CN109298451B - Method for automatically picking S wave seismic phase by improving skewness - Google Patents
Method for automatically picking S wave seismic phase by improving skewness Download PDFInfo
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Abstract
The invention provides an automatic S-wave seismic phase picking method for improving skewness, which comprises the following steps: respectively inputting earthquake records in the east-west direction and the south-north direction; calculating a characteristic function, namely the seismic oscillation horizontal combined amplitude; calculating an improved skewness of the characteristic function; calculating an improved relative change rate absolute value sequence of skewness; and picking the maximum value of the improved skewness relative change rate absolute value sequence, wherein the time corresponding to the maximum value is the S-wave first arrival time. The invention adopts the improved skewness, the main part of the improved skewness is inversely proportional to the high-order square of the standard deviation, and the effect of the standard deviation on describing fluctuation is highlighted; the improved method uses the standard deviation high power, so that the improved skewness calculation interval changes monotonously when entering the seismic signal area, the difference of the improved skewness of the seismic signal and the non-seismic signal is obvious, and the arrival time of the seismic phase is determined by improving the relative change rate of the skewness, so that the error of the arrival time of the picked seismic phase is small; the invention does not carry out any filtering processing and does not distort the waveform.
Description
Technical Field
The invention belongs to the technical field of seismic signal processing, and particularly relates to an automatic S-wave seismic phase pickup method for improving skewness.
Background
The picking of the seismic phase time of natural earthquake S waves is a basic work of earthquake wave research and is a necessary parameter for accurately determining the position of a seismic source. A large number of seismic records, if picked up manually, are time consuming and laborious. Due to the interference of the P wave seismic phase, the automatic pickup accuracy of the S wave seismic phase is relatively low, and the research is relatively less. By judging the extreme point of the skewness curve, the author of the paper takes the position with the maximum slope of the curve before the extreme point as the arrival time of the seismic phase of the micro seismic motion P wave. The method has the problems that the skewness curve is continuously fluctuated and descended on the whole, a plurality of extreme points can appear in the period, the extreme points required by people can be determined by manual analysis and pickup, but if the automatic pickup is realized by a computer, the extreme points required by people are difficult to accurately determine, which is the important reason for errors in the pickup; they think that the maximum position of the curve slope before the extreme point is the arrival time of seismic P wave seismic phase, but according to our research, the arrival time of the P wave seismic phase and the S wave seismic phase is often behind the maximum position of the curve slope; the record is subjected to 5-30Hz band-pass filtering before being picked up, and then the skewness calculation is carried out on the filtered record, but the filtering is carried out, the seismic wave deviates from the original position when in seismic phase, and the picked result has larger error.
Disclosure of Invention
Based on the problems existing when seismic facies are picked up by skewness at present, an automatic S-wave seismic facies picking method for improving skewness is provided and is applied to picking up natural seismic S-wave seismic facies with seismic magnitude larger than Ms4.0. An automatic S-wave seismic phase picking method for improving skewness comprises the following specific processes:
step 1: respectively inputting earthquake records in the east-west direction and the south-north direction;
step 2: calculating a characteristic function x by using a formula (1) according to the east-west, south-north seismic recordsi(t) is the combined horizontal seismic amplitude, where xEW(t) is east-west seismic record, xNS(t) is the north-south seismic record:
and step 3: calculating characteristic function improved skewness K by using formulas (2), (3) and (4) in the whole seismic recording time periodi(t)：
Wherein M is the number of recording points in the improved skewness calculation interval, the sampling time interval of the seismic acceleration record used by people is 0.005s, and M is the recording duration in the interval; the improved skewness is the skewness in the calculation interval M and is specified as the improved skewness of the first recording point corresponding to the moment;
to improveThe average value of the recorded data in the interval M is calculated by skewness, and σ (t) is the recorded data x in the interval Mi(t) standard deviation, n is a positive integer of 5 or more;
and 4, step 4: in the whole seismic recording time interval, the absolute value of the relative change rate of the improved skewness is calculated by using a formula (5) to obtain a sequence { ri(t)}：
Wherein, Ki-1(t-1) improvement of the skewness at the preceding moment, Ki(t) improving skewness at the current moment;
and 5: picking up the improved skewness relative rate of change absolute value sequence { r } using equation (6)iMaximum value r of (t) }maxThe corresponding time is the first arrival time of the S wave.
rmax＝max{ri(t)} (6)
Description of the significance of the improvement in skewness:
the current skewness calculation formula is as follows:
our improved skewness calculation formula is as follows:
formula (7), K (t) is skewness, and formula (2) is called Ki(t) improved skewness; x is the number ofi(t) is the received wobble signal; m is the number of record points, i.e. the duration of the record, the earthquake we usedRecording the sampling time interval as 0.005 s; the improved skewness is the skewness from the recording point 1 to the recording point M, actually is the skewness of a time period, and we stipulate that the improved skewness of the time period is defined as the improved skewness of the recording point 1 at the moment, and according to practice, the M is 200;
recording the average value of the data in the sampling time period M; σ (t) is recording data x in the period Mi(t) standard deviation, n is a positive integer, the improved skewness n is not less than 5, and the current skewness n is 4, see formula (7). In the method, the value of n can be changed, and the seismic magnitude of the earthquake researched by the inventor is more than or equal to Ms4.0, n is 5, and for a major earthquake, the larger n, the higher the accuracy of the time of pickup.
When no ground vibration occurs, signals such as ground pulsation are received and are interference signals; when an earthquake occurs, the received earthquake signal is a valid signal. The research of the inventor adopts the acceleration recorder unit as international universal cm/s2The ground ripple signal is of the order of 10-6-10-2cm/s2In average of 10-4cm/s2An order of magnitude; the magnitude of the seismic P-wave first-arrival signal is generally 10-2cm/s2Left and right, and MsThe S wave first arrival composite amplitude of the earthquake with the amplitude of more than 4.0 can reach 100cm/s2. In the formula (2), σ (t) is a standard deviation, and its physical meaning is to express the fluctuation degree of the signal, and when the earth pulse signal is received, its fluctuation level is low, so that it improves the skewness Ki(t) greater; when receiving the seismic signal, the fluctuation level of the seismic signal is increased, the improved skewness is reduced, and even becomes a negative value; the improved skewness formula (2) has no molecular terms of skewness at present, highlights the influence of standard deviation, and has very clear physical significance, namely: when no earthquake signal is input, the fluctuation degree is low, the standard deviation is small, the improved skewness is large, when the earthquake signal is input, the fluctuation is intensified, the standard deviation is large, the improved skewness is small, and the earthquake phase corresponds to the sudden change time of the skewness. The purpose of using the standard deviation of the power of 5 in the improved formula (2) instead of the original power of 4 is to enhance the targetThe influence of the alignment difference on the improved skewness value is that once the calculation interval 1-M of the improved skewness completely enters the seismic signal time period, the fluctuation is aggravated, the standard deviation is increased, and the improved skewness is immediately reduced. It is emphasized that because the improved skewness formula (2) has an "-3" term, the standard deviation is very small when no seismic signal is input, the improved skewness value is much larger than the value of "-3", and the "-3" has little effect on improving the skewness, namely positive or negative; when the improved skewness calculation interval contains seismic signals, the standard deviation becomes large, and the contribution of "-3" to either positive or negative improvement in skewness increases. When the improved skewness calculation interval gradually enters the seismic signal interval, the standard deviation of the improved skewness calculation interval gradually becomes larger, and the improved skewness gradually becomes smaller. When the improved skewness calculation interval completely enters and just completely enters the seismic signal interval, the improved skewness is greatly reduced, the absolute value of the relative change rate of the improved skewness between adjacent points is the largest, and the absolute value of the relative change rate of the improved skewness in the seismic recording time period can be calculated by using a formula (5) to obtain a relative change rate absolute value sequence. On the basis, the absolute value of the maximum relative change rate of the improved skewness is picked up by using a formula (6), and the corresponding time t is the arrival time of the S wave seismic phase. If the first arrival of the seismic S wave is stronger, the improved skewness calculation area is not completely occupied by the seismic signal, and the formula (6) is met, and the picked S wave is advanced; if the first arrival of the earthquake S wave is weak, the improved skewness calculation area enters the earthquake signal area for a period of time to satisfy the formula (6), and the earthquake phase of the picked S wave lags behind.
rmax＝max{ri(t)} (6)
Equation (5) is the relative rate of change of the improved skewness at time t, and choosing a suitably large n in equation (2) allows equations (5) and (6) to be satisfied immediately upon the improved skewness calculation interval fully entering the seismic recording area.
As further explained with respect to the role of n in equation (2), when the skewness calculation region is modifiedWhen the interval is in a non-seismic signal interval, including interference of P-waves, the amplitude is generally less than 10-2cm/s2The standard deviation is smaller than 1 and smaller after being larger than or equal to the n power of 5, and the improved skewness is very large; when the calculation interval enters the natural earthquake S wave signal interval, the natural earthquake is mainly shear fracture, and the S wave first arrival amplitude is very strong, especially MsNot less than 4.0, the first arrival combined amplitude of the horizontal direction can reach 100cm/s2Of order of magnitude, i.e. 1cm/s2Orders of magnitude, with standard deviations often greater than 1, and with the n-th power, the standard deviations become larger, with very little improved skewness. Thus, the improved skewness will decrease in value after entering the seismic signal area.
Because the earthquake phase of the earthquake P wave is relatively small in interference, the accuracy of the conventional methods for picking up the P wave is high; s wave seismic phase is influenced by P wave first, and interference is relatively large, so that the accuracy of S wave picking is not high at present. Our proposed improvement, due to the large absolute amplitude of the first arrival of the natural seismic S-wave, especially for MsAn earthquake of 4.0 or more, often 10 or more0cm/s2Order of magnitude, even if the amplitude is not greatly different from that of the interference wave, the amplitude is less than 100cm/s2The magnitude order, after the standard deviation passes through a power of several, the standard deviation of the interference wave is very small, and the improved skewness is very large; the magnitude of the combined amplitude of the S wave in the first arrival horizontal direction is more than 100cm/s2The standard deviation is rapidly increased to the power of the multiple, the improved skewness is rapidly reduced, and the difference between the improved skewness and the interference wave is increased, so that the improved method is very suitable for picking up the arrival time of the S wave.
Even if the first arrival amplitude of the S wave is less than 100cm/s2Of the order of magnitude, but 10-1cm/s2Order of magnitude if we assume that the amplitude of the interference wave is 10-2cm/s2In the order of magnitude, where n in formula (2) is 5, an improved skewness of the interference wave of about 10 can be obtained by rough calculation10cm/s2Order of magnitude, and improved skewness of seismic signals of about 105cm/s2And the relative difference between the two is also very obvious.
Seismic waves propagate along straight lines as they propagate in a homogeneous, isotropic medium. However, the crust medium is distributed in a layered way, and the closer to the ground, the lower the medium density is, and the wave speed is also reduced. According to the law of refraction, the sine of the incident angle of the seismic waves is proportional to the wave velocity, and when the seismic waves are transmitted to the ground from a deep part, the reduction of the wave velocity can reduce the incident angle of the seismic waves, so that the seismic waves received on the ground are almost vertically incident to the ground.
The S wave vibration direction is vertical to the propagation direction, and the vibration in the horizontal direction is strong, so that the S wave vibration phase is picked up and two horizontal directions are adopted, namely: the east-west, south-north direction earthquake records are used as earthquake motion signal input, the horizontal direction earthquake record amplitude value is calculated by formula (1), and the characteristic function x is obtainedi(t) wherein xEW(t) is east-west seismic record, xNSAnd (t) is the north-south direction seismic record.
The seismic facies arrival time is defined as the arrival time of the first peak or trough of the seismic wave, so that the physical meaning of the seismic wave S seismic facies arrival time picked up by the combined amplitude of east, west, south and north is clear. Some authors of the paper use the rate of energy change as a characteristic function to pick up the epicenter is not reliable because the rate of energy change at the peaks or troughs is often not significant.
The beneficial technical effects are as follows:
the invention provides an automatic S-wave seismic phase picking method for improving skewness, wherein the main part for improving the skewness is in inverse proportion to the high-order square of a standard deviation, and the effect of the standard deviation on describing fluctuation is highlighted; the use of the standard deviation high power of the improved method enables the improved skewness calculation interval to be monotonously changed when entering the seismic signal area, and also enables the difference of the improved skewness of the seismic signal and the non-seismic signal to be obvious, and the obvious difference enables the arrival time of the seismic phase to be determined by improving the relative change rate of the skewness, so that the error of the arrival time of the picked seismic phase is small; defining the horizontal direction seismic record composite amplitude as a characteristic function, and highlighting the abnormal expression of S wave arrival time; the improved method does not carry out any filtering processing when the seismic phase is picked up, and does not distort the waveform; the method can be popularized to the pickup of the arrival time of the P wave seismic phase.
Drawings
FIG. 1 is a flow chart of an improved skewness method for automatically picking S-wave seismic phases according to an embodiment of the present invention;
FIG. 2 is a north-south record of seismic acceleration according to an embodiment of the present invention;
FIG. 3 is a east-west recording of seismic acceleration according to an embodiment of the present invention;
FIG. 4 is a graph of the horizontal combined amplitude of an embodiment of the present invention;
FIG. 5 is an improved skewness of an embodiment of the present invention;
FIG. 6 is a graph of the relative rate of change of improved skewness for an embodiment of the present invention;
FIG. 7 illustrates the arrival time error of the picked S-wave in accordance with an embodiment of the present invention;
FIG. 8 is a time-to-pickup error analysis of an embodiment of the present invention;
FIG. 9 is an unmodified skew of an embodiment of the present invention;
FIG. 10 is a graph of the relative change ratio of the degree of unmodified skew for an embodiment of the present invention;
FIG. 11 is an improved skewness of an embodiment of the present invention;
FIG. 12 is a graph of the relative rate of change of the improved skewness of an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the accompanying drawings and specific embodiments, and an S-wave seismic phase automatic pickup method with improved skewness is shown in fig. 1, and the specific flow is as follows:
step 1: inputting the earthquake record in east-west direction and south-north direction respectively, wherein x is usedEW(t) represents the east-west seismic recording, as shown in FIG. 3, with xNS(t) represents north-south seismic recordings, as shown in FIG. 2;
step 2: calculating a characteristic function x by using a formula (1) according to the east-west, south-north seismic recordsi(t) is the resultant horizontal amplitude of seismic motion, where xEW(t) is east-west seismic record, xNS(t) isNorth-south seismic recordings, as shown in fig. 4:
feature function selection is different from Allen, reference to Allen R v. 1521-1532, and Allen R V.automatic Phase packers: the air Present use and future promoters [ J ]. BSSA, 1982, 72 (6B): S225-S242. The characteristic function of Allen selects the sum of amplitude magnitude and amplitude variation. Because the definition of the arrival time of the seismic wave is that the amplitude of the wave crest or the wave trough is extremely large, but the change of the amplitude is not extremely large generally, the method of Allen may be that the extreme point of the characteristic function is not the arrival time of the seismic wave; our eigenfunction selection is different from the related papers, which are unreliable for picking seismic phases with energy change rate as eigenfunction, because the energy change rate at the peak or trough is often not very large. The S wave, also called shear wave or transverse wave, is selected, the horizontal east-west direction, the south-north direction and the combined amplitude of the two directions are taken as a characteristic function, and the record of three components of east-west, south-north and vertical in the relevant paper is not taken, so that the characteristic of strong horizontal vibration of the S wave is highlighted, and the abnormal performance of the seismic facies is also highlighted after the amplitudes of the east-west direction, the south-north direction and the south-north direction are combined.
And step 3: calculating the skewness K improved by the characteristic function by using the formulas (2), (3) and (4) in the whole seismic recording time periodi(t), as shown in FIG. 5:
the improved skewness highlights that the standard deviation is small when no seismic signal is input, the skewness is large, the standard deviation is large when the seismic signal is input, the skewness is small, namely when no seismic signal exists, the improved skewness difference is obvious, the physical significance is quite clear, the improved skewness represents the signal fluctuation level, and at the moment, n is selected to be 5.
And 4, step 4: calculating the absolute value sequence of the relative change rate of the improved skewness r by using the formula (5) in the whole seismic recording time periodi(t) }, as shown in FIG. 6:
unlike the authors of the relevant papers, the S-wave seismic facies of the present invention are not at the maximum slope of the skewness curve, but at the maximum absolute value of the relative rate of change of the adjacent improved skewness.
And 5: the maximum value in the absolute value sequence of the relative change rate of the improved skewness is picked up by using the formula (6), the time corresponding to the maximum value is the first arrival time of the S wave, and as shown in FIG. 6, the first arrival time of the S wave is 18.975S.
rmax＝max{ri(t)} (6)
And (3) error analysis:
100 earthquakes with magnitude larger than Ms4.0 are selected, S wave arrival time is manually picked up to be used as a standard, S wave arrival time is picked up by using an improved skewness method, and an absolute error curve is shown in figure 7. When the picked S wave seismic phase is ahead of the standard value, the error is negative, otherwise, the error is positive.
As can be seen from fig. 7, the errors of the pick-ups are all within 0.1 s. We analyze the cause of the error using figure 8. Defining the arrival time of the seismic facies as the time corresponding to the wave crest or the wave trough of the seismic waves, namely when the improved skewness calculation interval completely enters and just completely enters the seismic signal interval, the position of the wave crest at the starting end of the improved skewness calculation area, namely the position of the time 1 in figure 8, wherein the standard deviation is very large, the improved skewness suddenly becomes very small, the absolute value of the relative change rate of the adjacent improved skewness is very large, and the arrival time is accurately picked up when the maximum value corresponds to the S-wave seismic facies; if the seismic wave first arrival amplitude is relatively large, the improved skewness is reduced quickly, so that the improved skewness calculation area does not completely enter the seismic signal area, the absolute value of the relative change rate of the improved skewness reaches the maximum value, such as the position corresponding to the time 2 in the figure 8, and the arrival time of the picked S wave seismic phase is advanced; if the first arrival amplitude of the seismic wave is relatively small, the improved skewness is slowly reduced, so that the improved skewness calculation area completely enters the seismic signal area and exceeds the time 1 in the figure 8, the absolute value of the relative change rate of the improved skewness reaches the maximum value, such as the position corresponding to the time 3 in the figure 8, and the arrival time of the picked S-wave seismic phase lags behind.
It has been mentioned that we define the arrival time of the seismic phase as the time corresponding to the wave crest or the wave trough of the seismic wave, which is the unified standard, but actually the seismic phase of the seismic wave has arrived before the wave crest or the wave trough, and in fig. 8, the defined S-wave seismic phase arrives at the time 1, but the seismic phase arrives at the time 2, so it is not necessary to require the arrival time too accurately, and the improved method is meaningful as long as the error is small.
There were paper authors picking up P-wave arrival times with skewness, and no study of S-wave arrival time pickup. The method is popularized and applied to the application of the magnitude of vibration larger than Ms4.0, the destructive earthquake S wave seismic facies pickup provides a method for picking up the S wave seismic facies by improving skewness, and the picking accuracy is not high due to the fact that the S wave seismic facies is interfered by P waves first, and the method provided by the inventor enriches the seismic facies pickup theory.
The effect of standard deviation on the improved skewness:
fig. 9 is an unmodified skewness function, and since the function uses a power of n-4, the rise and fall of the calculation interval entering the seismic signal period is relatively insignificant, and the skewness is not always reduced but increased by a skewness near the S-wave seismic phase. FIG. 10 is a graph of the absolute value of the relative rate of change of the skewness without modification, illustrating that the change of the skewness with modification fluctuates significantly, during which many maxima occur, and the absolute values of the ratios differ slightly, which causes many difficulties in determining the facies. Fig. 11 is a modified skewness curve, where n is 8, and since the power of the function is n 8, the calculation interval enters the seismic signal period, the rise and fall increase is relatively significant, and the modified skewness decreases in the vicinity of the arrival time of the S-wave seismic phase. Fig. 12 is a plot of the absolute value of the relative rate of change of the modified skewness, where n is 8, and the entire plot has only one distinct maximum over the entire time period. The improved skewness is not large overall, but because after entering the seismic signal area, an improved skewness very close to zero occurs, so that the absolute value of the relative rate of change is maximized. This example illustrates that a suitably large n-value is beneficial when accurately picking seismic phases.
Claims (1)
1. An automatic S-wave seismic phase picking method for improving skewness is characterized by comprising the following specific processes:
step 1: respectively inputting earthquake records in the east-west direction and the south-north direction;
step 2: calculating a characteristic function x by using a formula (1) according to the east-west, south-north seismic recordsi(t) is the combined horizontal seismic amplitude, where xEW(t) denotes east-west seismic records, xNS(t) represents north-south seismic recordings:
and step 3: calculating the skewness K (t) of the improvement of the characteristic function by using the formulas (2), (3) and (4) in the whole seismic recording time period:
wherein, M is the number of record points, namely the record duration;
to be the mean of the feature function over the sampling period M, σ (t) is the feature function x over the sampling period Mi(t) standard deviation, n is a positive integer greater than or equal to 5;
and 4, step 4: in the whole seismic recording time interval, the absolute value of the relative change rate of the improved skewness is calculated by using a formula (5) to obtain a sequence { ri(t)}：
Wherein, Ki-1(t-1) improving the skewness at the previous moment, and K (t) improving the skewness at the current moment;
and 5: picking up the improved skewness relative rate of change absolute value sequence { r } using equation (6)iMaximum value r of (t) }maxThe corresponding time is the first arrival time of the S wave:
rmax＝max{ri(t)} (6) 。
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