Timing alignment method for data acquired by monitoring units of borehole-surface micro-seismic monitoring system

Abstract

A timing alignment method for data acquired by monitoring units of a borehole-surface micro-seismic monitoring system includes acquiring two rock-burst waveform data segments with GPS timestamps; calculating a time difference and a number of sampling points between each pair of adjacent GPS timestamps; adding, on an equal-interval basis, a sampling time to a sampling point missing a timestamp between each pair of adjacent GPS timestamps; calculating average sampling frequencies of the two rock-burst waveform data segments, adding, on an equal-interval basis, a sampling time to a sampling point missing a timestamp except first and last GPS timestamps in each of the two data segments; obtaining sampling times of all sampling points, resampling the sampling times according to a uniform sampling frequency; calculating a rock-burst waveform data segment at a new sampling time with a linear interpolation formula, and aligning the sampling times of the two rock-burst waveform data segments.

Claims

1. A timing alignment method for data acquired by monitoring units of a borehole-surface micro-seismic monitoring system, comprising the following steps: (1) extracting a first rock-burst waveform data segment and a second rock-burst waveform data segment that are respectively acquired by a surface wireless monitoring unit and an underground wired monitoring unit of the borehole-surface micro-seismic monitoring system and each provided with multiple global positioning system (GPS) timestamps, wherein the first rock-burst waveform data segment and the second rock-burst waveform data segment have different lengths; (2) calculating a time difference and a number of sampling points between each pair of adjacent GPS timestamps in each of the first rock-burst waveform data segment and the second rock-burst waveform data segment; and adding, on an equal-interval basis, a sampling time to a sampling point missing a timestamp between each pair of adjacent GPS timestamps; (3) calculating an average sampling frequency of each of the first rock-burst waveform data segment and the second rock-burst waveform data segment; and adding, on an equal-interval basis, a sampling time to a sampling point missing a timestamp except first and last GPS timestamps in each of the first rock-burst waveform data segment and the second rock-burst waveform data segment; (4) resampling sampling times of all sampling points obtained in steps (2) and (3), according to a uniform sampling frequency; and (5) calculating, based on the sampling times of all of the sampling points obtained in steps (2) and (3) and rock-burst waveform data segments at the sampling times, a rock-burst waveform data segment at a new sampling time according to step (4) with a linear interpolation formula; and aligning the sampling times of the first rock-burst waveform data segment and the second rock-burst waveform data segment.

2. The timing alignment method for data acquired by monitoring units of the borehole-surface micro-seismic monitoring system according to claim 1, wherein in step (1), the surface wireless monitoring unit and the underground wired monitoring unit carry out independent high-precision GPS timing separately, and sample at sampling frequencies f.sub.s and f.sub.u, respectively; the first rock-burst waveform data segment and the second rock-burst waveform data segment are denoted as y.sub.i.sup.s and y.sub.j.sup.u, respectively; i=1, 2, . . . , l; l denotes a sampling length of the surface wireless monitoring unit; j=1, 2, . . . , p; p denotes a sampling length of the underground wired monitoring unit; the GPS timestamps are created for some sampling points of each of the first rock-burst waveform data segment and the second rock-burst waveform data segment; the timestamps created for a sampling point index.sub.i′.sup.s of the first rock-burst waveform data segment y.sub.i.sup.s form a GPS timing sequence T.sub.i′.sup.s; i′=1, 2, . . . , m; index.sup.s denotes a position number corresponding to the timestamp of the first rock-burst waveform data segment y.sub.i.sup.s; m denotes a number of sampling points with a GPS timestamp of the first rock-burst waveform data segment monitored by the surface wireless monitoring unit; the timestamps created for a sampling point index.sub.j′.sup.u of the second rock-burst waveform data segment y.sub.j.sup.u form a GPS timing sequence T.sub.j′.sup.u; j′=1, 2, . . . , n; index.sup.u denotes a position number corresponding to the timestamp of the second rock-burst waveform data segment y.sub.j.sup.u; and n denotes a number of sampling points with a GPS timestamp of the second rock-burst waveform data segment monitored by the underground wired monitoring unit.

3. The timing alignment method for data acquired by monitoring units of the borehole-surface micro-seismic monitoring system according to claim 2, wherein in step (2), the adding, on an equal-interval basis, a sampling time to a sampling point missing a timestamp between each pair of adjacent GPS timestamps further comprises: 201) calculating a time difference and a number of sampling points between each pair of adjacent timestamps in each of the GPS timing sequences T.sub.i′.sup.s and T.sub.j′.sup.u: time difference: ΔT.sup.s=T.sub.i′+1.sup.s−T.sub.i′.sup.s; ΔT.sup.u=T.sub.j′+1.sup.u−T.sub.j′.sup.u; number of sampling points: ΔN.sup.s=index.sub.i′+1.sup.s−index.sub.i′.sup.s+1; ΔN.sup.u=index.sub.j′+1.sup.u−index.sub.j′.sup.u+1; 202) bringing the time difference and the number of sampling points into the following equation: $T_{i^{\prime }}^s+\frac{\Delta T^s}{\Delta N^s-1}k=T_{i^{\prime }}^s+\frac{T_{i^{\prime }+1}^s-T_{i^{\prime }}^s}{{\mathrm{index}}_{i^{\prime }+1}^s-{\mathrm{index}}_{i^{\prime }}^s}k$ calculating the sampling time of a k-th sampling point after the sampling point index.sub.i′.sup.s in the first rock-burst waveform data segment y.sub.i.sup.s on an equal-interval basis, until a sampling point index.sub.i′+1.sup.s−1; bringing the time difference and the number of sampling points into the following equation: $T_{j^{\prime }}^u+\frac{\Delta T^u}{\Delta N^u-1}k=T_{j^{\prime }}^u+\frac{T_{j^{\prime }+1}^u-T_{j^{\prime }}^u}{{\mathrm{index}}_{j^{\prime }+1}^u-{\mathrm{index}}_{j^{\prime }}^u}k$ calculating the sampling time of a k-th sampling point after the sampling point index.sub.j′.sup.u in the second rock-burst waveform data segment y.sub.j.sup.u on an equal-interval basis, until a sampling point index.sub.j′+1.sup.u−1; and 203) repeating steps 201) and 202) until all sampling points missing a timestamp between each pair of adjacent GPS timestamps in each of the first rock-burst waveform data segment and the second rock-burst waveform data segment are added with a sampling time.

4. The timing alignment method for data acquired by monitoring units of the borehole-surface micro-seismic monitoring system according to claim 3, wherein in step (3), the adding, on an equal-interval basis, a sampling time to a sampling point missing a timestamp except first and last GPS timestamps in each of the first rock-burst waveform data segment and the second rock-burst waveform data segment further comprises: 301) calculating the average sampling frequency f.sub.s of the first rock-burst waveform data segment and the average sampling frequency f.sub.u of the second rock-burst waveform data segment: $\overline{f_s}=\frac{{.Math.}_{i^{\prime }=1}^{m-1}\frac{{\mathrm{index}}_{i^{\prime }+1}^s-{\mathrm{index}}_{i^{\prime }}^s}{T_{i^{\prime }+1}^s-T_{i^{\prime }}^s}}{m-1};$ $\overline{f_u}=\frac{{.Math.}_{j^{\prime }=1}^{n-1}\frac{{\mathrm{index}}_{j^{\prime }+1}^u-{\mathrm{index}}_{j^{\prime }}^u}{T_{j^{\prime }+1}^u-T_{j^{\prime }}^u}}{n-1};$ 302) adding, according to $T_1^s-\frac{1}{\overline{f_s}}*k$ and on an equal-interval basis, a sampling time to a k-th sampling point before the first GPS timestamp of the first rock-burst waveform data segment monitored by the surface wireless monitoring unit, until a first sampling point of the first rock-burst waveform data segment; and adding, according to $T_m^s+\frac{1}{\overline{f_s}}*k$ and on an equal-interval basis, a sampling time to a k-th sampling point after the last GPS timestamp of the first rock-burst waveform data segment monitored by the surface wireless monitoring unit, until a last sampling point of the first rock-burst waveform data segment; and adding, according to $T_1^u-\frac{1}{{\overline{f}}_u}*k$ and on an equal-interval basis, a sampling time to a k-th sampling point before the first GPS timestamp of the second rock-burst waveform data segment monitored by the underground wired monitoring unit, until a first sampling point of the second rock-burst waveform data segment; and adding, according to $T_n^u+\frac{1}{{\overline{f}}_u}*k$ and on an equal-interval basis, a sampling time to a k-th sampling point after the last GPS timestamp of the second rock-burst waveform data segment monitored by the underground wired monitoring unit, until a last sampling point of the second rock-burst waveform data segment.

5. The timing alignment method for data acquired by monitoring units of the borehole-surface micro-seismic monitoring system according to claim 4, wherein in step (4), the uniform sampling frequency is f; after addition, the sampling time corresponding to the first rock-burst waveform data segment y.sub.i.sup.s is denoted as T.sub.i.sup.s, and the sampling time corresponding to the second rock-burst waveform data segment y.sub.j.sup.u is denoted as T.sub.j.sup.u; and the resampling sampling times further comprises: 401) calculating a minimum value t.sub.min.sup.s and a maximum value t.sub.max.sup.s of the sampling time T.sub.i.sup.s and a minimum value t.sub.min.sup.u and a maximum value t.sub.max.sup.u of the sampling time T.sub.j.sup.u; 402) determining a start value ${\stackrel{\_}{\stackrel{\_}{T}}}_1^s==t_{\min }^s-\mathrm{mod}\left(t_{\min }^s-\frac{1}{f}\right)$ and an end value ${\stackrel{\_}{\stackrel{\_}{T}}}_{\mathrm{end}}^s=t_{\max }^s-\mathrm{mod}\left(t_{\max }^s,\frac{1}{f}\right)$ of a sampling time T.sub.i.sup.s and a start value ${\stackrel{\_}{\stackrel{\_}{T}}}_1^u==t_{\min }^u-\mathrm{mod}\left(t_{\min }^u-\frac{1}{f}\right)$ and an end value ${\stackrel{\_}{\stackrel{\_}{T}}}_{\mathrm{end}}^u==t_{\max }^u-\mathrm{mod}\left(t_{\max }^u,\frac{1}{f}\right)$ or a sampling time T.sub.j.sup.u for resampling, wherein mod denotes a modulus operation; and 403) determining the sampling time T.sub.i.sup.s for resampling: ${\stackrel{\_}{\stackrel{\_}{T}}}_i^s=t_{\min }^s-\mathrm{mod}\left(t_{\min }^s-\frac{1}{f}\right)+\left(i-1\right)\frac{1}{f};$ wherein, i=1, 2, . . . , l, l=(T.sub.end.sup.s−T.sub.1.sup.s)×f+1; and determining the sampling time T.sub.j.sup.u for resampling: ${\stackrel{\_}{\stackrel{\_}{T}}}_j^u=t_{\min }^u-\mathrm{mod}\left(t_{\min }^u-\frac{1}{f}\right)+\left(j-1\right)\frac{1}{f};$ wherein, j=1, 2, . . . p, p=(T.sub.end.sup.u−T.sub.1.sup.u)×f+1.

6. The timing alignment method for data acquired by monitoring units of the borehole-surface micro-seismic monitoring system according to claim 5, wherein step (5) further comprises calculating a corresponding rock-burst waveform data segment according to the sampling times T.sub.i.sup.s and T.sub.j.sup.u: 501) determining a subscript position index satisfying T.sub.index.sup.x<T.sub.k.sup.x<T.sub.index+1.sup.x; wherein, k=1, 2, . . . , z; index=1, 2, . . . , z−1; z=l or p; x=u or s; and 502) bringing the subscript position index into the linear interpolation formula: $\frac{y_{\mathrm{index}+1}^x-y_{\mathrm{index}}^x}{{\overline{T}}_{\mathrm{index}+1}^x-{\overline{T}}_{\mathrm{index}}^x}{\stackrel{\_}{\stackrel{\_}{T}}}_k^x+y_{\mathrm{index}}^x-\frac{y_{\mathrm{index}+1}^x-y_{\mathrm{index}}^x}{{\overline{T}}_{\mathrm{index}+1}^x-{\overline{T}}_{\mathrm{index}}^x}{\overline{T}}_{\mathrm{index}}^x$ obtaining a rock-burst waveform data segment y.sub.k.sup.x.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flowchart of a timing alignment method for data acquired by monitoring units of a borehole-surface micro-seismic monitoring system according to the present disclosure;

(2) FIG. 2 shows rock-burst waveform data monitored by a surface wireless monitoring unit and GPS timestamps according to an embodiment of the present disclosure;

(3) FIG. 3 shows rock-burst waveform data monitored by an underground wired monitoring unit and GPS timestamps according to an embodiment of the present disclosure;

(4) FIG. 4 shows the rock-burst waveform data, acquired by the surface wireless monitoring unit, with all sampling points with a sampling time after addition of missing sampling times, according to the embodiment of the present disclosure;

(5) FIG. 5 shows the rock-burst waveform data, acquired by the underground wired monitoring unit, with all sampling points with a sampling time after addition of missing sampling times, according to the embodiment of the present disclosure; and

(6) FIG. 6 shows the rock-burst waveform data acquired by the surface wireless monitoring unit and the underground wired monitoring unit after timing alignment, where a horizontal axis represents time, and a vertical axis represents amplitude.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(7) The present disclosure is further described below with reference to the drawings.

(8) As shown in FIG. 1, a timing alignment method for data acquired by monitoring units of a borehole-surface micro-seismic monitoring system includes the following steps:

(9) (1) A first rock-burst waveform data segment and a second rock-burst waveform data segment are extracted, which are respectively acquired by a surface wireless monitoring unit and an underground wired monitoring unit of the borehole-surface micro-seismic monitoring system, are each provided with multiple global positioning system (GPS) timestamps, and have different lengths.

(10) (2) A time difference and a number of sampling points between each pair of adjacent GPS timestamps in each of the first rock-burst waveform data segment and the second rock-burst waveform data segment are calculated, and on an equal-interval basis, a sampling time is added to a sampling point missing a timestamp between each pair of adjacent GPS timestamps.

(11) (3) An average sampling frequency of each of the first rock-burst waveform data segment and the second rock-burst waveform data segment is calculated, and on an equal-interval basis, a sampling time is added to a sampling point missing a timestamp except first and last GPS timestamps in each of the first rock-burst waveform data segment and the second rock-burst waveform data segment.

(12) (4) Sampling times of all sampling points obtained in steps (2) and (3) are resampled according to a uniform sampling frequency.

(13) (5) Based on the sampling times of all the sampling points obtained in steps (2) and (3) and rock-burst waveform data segments at the sampling times, a rock-burst waveform data segment at a new sampling time according to step (4) is calculated with a linear interpolation formula; and the sampling times of the first rock-burst waveform data segment and the second rock-burst waveform data segment are aligned.

(14) Further, in step (1), the surface wireless monitoring unit and the underground wired monitoring unit carry out independent high-precision GPS timing separately, and sample at sampling frequencies f.sub.s and f.sub.u, respectively; the first rock-burst waveform data segment and the second rock-burst waveform data segment are denoted as y.sub.i.sup.s and y.sub.j.sup.u, respectively; i=1, 2, . . . , l; l denotes a sampling length of the surface wireless monitoring unit; j=1, 2, . . . , p; p denotes a sampling length of the underground wired monitoring unit; the GPS timestamps are created for some sampling points of each of the first rock-burst waveform data segment and the second rock-burst waveform data segment; the timestamps created for sampling point index.sub.i′.sup.s of the first rock-burst waveform data segment y.sub.i.sup.s form a GPS timing sequence T.sub.i′.sup.s; i′=1, 2, . . . , m; index.sup.s denotes a position number corresponding to the timestamp of the first rock-burst waveform data segment y.sub.i.sup.s; m denotes a number of sampling points with a GPS timestamp of the first rock-burst waveform data segment monitored by the surface wireless monitoring unit; the timestamps created for sampling point index.sub.j′.sup.u of the second rock-burst waveform data segment y.sub.j.sup.u form a GPS timing sequence T.sub.j′.sup.u; j′=1, 2, . . . , n; index.sup.u denotes a position number corresponding to the timestamp of the second rock-burst waveform data segment y.sub.j.sup.u; and n denotes a number of sampling points with a GPS timestamp of the second rock-burst waveform data segment monitored by the underground wired monitoring unit.

(15) Further, in step (2), on an equal-interval basis, the sampling time is added to a sampling point missing a timestamp between each pair of adjacent GPS timestamps.

(16) 201) A time difference and a number of sampling points between each pair of adjacent timestamps in each of the GPS timing sequences T.sub.i′.sup.s and T.sub.j′.sup.u are calculated as follows:

(17) time difference: ΔT.sup.s=Y.sub.i′+1.sup.s−T.sub.i′.sup.s; ΔT.sup.u=T.sub.j′+1.sup.u−T.sub.j′.sup.u;

(18) number of sampling points: ΔN.sup.s=index.sub.i′+1.sup.s−index.sub.i′.sup.s+1; ΔN.sup.u=index.sub.j′+1.sup.u−index.sub.j′.sup.u+1.

(19) 202) The time difference and the number of sampling points are brought into the following equation:

(20) $T_{i^{\prime }}^s+\frac{\Delta T^s}{\Delta N^s-1}k=T_{i^{\prime }}^s+\frac{T_{i^{\prime }+1}^s-T_{i^{\prime }}^s}{{\mathrm{index}}_{i^{\prime }+1}^s-{\mathrm{index}}_{i^{\prime }}^s}k$

(21) The sampling time of a k-th sampling point after the sampling point index.sub.i′.sup.s in the first rock-burst waveform data segment y.sub.i.sup.s is calculated on an equal-interval basis, until sampling point index.sub.i′+1.sup.s−1.

(22) The time difference and the number of sampling points are brought into the following equation:

(23) $T_{j^{\prime }}^u+\frac{\Delta T^u}{\Delta N^u-1}k=T_{j^{\prime }}^u+\frac{T_{j^{\prime }+1}^u-T_{j^{\prime }}^u}{{\mathrm{index}}_{j^{\prime }+1}^u-{\mathrm{index}}_{j^{\prime }}^u}k$

(24) The sampling time of a k-th sampling point after the sampling point index.sub.j′.sup.u in the second rock-burst waveform data segment y.sub.j.sup.u is calculated on an equal-interval basis, until sampling point index.sub.j′+1.sup.u−1.

(25) 203) Steps 201) and 202) are repeated until all sampling points missing a timestamp between each pair of adjacent GPS timestamps in each of the first rock-burst waveform data segment and the second rock-burst waveform data segment are added with a sampling time.

(26) Further, in step (3), on an equal-interval basis, a sampling time is added to a sampling point missing a timestamp except first and last GPS timestamps in each of the first rock-burst waveform data segment and the second rock-burst waveform data segment.

(27) 301) The average sampling frequency f.sub.s of the first rock-burst waveform data segment and the average sampling frequency f.sub.u of the second rock-burst waveform data segment are calculated as follows:

(28) $\begin{array}{c}\overline{f_s}=\frac{{.Math.}_{i^{\prime }=1}^{m-1}\frac{{\mathrm{index}}_{i^{\prime }+1}^s-{\mathrm{index}}_{i^{\prime }}^s}{T_{i^{\prime }+1}^s-T_{i^{\prime }}^s}}{m-1};\\ \overline{f_u}=\frac{{.Math.}_{j^{\prime }=1}^{n-1}\frac{{\mathrm{index}}_{j^{\prime }+1}^u-{\mathrm{index}}_{j^{\prime }}^u}{T_{j^{\prime }+1}^u-T_{j^{\prime }}^u}}{n-1};\end{array}$

(29) 302) According to

(30) $T_1^s-\frac{1}{\overline{f_s}}*k$
and on an equal-interval basis, a sampling time is added to a k-th sampling point before the first GPS timestamp of the first rock-burst waveform data segment monitored by the surface wireless monitoring unit, until a first sampling point of the first rock-burst waveform data segment. According to

(31) $T_m^s+\frac{1}{\overline{f_s}}*k$
and on an equal-interval basis, a sampling time is added to a k-th sampling point after the last GPS timestamp of the first rock-burst waveform data segment monitored by the surface wireless monitoring unit, until a last sampling point of the first rock-burst waveform data segment.

(32) According to

(33) 0$T_1^u-\frac{1}{{\overline{f}}_u}*k$
and on an equal-interval basis, a sampling time is added to a k-th sampling point before the first GPS timestamp of the second rock-burst waveform data segment monitored by the underground wired monitoring unit, until a first sampling point of the second rock-burst waveform data segment. According to

(34) $T_n^u+\frac{1}{{\overline{f}}_u}*k$
and on an equal-interval basis, a sampling time is added to a k-th sampling point after the last GPS timestamp of the second rock-burst waveform data segment monitored by the underground wired monitoring unit, until a last sampling point of the second rock-burst waveform data segment.

(35) Further, in step (4), the uniform sampling frequency is f; after addition, the sampling time corresponding to the first rock-burst waveform data segment y.sub.i.sup.s is denoted as T.sub.i.sup.s, and the sampling time corresponding to the second rock-burst waveform data segment y.sub.j.sup.u is denoted as T.sub.j.sup.u; and the resampling of the sampling times is as follows:

(36) 401) A minimum value t.sub.min.sup.s and a maximum value t.sub.max.sup.s of the sampling time T.sub.i.sup.s and a minimum value t.sub.min.sup.u and a maximum value t.sub.max.sup.u of the sampling time T.sub.j.sup.u are calculated.

(37) 402) A start value

(38) ${\stackrel{=}{T}}_1^s=t_{\min }^s-\mathrm{mod}\left(t_{\min }^s-\frac{1}{f}\right)$
and an end value

(39) ${\stackrel{=}{T}}_{\mathrm{end}}^s=t_{\max }^s-\mathrm{mod}\left(t_{\max }^s,\frac{1}{f}\right)$
of a sampling time T.sub.i.sup.s and a start value

(40) ${\stackrel{=}{T}}_1^u=t_{\min }^u-\mathrm{mod}\left(t_{\min }^u-\frac{1}{f}\right)$
and an end value

(41) ${\stackrel{=}{T}}_{\mathrm{end}}^u=t_{\max }^u-\mathrm{mod}\left(t_{\max }^u,\frac{1}{f}\right)$
of a sampling time T.sub.j.sup.u for resampling are determined, where mod denotes a modulus operation.

(42) 403) The sampling time T.sub.i.sup.s for resampling is determined as follows:

(43) ${\stackrel{=}{T}}_i^s=t_{\min }^s-\mathrm{mod}\left(t_{\min }^s-\frac{1}{f}\right)+\left(i-1\right)\frac{1}{f};$

(44) where, i=1, 2, . . . , l, l=(T.sub.end.sup.s−T.sub.1.sup.s)×f+1;

(45) The sampling time T.sub.j.sup.u for resampling is determined as follows:

(46) ${\stackrel{=}{T}}_j^u=t_{\min }^u-\mathrm{mod}\left(t_{\min }^u-\frac{1}{f}\right)+\left(j-1\right)\frac{1}{f};$

(47) where, j=1, 2, . . . p, p=(T.sub.end.sup.u−T.sub.1.sup.u)×f+1.

(48) Further, in step (5), a corresponding rock-burst waveform data segment is calculated according to the sampling times T.sub.i.sup.s and T.sub.j.sup.u:

(49) 501) A subscript position index satisfying T.sub.index.sup.x<T.sub.k.sup.x<T.sub.index+1.sup.x is determined;

(50) where, k=1, 2, . . . , z; index=1, 2, . . . , z−1; z=l or p; x=u or s.

(51) 502) The subscript position index is brought into the linear interpolation formula:

(52) $\frac{y_{\mathrm{index}+1}^x-y_{\mathrm{index}}^x}{{\overline{T}}_{\mathrm{index}+1}^x-{\overline{T}}_{\mathrm{index}}^x}{\stackrel{\_}{\stackrel{\_}{T}}}_k^x+y_{\mathrm{index}}^x-\frac{y_{\mathrm{index}+1}^x-y_{\mathrm{index}}^x}{{\overline{T}}_{\mathrm{index}+1}^x-{\overline{T}}_{\mathrm{index}}^x}{\overline{T}}_{\mathrm{index}}^x$

(53) A rock-burst waveform data segment y.sub.k.sup.x is obtained.

(54) The sampling times T.sub.index.sup.x and T.sub.index+1.sup.x are simplified into T.sub.i.sup.s and T.sub.j.sup.u, respectively. If x takes s, T.sub.index.sup.s is the sampling time T.sub.i.sup.s corresponding to each sampling point after addition of the timestamp to the data acquired by the surface wireless monitoring unit. The value of index is determined by i=1, 2, . . . , l, that is, index=1, 2, . . . , l−1.

(55) If x takes u, T.sub.index.sup.u is the sampling time T.sub.j.sup.u corresponding to each sampling point after addition of the timestamp to the data acquired by the underground wired monitoring unit. The value of index is determined by j=1, 2, . . . , p, that is, index=1, 2, . . . , p−1.

(56) Embodiment

(57) (1) As shown in FIG. 2, rock-burst waveform data segment y.sub.i.sup.s, i=1, 2, . . . , 6000 with GPS timestamps acquired by the surface wireless monitoring unit of the borehole-surface micro-seismic monitoring system at a sampling frequency of f.sub.s=500 Hz is extracted, where the timestamps of sampling point index.sub.i′.sup.s,i′=1, 2 , . . . , 12 in y.sub.i.sup.s form sequence T.sub.i′.sup.s.

(58) As shown in FIG. 3, rock-burst waveform data segment y.sub.j.sup.u,j=1, 2, . . . , 6000 with GPS timestamps acquired by the underground wired monitoring unit of the borehole-surface micro-seismic monitoring system at a sampling frequency of f.sub.u=500 Hz is extracted, where the timestamps of sampling point index.sub.j′.sup.u, j′=1, 2, . . . , 94 in y.sub.j.sup.u form sequence T.sub.j′.sup.u.

(59) (2) A sampling time is added, on an equal-interval basis, to a sampling point missing a timestamp between each pair of adjacent GPS timestamps.

(60) 201) A time difference between GPS timestamp T.sub.1.sup.s and an adjacent timestamp of the waveform data segment y.sub.i.sup.s is calculated as ΔT.sup.s=T.sub.2.sup.s−T.sub.1.sup.s=1s, and a number of sampling points between the two adjacent timestamps is calculated as ΔN.sup.s=index.sub.2.sup.s−index.sub.1.sup.s+1=501−1+1=501. A time difference between GPS timestamp T.sub.1.sup.u and an adjacent timestamp of the waveform data segment y.sub.j.sup.u(j=1, 2, . . . , 6000) is calculated as ΔT.sup.u=T.sub.2.sup.u−T.sub.1.sup.u=0.128s, and a number of sampling points between the two adjacent timestamps is calculated as ΔN.sup.u=index.sub.2.sup.u−index.sub.1.sup.u+1=112−48+1=65.

(61) 202) The time difference and the number of sampling points are brought into the following equation:

(62) $T_1^s+\frac{\Delta T^s}{\Delta N^s-1}\times k=T_1^s+\frac{T_2^s-T_1^s}{{\mathrm{index}}_2^s-{\mathrm{index}}_1^s}\times k=739+\frac{1}{500}\times k$

(63) The sampling time of a k-th sampling point after the sampling point index.sub.1.sup.s=1 in y.sub.i.sup.s(i=1, 2, . . . , 6000) is calculated on an equal-interval basis, until sampling point index.sub.2.sup.s−1=501−1=500.

(64) The time difference and the number of sampling points are brought into the following equation:

(65) 0$T_1^u+\frac{\Delta T^u}{\Delta N^u-1}\times k=T_1^u+\frac{T_2^u-T_1^u}{{\mathrm{index}}_2^u-{\mathrm{index}}_1^u}\times k=738.992+\frac{0.128}{64}\times k$

(66) The sampling time of a k-th sampling point after the sampling point index.sub.1.sup.u=48 in y.sub.j.sup.u(j=1, 2, . . . , 6000) is calculated on an equal-interval basis, until sampling point index.sub.2.sup.u−1=112−1=111.

(67) 203) Steps 201) and 202) are repeated until all sampling points missing a timestamp between each pair of adjacent GPS timestamps in each of the two waveform data segments are added with a sampling time.

(68) (3) A sampling time is added, on an equal-interval basis, to a sampling point missing a timestamp except first and last GPS timestamps in each of the waveform data segments y.sub.i.sup.s and y.sub.j.sup.u.

(69) 301) The average sampling frequency f.sub.s of the waveform data segment y.sub.i.sup.s and the average sampling frequency f.sub.u of the waveform data segment y.sub.j.sup.u are calculated, respectively.

(70) $\overline{f_s}=\frac{{.Math.}_{i^{\prime }=1}^{12-1}\frac{{\mathrm{index}}_{i^{\prime }+1}^s-inde{x}_{i^{\prime }}^s}{T_{i^{\prime }+1}^s-T_{i^{\prime }}^s}}{12-1}=500;$

(71) $\overline{f_u}=\frac{{.Math.}_{j^{\prime }=1}^{94-1}\frac{{\mathrm{index}}_{j^{\prime }+1}^u-inde{x}_{j^{\prime }}^u}{T_{j^{\prime }+1}^u-T_{j^{\prime }}^u}}{94-1}=461.2523$

(72) 302) According to

(73) $T_1^s-\frac{k}{\overline{f_s}}=739-k\times 0.002$
and on an equal-interval basis, a sampling time is added to a k-th sampling point before the first GPS timestamp in the waveform data segment y.sub.i.sup.s monitored by the surface wireless monitoring unit, until a first sampling point in the waveform data segment. According to

(74) $T_{12}^s+\frac{k}{\overline{f_s}}=750+k\times 0.002$
and on an equal-interval basis, a sampling time is added to a k-th sampling point after the last GPS timestamp in the waveform data segment y.sub.i.sup.s monitored by the surface wireless monitoring unit, until a last sampling point in the waveform data segment. According to

(75) $T_1^u-\frac{k}{{\overline{f}}_u}=738.992-0.002168\times k$
and on an equal-interval basis, a sampling time is added to a k-th sampling point before the first GPS timestamp in the waveform data segment y.sub.j.sup.u monitored by the underground wired monitoring unit, until a first sampling point in the waveform data segment. According to

(76) $T_{94}^u+\frac{k}{{\overline{f}}_u}=751.896+0.002168\times k$
and on an equal-interval basis, a sampling time is added to a k-th sampling point after the last GPS timestamp in the waveform data segment y.sub.j.sup.u monitored by the underground wired monitoring unit, until a last sampling point in the waveform data segment.

(77) (4) As shown in FIGS. 4 and 5, the sampling times T.sub.i.sup.s and T.sub.j.sup.u of all sampling points are obtained by means of addition in steps (2) and (3), and the sampling times are resampled according to a uniform sampling frequency f=500 Hz.

(78) 401) A minimum value t.sub.min.sup.s=739 and a maximum value t.sub.max.sup.s=750.998 of the sampling time T.sub.i.sup.s, as well as a minimum value t.sub.min.sup.u=738.8901 and a maximum value t.sub.max.sup.u=751.896 of the sampling time T.sub.j.sup.u, are calculated.

(79) 402) A start value of the sampling time T.sub.i.sup.s for resampling is determined as:

(80) ${\stackrel{\_}{\stackrel{\_}{T}}}_1^s=t_{\min }^s-\mathrm{mod}\left(t_{\min }^s,\frac{1}{f}\right)=739-\mathrm{mod}\left(739,0.002\right)=739,$

(81) An end value of the sampling time for resampling is determined as:

(82) ${\stackrel{\_}{\stackrel{\_}{T}}}_{\mathrm{end}}^s=t_{\max }^s-\mathrm{mod}\left(t_{\max }^s,\frac{1}{f}\right)=750.998-\mathrm{mod}\left(750.998,0.002\right)=750.998.$

(83) A start value of the sampling time T.sub.j.sup.u for resampling is determined as:

(84) ${\stackrel{\_}{\stackrel{\_}{T}}}_1^u==t_{\min }^u-\mathrm{mod}\left(t_{\min }^u,\frac{1}{f}\right)=738.8901-\mathrm{mod}\left(738.8901,0.002\right)=738.89;$

(85) An end value of the sampling time for resampling is determined as:

(86) 0${\stackrel{\_}{\stackrel{\_}{T}}}_{\mathrm{end}}^u=t_{\max }^u-\mathrm{mod}\left(t_{\max }^u,\frac{1}{f}\right)=751.896-\mathrm{mod}\left(751.896,0.002\right)=751.896$

(87) 403) The sampling time T.sub.i.sup.s for resampling is determined as:

(88) ${\stackrel{\_}{\stackrel{\_}{T}}}_i^s={\stackrel{\_}{\stackrel{\_}{T}}}_1^s+\left(i-1\right)\frac{1}{f}=739+\left(i-1\right)\times 0.002,i=1,2,.Math.,l,$$l=\left({\stackrel{\_}{\stackrel{\_}{T}}}_{\mathrm{end}}^s-{\stackrel{\_}{\stackrel{\_}{T}}}_1^s\right)\times f+1=6000$

(89) The sampling time T.sub.j.sup.u for resampling is determined as:

(90) ${\stackrel{\_}{\stackrel{\_}{T}}}_j^u={\stackrel{\_}{\stackrel{\_}{T}}}_1^u+\left(j-1\right)\frac{1}{f}=738.89+\left(i-1\right)\times 0.002,,j=1,2,.Math.p,$$p=\left({\stackrel{\_}{\stackrel{\_}{T}}}_{\mathrm{end}}^u-{\stackrel{\_}{\stackrel{\_}{T}}}_1^u\right)\times f+1=6505.$

(91) (5) The new sampling times T.sub.i.sup.s, i=1, 2, . . . , 6000 and T.sub.j.sup.u, j=1, 2, . . . , 6505 in step (4) are calculated according to the linear interpolation formula, and the corresponding waveform data are calculated so as to align the sampling times.

(92) 501) A subscript position index satisfying T.sub.index.sup.x<T.sub.k.sup.x<T.sub.index+1.sup.x, k=1, 2, . . . , l or p, l=6000, p=6505, index=1, 2, . . . , 5999, x=u or s, is determined.

(93) 502) The subscript position index is brought into the linear interpolation formula:

(94) $\frac{y_{\mathrm{index}+1}^x-y_{\mathrm{index}}^x}{{\overline{T}}_{\mathrm{index}+1}^x-{\overline{T}}_{\mathrm{index}}^x}{\stackrel{\_}{\stackrel{\_}{T}}}_k^x+y_{\mathrm{index}}^x-\frac{y_{\mathrm{index}+1}^x-y_{\mathrm{index}}^x}{{\overline{T}}_{\mathrm{index}+1}^x-{\overline{T}}_{\mathrm{index}}^x}{\overline{T}}_{\mathrm{index}}^x$

(95) The waveform data segment y.sub.k.sup.x, k=1, 2, . . . , l or p, l=6000, p=6505, x=u or s shown in FIG. 6 is calculated.