Micro-seismic positioning confidence ellipsoid construction method based on station residual error and signal-to-noise ratio weighting

Abstract

A micro-seismic positioning confidence ellipsoid construction method based on station residual error and signal-to-noise ratio weighting comprises the following steps: acquiring P-wave arrival time data of a plurality of stations arranged in a monitoring area to obtain an observation data set containing the stations; building an event model parameter vector under the condition of a given speed model, calculating the theoretical arrival time of each station, and solving an event positioning result; for the micro-seismic waveform of the station, calculating a signal-to-noise ratio and a signal-to-noise ratio normalization index based on characteristic amplitudes in a P-wave effective signal window and a background noise window; constructing a diagonal weight matrix reflecting the signal quality of all stations by taking a signal-to-noise ratio normalization index as the weight of the stations; constructing a sensitivity matrix at a final event positioning result; solving a covariance matrix by adopting a weighting normal equation; and extracting a sub-matrix of a corresponding position parameter from the covariance matrix, and constructing an event positioning confidence ellipsoid by performing eigenvalue decomposition on the sub-matrix and combining a chi-square distribution threshold value under a preset confidence level. The method can significantly improve the construction precision of the confidence ellipsoid.

Description

Technical Field

[0001] This invention belongs to the technical field of microseismic monitoring technology and location evaluation, specifically involving a method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting. Background Technology

[0002] In mining operations, the use of multiple microseismic monitoring stations to collect waveform signals generated by microseismic events, and the analysis of the P-wave arrival times of each station to invert the spatial location and occurrence time of the event, is a commonly used monitoring and early warning method. Existing microseismic location technology typically includes two parts: (1) using P-wave arrival time data from multiple stations to locate the event and solve for the spatial location and occurrence time of the event; (2) calculating the covariance matrix of the event location parameters based on the location residuals, and constructing a corresponding confidence ellipsoid to describe the location uncertainty. In most engineering applications, the event location process usually adopts the unweighted least squares method, assuming that the observations from each station have the same accuracy and reliability; in the covariance and confidence ellipsoid calculation process, it is also often assumed that all stations contribute equally to the error statistics. However, in actual microseismic monitoring, different stations exhibit differences in sensor performance, installation conditions, noise environment, and geological structure. Some stations are significantly affected by noise interference, resulting in P-wave pickup errors that are considerably higher than other stations. Some stations experience long-term recording quality deviations due to site conditions or instrument status. Furthermore, there are individual instances of abnormal travel time pickup that have not been completely eliminated. If the residuals of all stations are used indiscriminately in the confidence ellipsoid calculation, it can easily lead to a significant increase in the overall residual variance estimation by a few stations with high residuals and low signal-to-noise ratios. This, in turn, amplifies the major axis length of the confidence ellipsoid through the covariance matrix, resulting in an oversized error ellipsoid or even abnormally elongated ellipsoid in certain directions, which is detrimental to accurately reflecting the location error of the event.

[0003] On the other hand, in practical engineering, well-established microseismic location algorithms are often not suitable for modification. Many systems have already conducted long-term comparisons and calibrations of existing location results. If the solution process is modified to introduce station weights, it may affect the comparability with historical data and the continuity of regulatory requirements.

[0004] Therefore, in order to consider the differences in station data quality only in the error assessment and confidence ellipsoid construction stages without changing the microseismic event location results, and to introduce station weights through "post-processing" to suppress the amplification effect of problematic stations on the error ellipsoid, it is urgent to provide a microseismic location confidence ellipsoid construction method based on station residuals and signal-to-noise ratio weighting. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting. This method is simple to implement, has low implementation cost, and can significantly improve the construction accuracy of the confidence ellipsoid. It can effectively solve the problems of existing technologies that fail to distinguish station data quality during the confidence ellipsoid construction stage and are easily affected by individual stations, leading to abnormal amplification of the error ellipsoid. This can provide a more accurate basis for subsequent engineering decisions.

[0006] To achieve the above objectives, the present invention provides a method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting, comprising the following steps; Step 1: Data Acquisition and Preprocessing; P-wave arrival time data were collected from multiple microseismic monitoring stations deployed in the monitoring area, resulting in data including... Observational datasets from individual stations And perform preprocessing; Step 2: Solving for the location of microseismic events; Given a velocity model, construct the event model parameter vector. And calculate the theoretical arrival time of each station. The event localization results are obtained using unweighted least squares method or existing engineering localization algorithms. ; Step 3: Calculate the signal-to-noise ratio of each station and normalize it; For the The microseismic waveforms of each station are based on the characteristic amplitudes within the effective signal window of the P-wave. Characteristic amplitude within the background noise window Calculate the signal-to-noise ratio And calculate the first Normalized signal-to-noise ratio of individual stations ; Step 4: Construct a diagonal weight matrix reflecting signal quality based on the signal-to-noise ratio of each station; Using signal-to-noise ratio normalization index As the first The weight of individual stations Construct a diagonal weight matrix that reflects the signal quality of all stations. ; Step 5: Calculate the position covariance matrix and confidence ellipsoid based on the diagonal weight matrix that reflects signal quality; Final location of the incident Constructing a sensitivity matrix Based on a diagonal weight matrix that reflects the signal quality of all stations. The covariance matrix is ​​solved using the weighted method equation. From the covariance matrix Extract the corresponding position parameters )of submatrix By pairing submatrices Eigenvalue decomposition is performed and combined with a pre-set chi-square distribution threshold to construct an event location ellipsoid.

[0007] Furthermore, in order to achieve accurate and efficient microseismic location based on the observation data, in step one, the event model parameter vector is constructed according to formula (1). The theoretical arrival time of each station is calculated based on ray tracing or travel time tables. ,in, The event location result is obtained according to formula (2). ; (1); In the formula, Let these be the spatial coordinates of the microseismic event in the coordinate system. The moment the earthquake struck; (2).

[0008] Furthermore, in order to make the quality assessment process among various stations more fair and intuitive, in step three, the first step is calculated according to formula (3). Signal-to-noise ratio of individual stations Calculate the first according to formula (4) Normalized signal-to-noise ratio of individual stations ; (3); (4); In the formula, ; It is the maximum signal-to-noise ratio among all stations.

[0009] Furthermore, in order to achieve accurate quantification of station contributions and effective improvement of positioning accuracy, in step four, a diagonal weight matrix reflecting the signal quality of all stations is constructed according to formula (5). ; (5); In the formula, .

[0010] Furthermore, in order to more accurately quantify the statistical uncertainty of the positioning parameters based on the diagonal weight matrix, in step five, the covariance matrix is ​​obtained according to formula (6). ; (6); In the formula, For weighted residual variance estimation, , , To achieve the final localization results The linearized residual fit at the point, The minimum number of stations required to locate an event.

[0011] Furthermore, in order to improve the stability and anti-interference capability of the signal-to-noise ratio calculation, in step three, the characteristic amplitude within the effective signal window of the P-wave is... Characteristic amplitude within the background noise window The process of obtaining it is as follows: Starting from the P-wave arrival time marker, the absolute value of the first peak or trough on the timeline is denoted as... The absolute value of the first peak or trough in the timeline forward is denoted as The absolute value of the maximum peak value in the d1 interval forward of the timeline is denoted as The absolute value of the maximum peak value in the time interval d1 forward is denoted as The characteristic amplitude within the effective signal window of the P-wave is calculated according to formula (7). The characteristic amplitude within the P-wave background noise window is calculated according to formula (8). ; (7); (8).

[0012] As a preferred approach, the preprocessing in step one is as follows: first, the observation data is quality checked, and then obviously abnormal data is removed.

[0013] This invention discloses a method for characterizing the uncertainty of microseismic event location, which introduces station weights only in the confidence ellipsoid construction stage after the microseismic event location, without changing the event location result. First, by collecting P-wave arrival time data from multiple stations, comprehensive data coverage is ensured, providing a reliable input basis for subsequent location. Second, unweighted least squares or engineering algorithms are employed, offering high computational efficiency and suitability for real-time processing, meeting the timeliness requirements of microseismic monitoring. Subsequently, the signal quality of each station is quantified using its signal-to-noise ratio (SNR), and normalization eliminates the influence of dimensions, making subsequent weight allocation more fair and objective. Next, the SNR normalization index is mapped to station weights, achieving an effective conversion from station signal quality to weights. Stations with high-quality signals have higher weights, while stations with low-quality signals have lower weights, ensuring that the constructed diagonal weight matrix accurately reflects the signal quality of each station, significantly improving location accuracy. Finally, while maintaining the event location result, the weight matrix is ​​used... By weighting the sensitivity matrix and calculating the covariance matrix of the event location parameters, the signal-to-noise ratio (SNR) weights suppress the location contribution of stations with low signal quality, making the location results more reliable. Based on this, a weighted confidence ellipsoid is constructed using eigenvalue decomposition and chi-square distribution thresholding, significantly improving the accuracy of the confidence ellipsoid construction. This invention utilizes the SNR normalization index of each station to construct station weights and explicitly limits these weights to only participating in the calculation of the covariance matrix and confidence ellipsoid, not in the solution process for event location and seismic occurrence time. Furthermore, by using weights reflecting signal quality, the covariance matrix of the event location parameters and the confidence ellipsoid are re-estimated. This effectively suppresses the influence of low SNR stations on the abnormal amplification of the error ellipsoid without changing the microseismic event location results, making the obtained confidence ellipsoid more compact and reasonably reflecting the actual error range.

[0014] This method is simple to implement and has low implementation costs. It can significantly improve the accuracy of confidence ellipsoid construction and effectively solve the problems of existing technologies that fail to distinguish the quality of station data during the confidence ellipsoid construction stage and are easily affected by individual stations, leading to abnormal amplification of the error ellipsoid. It can provide a more accurate basis for subsequent engineering decisions. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0016] The invention will now be further described with reference to the accompanying drawings.

[0017] like Figure 1 As shown, the present invention provides a method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting, comprising the following steps; Step 1: Data Acquisition and Preprocessing; P-wave arrival time data were collected from multiple microseismic monitoring stations deployed in the monitoring area, resulting in data including... Observational datasets from individual stations ; and perform preprocessing; among which, For the first The arrival time of the P wave observed at each station; Preferably, during the preprocessing process, the observation data is first subjected to quality inspection, and then obviously abnormal data is removed; Step 2: Solving for the location of microseismic events; Given a velocity model, construct the event model parameter vector. And calculate the theoretical arrival time of each station. The event localization results are obtained using unweighted least squares method or existing engineering localization algorithms. During this process, the station weights do not participate in the event location calculation. Step 3: Calculate the signal-to-noise ratio of each station and normalize it; For the The microseismic waveforms of each station are based on the characteristic amplitudes within the effective signal window of the P-wave. Characteristic amplitude within the background noise window Calculate the signal-to-noise ratio This is used to evaluate signal quality and calculate the first... Normalized signal-to-noise ratio of individual stations Unifying the SNR values ​​of different stations to the range of [0,1] can eliminate the influence of dimensional differences and facilitate subsequent analysis and comparison. Step 4: Construct a diagonal weight matrix reflecting signal quality based on the signal-to-noise ratio of each station; Using signal-to-noise ratio normalization index As the first The weight of individual stations Construct a diagonal weight matrix that reflects the signal quality of all stations. Diagonal weight matrix It is used only for subsequent calculations of the covariance matrix and confidence ellipsoid, and not for modifying the event localization results. ; Step 5: Calculate the position covariance matrix and confidence ellipsoid based on the diagonal weight matrix that reflects signal quality; Final location of the incident Constructing a sensitivity matrix Based on a diagonal weight matrix that reflects the signal quality of all stations. The covariance matrix is ​​solved using the weighted method equation. From the covariance matrix Extract the corresponding position parameters )of submatrix By pairing submatrices Eigenvalue decomposition is performed, and an event location ellipsoid is constructed by combining it with a pre-set chi-square distribution threshold at a certain information level. Preferably, ,in, For the eigenvalue matrix, The eigenvector matrix is ​​preferably the length of the major axis of the confidence ellipsoid. The length of the central axis of the confidence ellipsoid The length of the minor semi-axis of the ellipsoid is certain. , The threshold value is a chi-square distribution with 3 degrees of freedom. During the calculation of the covariance matrix and confidence ellipsoid, the event localization results are preserved. constant.

[0018] In order to achieve accurate and efficient microseismic location based on observation data, in step one, the event model parameter vector is constructed according to formula (1). The theoretical arrival time of each station is calculated based on ray tracing or travel time tables. ,in, The event location result is obtained according to formula (2). ; (1); In the formula, Let these be the spatial coordinates of the microseismic event in the coordinate system. The moment the earthquake struck; (2).

[0019] To make the quality assessment process among stations more fair and intuitive, in step three, the first step is calculated according to formula (3). Signal-to-noise ratio of individual stations Calculate the first according to formula (4) Normalized signal-to-noise ratio of individual stations ; (3); (4); In the formula, ; It is the maximum signal-to-noise ratio among all stations.

[0020] In order to achieve accurate quantification of station contributions and effective improvement of positioning accuracy, in step four, a diagonal weight matrix reflecting the signal quality of all stations is constructed according to formula (5). Weight matrix It is used only for subsequent calculations of the covariance matrix and confidence ellipsoid, and not for modifying the event localization results. ; (5); In the formula, .

[0021] In order to more accurately quantify the statistical uncertainty of the positioning parameters based on the diagonal weight matrix, the covariance matrix is ​​obtained in step five according to formula (6). ; (6); In the formula, This is a weighted residual variance estimation. Weighted residual fitting is only used for estimating the covariance matrix and not for updating it. The value of , , , To achieve the final localization results The linearized residual fit at the point, The minimum number of stations required for event localization is set to 4 in this embodiment.

[0022] To improve the stability and anti-interference capability of the signal-to-noise ratio calculation, in step three, the characteristic amplitude within the effective signal window of the P-wave is... Characteristic amplitude within the background noise window The process of obtaining it is as follows: Starting from the P-wave arrival time marker, the absolute value of the first peak or trough on the timeline is denoted as... The intensity represents the starting point of the signal; the absolute value of the first peak or trough on the timeline forward is denoted as . , representing the intensity at the noise initiation point, the absolute value of the maximum peak value in the d1 interval forward in the timeline is denoted as Reflecting the main energy of the signal, the absolute value of the maximum peak value in the forward d1 interval of the timeline is denoted as... The characteristic amplitude within the effective signal window of the P-wave is calculated according to formula (7), reflecting the main energy of the noise. The characteristic amplitude within the P-wave background noise window is calculated according to formula (8). ; (7); (8).

[0023] This invention discloses a method for characterizing the uncertainty of microseismic event location, which introduces station weights only in the confidence ellipsoid construction stage after the microseismic event location, without changing the event location result. First, by collecting P-wave arrival time data from multiple stations, comprehensive data coverage is ensured, providing a reliable input basis for subsequent location. Second, unweighted least squares or engineering algorithms are employed, offering high computational efficiency and suitability for real-time processing, meeting the timeliness requirements of microseismic monitoring. Subsequently, the signal quality of each station is quantified using its signal-to-noise ratio (SNR), and normalization eliminates the influence of dimensions, making subsequent weight allocation more fair and objective. Next, the SNR normalization index is mapped to station weights, achieving an effective conversion from station signal quality to weights. Stations with high-quality signals have higher weights, while stations with low-quality signals have lower weights, ensuring that the constructed diagonal weight matrix accurately reflects the signal quality of each station, significantly improving location accuracy. Finally, while maintaining the event location result, the weight matrix is ​​used... By weighting the sensitivity matrix and calculating the covariance matrix of the event location parameters, the signal-to-noise ratio (SNR) weights suppress the location contribution of stations with low signal quality, making the location results more reliable. Based on this, a weighted confidence ellipsoid is constructed using eigenvalue decomposition and chi-square distribution thresholding, significantly improving the accuracy of the confidence ellipsoid construction. This invention utilizes the SNR normalization index of each station to construct station weights and explicitly limits these weights to only participating in the calculation of the covariance matrix and confidence ellipsoid, not in the solution process for event location and seismic occurrence time. Furthermore, by using weights reflecting signal quality, the covariance matrix of the event location parameters and the confidence ellipsoid are re-estimated. This effectively suppresses the influence of low SNR stations on the abnormal amplification of the error ellipsoid without changing the microseismic event location results, making the obtained confidence ellipsoid more compact and reasonably reflecting the actual error range.

[0024] This method is simple to implement and has low implementation costs. It can significantly improve the accuracy of confidence ellipsoid construction and effectively solve the problems of existing technologies that fail to distinguish the quality of station data during the confidence ellipsoid construction stage and are easily affected by individual stations, leading to abnormal amplification of the error ellipsoid. It can provide a more accurate basis for subsequent engineering decisions.

Claims

1. A method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting, characterized in that, Includes the following steps; Step 1: Data Acquisition and Preprocessing; P-wave arrival time data were collected from multiple microseismic monitoring stations deployed in the monitoring area, resulting in data including... Observational datasets from individual stations And perform preprocessing; Step 2: Microseismic event location solution; Under the given velocity model conditions, construct the event model parameter vector. And calculate the theoretical arrival time of each station. The event localization results are obtained using unweighted least squares method or existing engineering localization algorithms. ; Step 3: Calculate the signal-to-noise ratio (SNR) of each station and normalize it; for the... The microseismic waveforms of each station are based on the characteristic amplitudes within the effective signal window of the P-wave. Characteristic amplitude within the background noise window Calculate the signal-to-noise ratio And calculate the first Normalized signal-to-noise ratio of individual stations ; Step 4: Construct a diagonal weight matrix reflecting signal quality based on the signal-to-noise ratio (SNR) of each station; use the SNR normalization index... As the first The weight of individual stations Construct a diagonal weight matrix that reflects the signal quality of all stations. ; Step 5: Calculate the location covariance matrix and confidence ellipsoid based on the diagonal weight matrix reflecting signal quality; in the final event localization result. Constructing a sensitivity matrix Based on a diagonal weight matrix that reflects the signal quality of all stations. The covariance matrix is ​​solved using the weighted method equation. From the covariance matrix Extract the corresponding position parameters )of submatrix By pairing submatrices Eigenvalue decomposition is performed and combined with a pre-set chi-square distribution threshold to construct an event location ellipsoid.

2. The method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting as described in claim 1, characterized in that, In step one, the event model parameter vector is constructed according to formula (1). The theoretical arrival time of each station is calculated based on ray tracing or travel time tables. ,in, The event location result is obtained according to formula (2). ; （1）； In the formula, Let these be the spatial coordinates of the microseismic event in the coordinate system. The moment the earthquake struck; （2）。 3. A method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting, as described in claim 1 or 2, characterized in that... In step three, the first step is calculated according to formula (3). Signal-to-noise ratio of individual stations Calculate the first according to formula (4) Normalized signal-to-noise ratio of individual stations ; （3）； （4）； In the formula, ; It is the maximum signal-to-noise ratio among all stations.

4. The method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting as described in claim 3, characterized in that, In step four, a diagonal weight matrix reflecting the signal quality of all stations is constructed according to formula (5). ; （5）； In the formula, .

5. The method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting as described in claim 4, characterized in that, In step five, the covariance matrix is ​​obtained according to formula (6). ; （6）； In the formula, For weighted residual variance estimation, , , To achieve the final localization results The linearized residual fit at the point, Minimum number of stations required to locate an event.

6. The method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting as described in claim 3, characterized in that, In step three, the characteristic amplitude within the effective signal window of the P-wave... Characteristic amplitude within the background noise window The process of obtaining it is as follows: Starting from the P-wave arrival time marker, the absolute value of the first peak or trough on the timeline is denoted as... The absolute value of the first peak or trough in the timeline forward is denoted as The absolute value of the maximum peak value in the d1 interval forward of the timeline is denoted as The absolute value of the maximum peak value in the time interval d1 forward is denoted as The characteristic amplitude within the effective signal window of the P-wave is calculated according to formula (7). The characteristic amplitude within the P-wave background noise window is calculated according to formula (8). ; （7）； （8）。 7. The method for constructing a microseismic location ellipsoid based on station residuals and signal-to-noise ratio weighting as described in claim 3, characterized in that, In step one, the preprocessing process is as follows: first, the observation data is quality checked, and then obviously abnormal data is removed.

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