multi-channel information. Furthermore, they require high precision in time alignment between the observed and reference signals.

[0003] Statistical methods directly estimate the wave source based on signal data. The autocorrelation method and the spectral method rely on the assumptions that the wave source is time-invariant and that the reflection coefficient is a random sequence of white noise spectrum. The autocorrelation method directly approximates the wave source's autocorrelation by taking the signal channel's autocorrelation in the time domain, while the spectral method approximates the wave source's power spectrum by taking the signal channel's power spectrum in the spectrum. These methods, combined with phase assumptions, then reconstruct the time-domain wave source. This approach is highly adaptable, but its estimation results are prone to bias when the wave source exhibits mixed phase or the reflection coefficient spectrum deviates from the white noise distribution. Furthermore, the phase component still requires additional estimation or assumptions to determine.

[0004] Based on this, researchers have proposed several improvement approaches. For example, the statistical method mentioned above, which estimates the amplitude spectrum using only signal data, can be combined with minimum phase or constant phase assumptions to recover the waveform. This method is computationally simple but loses true phase information and is sensitive to phase assumptions. The full-source method uses signal data and reflection coefficient sequences to construct least-squares filtering equations and simultaneously inverts the amplitude and phase spectra. It has high accuracy but requires strict alignment of the two types of well-seismic data and is susceptible to noise. The constant-phase method introduces well data correction based on the amplitude spectrum of the statistical method. It determines the optimal phase by scanning different phase angles and calculating correlation indices, which can partially alleviate the phase distortion problem of the statistical method, but it has shortcomings in energy and amplitude consistency control. Another approach is to search for the optimal time shift by calculating the coherence between well data and signal data, and then estimate the frequency domain source. This method has good robustness, but it is also limited by alignment accuracy and data quality.

[0005] Among these methods, the constant-phase method provides the best phase estimation. However, this method generally relies on phase scanning to find the optimal match. Existing phase scanning methods often fail to rigorously normalize the energy of rotated candidate sources, and amplitude differences between different phases affect the comparison of cross-correlation coefficients, introducing bias into phase selection. Furthermore, the commonly used Hilbert transform rotation method suffers from boundary effects and energy drift in its discrete implementation, leading to unstable root-mean-square (RMS) energy. This reduces the robustness of phase matching in high-precision impedance retrieval and detailed characterization of complex reservoirs. Therefore, there is an urgent need for a full-phase scanning source extraction and optimization method that maintains constant RMS energy. This method should be able to ensure that phase matching is dominated solely by phase differences, without amplitude bias interference, based on statistical source estimation and through high-precision phase rotation and normalization. This would provide a more reliable input source for impedance retrieval in complex structural regions. Summary of the Invention

[0006] To address the technical problems of existing wave source extraction methods, such as insufficient accuracy under mixed phase conditions, unstable energy during phase scanning, and amplitude differences interfering with phase matching, this invention proposes an optimized scheme for full-phase scanning of wave sources while maintaining constant RMS energy.

[0007] The technical solution adopted in this invention is as follows:

[0008] A source estimation method based on optimal phase matching with first-wave statistics and norm constraints, comprising the following steps:

[0009] Step 1: Perform data preprocessing on the input fluctuation signal, including correction, denoising and alignment; then use sample-by-sample arithmetic average to extract the time-domain statistical wave source as the initial time-domain wave source under minimum phase.

[0010] Step 2, construct a full-phase phase rotation wave source library:

[0011] The initial time-domain wave source is subjected to Hilbert transform to obtain the adjoint component orthogonal to the initial time-domain wave source; the adjoint component and the initial time-domain wave source constitute the real part and imaginary part of the analytic signal.

[0012] Perform constant phase rotation according to the set rotation step value to obtain candidate wave sources at each phase angle, where the value range of the phase angle is [0°, 359°]; each candidate wave source at each phase angle retains the same time window length as the initial time domain wave source, and all candidate wave sources constitute a full-phase phase rotation wave source library;

[0013] To avoid amplitude distortion caused by different phase rotations, energy consistency constraint processing is performed on each candidate wave source, and then a full-phase phase rotation wave source library is generated based on the candidate wave sources after energy consistency constraint processing.

[0014] This step ensures that phase rotation only changes the phase characteristics of the wave source without introducing amplitude or energy bias, thus making subsequent comparisons fairer;

[0015] Step 3: Based on the measured signal record (i.e., measured signal data), the corresponding reflection coefficients are inverted to obtain the reflection coefficient sequence; then, each candidate wave source is convolved with the reflection coefficient at the corresponding position in the reflection coefficient sequence to generate the corresponding synthetic signal record.

[0016] Step 4: Source estimation based on cross-correlation analysis and optimal phase matching;

[0017] Cross-correlation analysis is performed on the synthetic signal records generated by different candidate wave sources and the actual signal records. The phase angle corresponding to the maximum cross-correlation coefficient is the optimal phase; and the time shift during alignment processing corresponding to the maximum cross-correlation coefficient is the optimal time shift, that is, the time delay for optimal alignment is determined by the time shift.

[0018] The optimal waveform parameters of the target signal are obtained and output based on the optimal phase and optimal time shift, which can be used for target signal generation in the target scene.

[0019] Furthermore, in step 1, the alignment in the preprocessing refers to channel alignment, which specifically includes:

[0020] The time offset of each channel is calculated based on the first wave time or the target characteristic event time of the wave signal of each channel (one channel corresponds to one detection depth), and the time offset is converted into the number of sampling points.

[0021] An interpolation alignment method is adopted to align each wave signal according to the time offset, and the gaps at the beginning or end of the alignment are filled to unify the signal length. This achieves the purpose of time correction of all signal channels with a unified reference time as the benchmark, and finally obtains a unified alignment result of all signal channels on the time axis, providing a reliable input for subsequent wave source interception and averaging.

[0022] Furthermore, during channel alignment, the fluctuating signals of each channel are shifted one by one based on the time series consistent with the sampling interval of the fluctuating signals: when the time offset is an integer multiple of the sampling points, the whole-point shift is used; when the time offset is not an integer multiple, the waveform continuity is maintained by resampling on the new time axis through cubic spline interpolation.

[0023] Furthermore, when filling the gaps at the front or rear ends after alignment, zero values ​​or constant values ​​at the end of the track are used for filling.

[0024] Furthermore, in step 1, the time-domain statistical wave sources are extracted, including:

[0025] Based on the preset wave source time window length parameter, a corresponding time period is extracted from each signal channel to obtain a channel segment for each signal channel (each channel segment has the same signal length); this time window covers the main energy range of the wave source while avoiding subsequent wave train and noise interference. By using a uniform extraction length, the consistency of wave source samples on different channels in the time dimension is ensured, thereby avoiding the introduction of non-consistent waveform components during the averaging process;

[0026] The sample-by-sample arithmetic mean of all the extracted segments is taken, and the time-domain statistical wave source is obtained based on the sample-by-sample arithmetic mean result, that is, the initial time-domain wave source under the minimum phase.

[0027] The arithmetic averaging operation effectively suppresses uncorrelated noise between channels while highlighting stable source morphology. The resulting arithmetic average is the time-domain statistical source used in this invention. It does not rely on the white noise assumption of the reflection coefficient and does not require autocorrelation calculation in the spectral domain, directly reflecting the source characteristics in the measured wave signal data. This source, as the initial input for subsequent full-phase scanning, has higher stability and practicality.

[0028] Furthermore, in step 2, the energy consistency constraint processing includes:

[0029] The DC component is removed and the signal is bandpass filtered to a frequency range consistent with the measured signal recording. Then, L2 norm energy normalization is performed to ensure that the L2 energy of the candidate wave source obtained after rotation is consistent with the initial time-domain wave source.

[0030] Furthermore, in step 2, the rotation step value is set to 1 degree.

[0031] Furthermore, step 3 includes:

[0032] Based on the measured signal records, velocity and density curves are calculated, and the reflection coefficients of the interfaces corresponding to each signal channel are deduced. The reflection coefficients are arranged sequentially according to the time sampling points to construct a reflection coefficient convolution matrix. This reflection coefficient convolution matrix can realize the convolution operation between the wave source and the formation reflection coefficients. Each column of the reflection coefficient convolution matrix corresponds to a delayed reflection coefficient sequence, thus ensuring that the composite signal recording matrix can be generated by multiplying the input wave source matrix composed of candidate wave sources with the reflection coefficient matrix.

[0033] Candidate wave sources from the phase-rotated wave source library of all phases are sequentially input into the reflection coefficient convolution matrix to calculate the synthetic signal record at each phase angle; the number of sampling points of the synthetic signal record is consistent with that of the measured signal record to achieve point-by-point comparison;

[0034] Each synthetic signal record is subjected to amplitude normalization processing, and its maximum amplitude is adjusted to be consistent with the maximum amplitude of the measured signal record. This processing can eliminate the overall energy deviation caused by the difference in wave source amplitude or the difference in reflection coefficient, and ensure that the synthetic signal record and the measured signal record are comparable in amplitude.

[0035] Furthermore, in step 4, the cross-correlation analysis is performed by cross-correlation calculation between each synthetic signal record and the target channel of the measured signal record. The resulting cross-correlation curve reflects the similarity between the synthetic signal record and the measured signal record under different time delays.

[0036] Furthermore, in step 4, the optimal time shift is: the ratio of the optimal phase to 360° multiplied by the center period of the wave signal.

[0037] The technical solution provided by this invention brings at least the following beneficial effects:

[0038] This invention provides a wave source estimation method based on optimal phase matching using first-wave statistics and norm constraints. Addressing the problems of insufficient phase estimation accuracy and unstable energy normalization control in existing statistical wave source extraction methods, this invention proposes a statistical wave source extraction scheme based on full-phase scanning and RMS energy preservation. This scheme, building upon wave signal data preprocessing and statistical wave source extraction, introduces a full-phase wave source library generated by Hilbert transform and achieves optimal phase selection through energy consistency constraints and cross-correlation analysis, thereby improving the accuracy and robustness of wave source extraction. Comparative experiments and analysis demonstrate the following significant advantages of this method:

[0039] (1) Construction and optimal extraction of full-phase statistical wave sources

[0040] This invention constructs a candidate source library directly in the time domain based on statistical sources obtained by averaging wave signal data. It then achieves full phase coverage from 0° to 360° through Hilbert transform, enabling a global search for source phase information. By convolving candidate sources with reflection coefficients to generate synthetic signal records, and performing cross-correlation analysis with measured wave signal records, the optimal phase source is automatically selected. This approach balances waveform matching and energy consistency, effectively avoiding local extrema and noise interference, and overcomes the reliance of traditional methods on minimum or zero-phase assumptions.

[0041] (2) High robustness of L2 scaling to preserve energy and scale according to the original source amplitude

[0042] During the full-phase rotation process, the L2 norm energy preservation constraint is introduced to ensure that the energy of wave sources in different phases is consistent. Then, the original scale is introduced to ensure that the maximum amplitude is close to the original wave source, which is beneficial to subsequent inversion. This makes the cross-correlation analysis results only affected by the phase difference, which greatly improves the accuracy of phase estimation and the reliability of wave source selection.

[0043] (3) Application value of inversion and reservoir prediction

[0044] The wave source extracted by this invention exhibits higher phase accuracy and amplitude stability, providing a more reliable input wave source for impedance retrieval and fine description of complex reservoirs. This method not only improves the resolution and reliability of the inversion results but also provides a robust data foundation for subsequent analyses (such as well-seismic combined analysis). Compared with wave sources extracted by traditional statistical methods, the wave source extracted by the method of this invention shows a better matching effect in the impedance retrieval process. Comparative experimental results show that this invention has significant advantages in maintaining lower inversion residuals, better fitting of profile waveforms with well logging data, and higher inversion resolution, thus further demonstrating the application value of this method in the prediction and fine description of complex reservoirs. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a schematic diagram of the processing procedure of the method in an embodiment of the present invention;

[0047] Figure 2 The images show a comparison before and after wave signal gather alignment, where 2a is the signal record gather before wave signal gather alignment and 2b is the signal record gather after wave signal gather alignment.

[0048] Figure 3 Waveform diagram of zero-phase wave source;

[0049] Figure 4 A schematic diagram of the Hilbert transform;

[0050] Figure 5 A schematic diagram of a disk-type phase rotation (60° interval);

[0051] Figure 6 A comparison of waveforms before and after L2 norm energy normalization;

[0052] Figure 7 This is a distribution diagram of the reflection coefficient;

[0053] Figure 8 The diagram shows the waveform of the wave source. In the diagram, 8a is the waveform of the wave source corresponding to the maximum correlation coefficient, and 8b is a comparison diagram of the optimal wave source and the original wave source.

[0054] Figure 9A comparison of the synthetic signal record and wave signal record, and the residuals, when the zero-phase wave source is used for estimation.

[0055] Figure 10 The image shows a comparison of the synthetic signal record and the wave signal record, along with the residuals, when the wave source corresponding to the maximum correlation coefficient is used as the estimate. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be described in detail and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Generally, the components of the embodiments of the present invention described and shown in the accompanying drawings can be arranged and designed using different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of the present invention.

[0057] This invention proposes a wave source estimation method based on first-wave statistics and norm constraints with optimal phase matching. It extends the traditional statistical wave source estimation method by introducing a high-precision phase rotation and energy normalization mechanism, constructing a complete RMS energy-preserving full-phase scanning wave source extraction system. The method first truncates and aligns the wave signal recording channels according to the required length. The time-domain wave source is obtained by averaging the aligned channel sets, yielding the initial time-domain wave source under the minimum phase assumption. Then, a Hilbert transform is used to generate an adjoint component orthogonal to this wave source, and orthogonalization and amplitude normalization are used to ensure energy consistency between the two components. Based on this, a phase rotation of 0° to 359° is performed in 1° steps. The wave source set obtained after each rotation is called the candidate wave source set. After each rotation, an L2 norm energy preservation operation is performed to ensure that the energy of wave sources with different phases remains constant.

[0058] After generating a set of candidate wave sources, each candidate wave source is convolved with the reflection coefficient sequence calculated from well logging data to generate a corresponding synthetic signal record. By calculating the maximum cross-correlation coefficient between the synthetic signal record and the measured signal record, the wave source corresponding to the optimal phase is determined. This invention can be used for high-precision wave sources in well-seismic combined analysis, deconvolution, or wave impedance inversion.

[0059] Numerical experiments show that the method of the present invention can effectively maintain the RMS energy consistency of candidate wave sources with different phases, significantly improve the stability and accuracy of phase matching, and reduce the interference of amplitude differences on correlation. Under complex structural regions and mixed phase conditions, it can provide more reliable wave source input for wave impedance inversion and fine reservoir description.

[0060] like Figure 1As shown, in one embodiment, taking vertical seismic profile (VSP) data as the processed wave signal data as an example, the specific implementation steps of the wave source estimation of the present invention are described, which specifically include the following steps:

[0061] (1) Preprocessing of wave signal data and statistical method for wave source extraction to obtain the initial time-domain wave source under the minimum phase assumption;

[0062] (1a) Signal channel alignment

[0063] First, convert the time offset into the number of sampling points, according to the following formula:

[0064]

[0065] in, For the first Time offset of the channel This serves as the global reference time, or alignment base. The sampling interval is... The number represents the number of integer sample point movements.

[0066] Secondly, an interpolation alignment method is used to align each data point according to the offset. The interpolation principle is as follows:

[0067]

[0068] in, This represents the output result of the interpolation alignment, i.e., the aligned signal trace matrix; This represents the interpolation alignment function. Indicates the sampling time.

[0069] And for When the sampling interval is not an integer multiple, cubic spline interpolation is used to ensure smooth processing even for non-integer sampling shifts. The core objective is to construct a smooth curve passing through all given data points using a piecewise cubic polynomial, ensuring continuity of the function values, first and second derivatives. Each curve segment (interval) Represented as:

[0070]

[0071] The condition for the above formula is: parameters = ,parameter , and The following constraints must be satisfied: the function values, first-order and second-order derivatives of adjacent segments are equal at the connection point, and the boundary condition that the second-order derivative is zero must be satisfied. The dependent variable represents the cubic spline interpolation, i.e., the cubic spline interpolation output; Then, this corresponds to the independent variable. The solution is obtained by establishing a system of tridiagonal equations and solving for the second derivative. The remaining coefficients are from Export:

[0072]

[0073] Finally, the portion outside the boundary is filled with 0, and the filling principle is as follows:

[0074]

[0075] Obtain the aligned signal trace matrix .like Figure 2 The image shows a comparison before and after the alignment of the wave signal gathers. It can be seen that after alignment, the starting points of the records from different signal gathers were corrected to the same time.

[0076] (1b) Wave source length interception

[0077] After alignment is completed, a time window segment covering the main energy of the wave source needs to be extracted from each signal record. In this embodiment, the sampling interval is first determined... With the set time window length (unit ), calculate the number of sample points required for interception:

[0078]

[0079] in, This indicates the length of the sampling points corresponding to the wave source time window. This refers to the signal data sampling interval. This represents the rounding function.

[0080] Subsequently, in each aligned signal channel, starting from the position of the unified reference time, a length of [length missing] is extracted. The time period is defined. If some channels are insufficient to cover all samples within the intercepted range, zeros are padded at the end to maintain a consistent length for all intercepted segments. This uniform interception method ensures the consistency of different channel sources in the time dimension, thereby avoiding waveform misalignment or inconsistent components during subsequent averaging.

[0081] (1c) Time-domain source extraction

[0082] After obtaining uniformly aligned and equally truncated channel segments, this embodiment uses a sample-by-sample arithmetic averaging method to extract the wave source. Specifically:

[0083]

[0084] in, The extracted wave source sequence, Indicates the first The path is used to capture sample values ​​within the window. The number of signal channels involved in the calculation.

[0085] The extracted wave sources are directly derived from measured wave signal data, without relying on the white noise assumption of the reflection coefficient commonly found in traditional statistical wave source extraction methods, nor requiring the use of spectral domain autocorrelation calculations. However, it should be noted that this method assumes the aligned wave sources have consistent phase (usually close to zero phase or already phase-corrected). Under this condition, arithmetic averaging can effectively suppress noise and highlight stable wave source morphology. The resulting statistical wave sources are superior in stability and practicality, and can serve as initial inputs for subsequent phase rotation and RMS energy preservation processing, thereby further optimizing the wave source phase characteristics and laying a reliable foundation for the generation of synthetic signal records and cross-correlation analysis. Figure 3 The image shows the waveform of the time-domain source extracted according to the above steps, based on the zero-phase assumption, i.e., the initial time-domain source.

[0086] (2) Construction of a full-phase source library and energy constraints to obtain candidate sources at different phase angles;

[0087] Based on the time-domain wave sources obtained by the initial statistical method in step (1), this embodiment proposes a wave source construction method based on full-phase rotation and energy preservation to further optimize their phase characteristics. This method generates orthogonal components through Hilbert transform and performs constant-phase rotation within the range of 0°-359° to form a candidate wave source library; at the same time, L2 norm energy normalization is introduced to ensure the energy consistency between wave sources with different phases, providing reliable input for subsequent synthetic signal recording fitting and cross-correlation analysis.

[0088] (2a) Hilbert Transform and Phase Rotation

[0089] In the embodiment, the time-domain statistical wave source obtained in step (1) is first analyzed. Applying the Hilbert transform, we obtain the adjoint component orthogonal to it:

[0090]

[0091] in, This represents the Hilbert transform operation. and The real and imaginary parts constitute the analytic signal. Based on this, the constant phase rotation formula is used:

[0092]

[0093] This can generate 360 ​​candidate wave sources with different phases, among which, Indicates the rotation angle Candidate wave sources with lower (i.e., phase angle). For example... Figure 4 The image shows a comparison between the initial wave source and the wave source after Hilbert transformation.

[0094] Each wave source at each rotation angle retains the same time window length as the original wave source, thus forming a complete phase-rotated wave source library. For example... Figure 5 The diagram shows a disk-type phase rotation (60° interval). It can be seen that this method can generate a wave source covering a full range of phases based on the initial wave source.

[0095] (2b) Energy consistency constraints and amplitude normalization

[0096] After generating 360 candidate wave sources with different phases, without additional processing, the energy levels of each source may differ due to Hilbert transform and rotation operations, leading to amplitude distortion. This difference will directly affect the subsequent comparison results with measured signal data, and may even cause deviations in the selection of the optimal phase. Therefore, this embodiment introduces an L2 norm energy preservation constraint to ensure that all candidate wave sources are consistent with the original statistical wave sources in terms of energy scale.

[0097] The specific process is as follows: First, calculate the L2 norm energy of the wave source obtained from each rotation:

[0098]

[0099] Simultaneously calculate the energy of the original statistical wave source:

[0100]

[0101] like Figure 6 The image shows a comparison of several typical phase sources before and after L2 norm energy normalization. It can be seen that only the source amplitude value changed before and after normalization, while the source waveform remained unchanged.

[0102] Finally, amplitude scaling is applied to the candidate wave sources:

[0103]

[0104] in, These are the candidate sources after amplitude preservation. Through the above steps, the candidate sources obtained at each phase angle have the same L2 norm energy level as the original statistical source, differing only in phase characteristics. This effectively eliminates interference introduced by amplitude or energy inconsistencies, ensuring that subsequent synthetic signal recording fitting and cross-correlation analysis only reflect differences in phase matching, thereby guaranteeing the objectivity and reliability of optimal phase selection.

[0105] (3) Synthetic signal recording generation

[0106] After completing step (2) phase rotation and L2 norm energy preservation, this embodiment further generates a synthetic signal record comparable to the measured wave signal record based on the velocity profile and reflection coefficient sequence obtained from the inversion of in-well acoustic logging data and density logging data. This step mainly includes the following three sub-steps:

[0107] (3a) Construction of convolution matrix

[0108] First, based on the measured signal data (well logging data in this embodiment), the reflection coefficient sequence of each interface is calculated. The sampled reflection coefficient sequence is obtained while maintaining consistency with the signal recording and wave source sampling rates. That is, in this embodiment, the well logging data and VSP data sampling rates are kept consistent, and the reflection coefficient sequence is obtained after sampling the well logging data.

[0109] Secondly, to achieve linear convolution between the wave source and the reflection coefficients, the reflection coefficient sequence is extended into a convolution matrix form: each column of the convolution matrix corresponds to a time-delayed version of the reflection coefficient sequence; when different candidate wave sources are input, point-by-point convolution with the reflection coefficients can be achieved through matrix multiplication. This construction method avoids repetitive point-by-point sliding multiplication and ensures that the output results match the actual reflection effect of the formation. Figure 7 The diagram shows the distribution of the reflection coefficient sequence. Observation shows that the reflection coefficient approximately follows a random distribution with zero mean and finite variance, but it deviates from the characteristics of ideal white noise. Therefore, in the statistical method section of step (1), the autocorrelation method or the spectrum method under the zero-phase assumption, which both rely on the white noise distribution assumption of the reflection coefficient, were not used. Instead, the method of averaging after alignment was selected to minimize the error.

[0110] Reflection coefficient matrix The specific form is as follows:

[0111]

[0112] Where n represents the stratum number and m represents the sampling point index of each stratum, i.e., the time index.

[0113] (3b) Synthetic signal recording generation

[0114] Based on the constructed convolution matrix, the 360 ​​candidate phase sources obtained in step (2) are input one by one:

[0115]

[0116] in, Represents the convolution matrix of reflection coefficients. This indicates that a candidate wave source with RMS energy preservation has been identified. This is a synthetic signal record under corresponding phase conditions. The generated synthetic signal record maintains consistency with the measured fluctuation signal data in terms of sampling rate and channel length, thus enabling point-by-point comparison and correlation analysis.

[0117] (3c) Amplitude normalization

[0118] Considering that different wave sources or reflection coefficients may introduce overall energy deviations, in order to ensure that the synthesized signal recording and the measured signal recording are comparable in amplitude, this embodiment performs amplitude normalization processing on the synthesized signal recording:

[0119]

[0120] in, This represents the maximum amplitude of the measured wave signal record. This processing ensures that the overall amplitude scale of the synthesized signal record is consistent with that of the measured signal record, eliminating energy distortion caused by differences in wave source amplitude or variations in formation reflection coefficients.

[0121] (4) Cross-correlation analysis between synthetic signal recordings and measured signal recordings to select the optimal phase and time shift;

[0122] After obtaining the synthesized signal records under different phase angle conditions in step (3), this embodiment determines the optimal phase source through cross-correlation analysis. This step mainly includes the following three sub-parts:

[0123] (4a) Cross-correlation calculation

[0124] First, the measured waveform of the fluctuation signal within the well depth range of 0-4445m is selected as the target trace. For each candidate phase angle (set to 0° to +359° in this embodiment, with a step size of 1°, for a total of 360), the corresponding synthetic signal record is cross-correlated with the target trace. The cross-correlation function calculation formula is as follows:

[0125]

[0126] in, For recording synthetic signals, (t) represents the measured signal record. The time delay is represented by an instantaneous shift. The output cross-correlation curve depicts the similarity between the two under different time delays.

[0127] (4b) Determination of optimal phase and time shift

[0128] For each phase angle, extract the maximum value of the cross-correlation curve and its corresponding time delay. Maximum cross-correlation number. Characterizes the matching degree between the synthesized signal record and the measured signal record; the corresponding time delay. This indicates the time shift that the two need to be aligned.

[0129] For example, in a test of a certain well section, the phase angle obtained was +340°. =0.285, time shift ,Right now The zero-phase wave source obtained in step (1) is combined with... Figure 3 And the center period of the wave source with a sampling rate of 2ms Approximately 20ms, therefore corresponding time shift It is 18.89ms. All candidate phases... The values ​​are compared, and the phase angle corresponding to the largest value is selected as the "optimal phase".

[0130] (4c) Optimal Wave Source Selection

[0131] After determining the optimal phase angle, the corresponding candidate wave sources are extracted as the final statistically optimal wave source.

[0132] Then time delay compensation was performed on the wave source (i.e., according to...). (Alignment), and resynthesized signal records, the results show that the matching coefficient of the wave source in the target well section reaches 0.285, and the optimal wave source is as follows: Figure 8 As shown in 8a, Figure 8 Figure 8b visually illustrates the phase difference between the initial wave source and the optimal wave source.

[0133] In existing inversion models, impedance inversion is performed by inputting both a zero-phase wave source and an optimal wave source, demonstrating that using the optimal wave source as the estimated source yields better results than using the zero-phase wave source. For example... Figure 9 The image shows a comparison of the synthetic signal record and the wave signal record, along with the residuals, obtained when the zero-phase wave source is used for estimation. Figure 10 The figure shows a comparison of the synthetic signal record and the wave signal record when the optimal phase wave source is used for estimation, as well as the residual. It can be seen that the residual of the latter is significantly reduced, which indicates that the wave source obtained by this method has a very effective improvement effect on the inversion effect. The reduction of the residual indicates the improvement of the inversion accuracy.

[0134] This invention proposes an optimization scheme for full-phase scanning of wave sources that maintains constant L2 norm energy under mixed-phase conditions. Based on statistical source estimation, it introduces Hilbert orthogonal components and a constant-phase rotation mechanism to establish an RMS energy-preserving full-phase scanning source extraction process. Specifically, it includes: performing dynamic correction, first-arrival alignment, and truncation on the wave signal observation gather to obtain the initial time-domain wave source under the minimum phase assumption; generating the adjoint component through Hilbert transform and performing phase rotation from 0° to 359° with a step size of 1°, implementing L2 norm energy preservation after each rotation to construct a candidate source library with consistent energy; subsequently, keeping the amplitude of each candidate source consistent with the original source, convolving it with the well logging reflection coefficient to generate a synthetic signal record, and performing cross-correlation analysis with the measured wave signal record to determine the optimal phase and the corresponding wave source.

[0135] The method of this invention can effectively eliminate the interference of amplitude differences on correlation during phase scanning, significantly improving the stability and accuracy of phase matching. Numerical experiments show that this invention can stably extract the optimal wave source that highly matches the measured data in complex structural regions and mixed phase conditions, providing reliable waveform input for well-seismic integration, deconvolution, and wave impedance inversion, and has significant application value.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0137] The above descriptions are merely some embodiments of the present invention. For those skilled in the art, various modifications and improvements can be made without departing from the inventive concept of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints, characterized in that, Includes the following steps: Step 1: Perform data preprocessing on the input fluctuation signal, including correction, denoising and alignment; then use sample-by-sample arithmetic average to extract the time-domain statistical wave source as the initial time-domain wave source under minimum phase. Step 2, construct a full-phase phase rotation wave source library: The Hilbert transform is applied to the acquired initial time-domain wave source to obtain the adjoint component orthogonal to the initial time-domain wave source; the adjoint component and the initial time-domain wave source constitute the real part and imaginary part of the analytic signal. Perform constant phase rotation according to the set rotation step value to obtain candidate wave sources at each phase angle, where the value range of the phase angle is [0°, 359°]; each candidate wave source at each phase angle retains the same time window length as the initial time domain wave source, and all candidate wave sources constitute a full-phase phase rotation wave source library; Energy consistency constraint processing is performed on each candidate wave source, and then a full-phase phase rotation wave source library is generated based on the candidate wave sources after energy consistency constraint processing; Step 3: Based on the measured signal record, the corresponding reflection coefficients are inverted to obtain the reflection coefficient sequence; then, each candidate wave source is convolved with the reflection coefficient at the corresponding position in the reflection coefficient sequence to generate the corresponding synthetic signal record. Step 4: Source estimation based on cross-correlation analysis and optimal phase matching; Cross-correlation analysis is performed on the synthetic signal records generated by different candidate wave sources and the actual signal records. The phase angle corresponding to the maximum cross-correlation coefficient is the optimal phase; and the time shift during alignment processing corresponding to the maximum cross-correlation coefficient is the optimal time shift. The optimal waveform parameters of the target signal are obtained and output based on the optimal phase and the optimal time shift.

2. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 1, characterized in that, In step 1, the alignment in preprocessing refers to channel alignment, which specifically includes: The time offset of each channel is calculated based on the first wave time or the target characteristic event time of the fluctuating signal of each channel, and the time offset is converted into the number of sampling points. Interpolation alignment is used to align each fluctuation signal according to the time offset, and the gaps at the beginning or end of the alignment are filled to unify the signal length.

3. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 2, characterized in that, In step 1, during channel alignment, the fluctuating signals of each channel are shifted one by one based on the time series that is consistent with the sampling interval of the fluctuating signals: when the time offset is an integer multiple of the sampling points, the whole-point shift is used; when the time offset is not an integer multiple, the signals are resampled on the new time axis by cubic spline interpolation.

4. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 2 or 3, characterized in that, In step 1, when filling the gaps at the front or rear ends after alignment, zero values ​​or constant values ​​at the end of the track are used for filling.

5. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 1, characterized in that, In step 1, the time-domain statistical sources are extracted, including: Based on the preset wave source time window length parameter, the corresponding time period is extracted from each signal channel to obtain the channel segment of each signal channel; wherein, the signal length of each channel segment is the same; The time-domain statistical wave source is obtained by taking the arithmetic mean of all the extracted segments.

6. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 1, characterized in that, Step 2, the energy consistency constraint processing includes: The DC component is removed and the signal is bandpass filtered to a frequency range consistent with the measured signal recording. Then, L2 norm energy normalization is performed to make the L2 energy of the candidate wave source consistent with that of the initial time-domain wave source.

7. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 1, characterized in that, In step 2, the rotation step value is set to 1 degree.

8. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 1, characterized in that, Step 3 includes: The velocity curve and density curve are calculated based on the measured signal records, and the reflection coefficient of the interface corresponding to each signal channel is deduced. The reflection coefficients are arranged in order according to the time sampling points, where each column of the reflection coefficient convolution matrix corresponds to a delayed reflection coefficient sequence. Candidate wave sources from the phase-rotated wave source library of all phases are sequentially input into the reflection coefficient convolution matrix to calculate the synthetic signal record at each phase angle; wherein, the number of sampling points of the synthetic signal record is consistent with that of the measured signal record; Each synthetic signal record is subjected to amplitude normalization processing to adjust its maximum amplitude to match the maximum amplitude of the measured signal record.

9. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 1, characterized in that, In step 4, the cross-correlation analysis is performed by cross-correlation calculation between each synthetic signal record and the target channel of the measured signal record.

10. The wave source estimation method based on optimal phase matching with first-wave statistics and norm constraints as described in claim 1, characterized in that, In step 4, the optimal time shift is: the ratio of the optimal phase to 360° multiplied by the center period of the wave signal.

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