A baseline correction method for permanent displacement of near-fault ground motion

Abstract

This application relates to a baseline correction method for permanent displacement of near-fault ground motion, including the following steps: using an acceleration recorder to record the original acceleration of ground motion, and then integrating to obtain the initial velocity and initial displacement; selecting the value ranges of t1 and t2 and defining their initial values, using linear function fitting for baseline correction, and fitting the corrected displacement time history with a smooth ramp displacement function model to obtain the corrected acceleration, velocity, and displacement time histories. According to the baseline correction method of this application, the baseline drift of near-fault ground motion can be effectively corrected, the permanent displacement of near-fault ground motion can be reasonably characterized, and the correction result has a very high degree of coincidence with the coseismic displacement observed by, for example, GPS devices.

Description

Technical Field

[0001] The present application relates to a baseline correction method for permanent displacement of near-fault ground motion, which is applicable to the technical field of disaster prevention and mitigation. Background Art

[0002] The forward directivity effect and the slip and pulse effect of fault rupture may cause large velocity pulses and permanent ground displacements in near-fault ground motion. Therefore, in the processing of original seismic records, the baseline correction method should not only remove the noise in the records, but also retain its true permanent displacement to the greatest extent. As Figure 1 shown, actual observations show that the baseline drift error of near-fault ground motion is sharply amplified in velocity and displacement, resulting in the obvious deviation of the tail section of the velocity time history from the equilibrium position and approximately presenting a straight line, and the displacement time history seriously deviating from the equilibrium position and diverging outward, as Figure 1 shown by the dotted line. A suitable baseline correction method can restore the true acceleration record to the greatest extent. After correction, the velocity time history will return to the equilibrium position and finally converge to zero, and the displacement time history after correction will gradually converge and finally stabilize at the permanent displacement, as Figure 1 shown by the solid line. How to retain the true permanent displacement information through a reasonable baseline correction method is the key problem to be solved in the current baseline correction of seismic records. Summary of the Invention

[0003] The present application proposes a baseline correction method for permanent displacement of near-fault ground motion, which can not only remove the noise in the records, but also reasonably retain the true permanent displacement.

[0004] According to a baseline correction method for permanent displacement of near-fault ground motion of the present application, the method includes the following steps:

[0005] (1) Use an acceleration recorder to record the original acceleration of ground motion, calculate the arrival time t P of the P wave of the original acceleration record, subtract the acceleration mean value in the 10 - 15 s before the arrival of the P wave from the entire acceleration time history, remove the error before the event to obtain the initialized acceleration, and then integrate to obtain the initialized velocity and initialized displacement;

[0006] (2) Select the value range of t 1 , t 2 and define the initial values of t 1 , t 2 ;

[0007] Among them, the value range of t 2 is max(t PGA , t d0 ) ≤ t 2 ≤ t end , and the value range of t 1 satisfies tP ≤t 1 ≤t 2 ; t 1 is the starting point of the instantaneous offset in the strong earthquake section, t 2 is the starting point of the permanent offset, t end is the end time of the intercepted record, t PGA is the time corresponding to the peak value of the uncorrected acceleration, t d0 is the last zero-crossing time of the uncorrected displacement and the equilibrium position;

[0008] (5) Perform baseline correction;

[0009] Use a linear function to fit the tail section t 2 ~t end , and obtain the offset a 2 ~t end for the section through Equation (1) f ;

[0010] V f (t) = V 0 + a f t(1)

[0011] Determine the offset a 1 ~t 2 for the section through Equation (2) m ;

[0012]

[0013] Subtract a 1 ~t 2 from the t m section of the initial acceleration, and subtract a 2 ~t end from the t f section to obtain the corrected acceleration Acc_new, and integrate to obtain the corrected velocity and displacement;

[0014] In the formula, V f is obtained by linear least squares fitting of the velocity time history t 2 ~t end section, V 0 is the velocity value V 2 corresponding to t f (t 2 ), a f is the slope of the fitted line, and a m is the average value of the complex baseline drift in the strong earthquake section;

[0015] (6) Fit the displacement time history;

[0016] The corrected displacement Disp_new is fitted with the smooth ramp displacement function model expressed by Equation (3), where β 1 represents the starting time when the displacement deviates from the equilibrium position, and β 2 represents the time when the displacement first reaches the permanent displacement value, and β 3 represents the permanent displacement value, and D(t) represents the displacement time history; then the error rms between the displacement model and the corrected displacement is calculated, and rms is shown in Equation (4);

[0017]

[0018]

[0019] where T is the total duration, D(t) is the displacement function model, and disp(t) is the corrected displacement;

[0020] (5) Obtain the corrected acceleration, velocity, and displacement time histories

[0021] Iterate t in a loop with δt as the time increment 1 , t 2 for all possible values, and select the t 1 that minimizes the fitting error rms between the displacement function model of Equation (4) and the corrected displacement, and t 2 as the final value, and then repeat the correction procedure in step (3) to obtain the final corrected acceleration, velocity, and displacement time histories, and take the mean value of the tail section of the displacement as the permanent displacement.

[0022] Among them, in the iteration process of step (5), the initial value of t 2 can be selected as max(t PGA , t d0 ), the initial value of t 1 is selected as t P , and the initial value of rms can be selected as 200; if rms(i) < rms, then let rms = rms(i), and save the t 1 and t 2 at this time, as well as the corrected acceleration Acc_new, and then proceed to the next step;

[0023] If rms(i) ≥ rms, then directly proceed to the next step; if t 1 < t 2 , then let t 1 = t 1 + δt, and continue to loop until t 1 = t 2 , and then jump out of the t 1 loop and proceed to the next step; if t 2 < t end , then let t 2 = t2 +δt, t 1 = t P , continue the loop until t 2 = t end , jump out of t 2 Loop, end the calculation; at this time, Acc_new in the memory is the finally corrected acceleration time history, and integrating Acc_new gives the corrected velocity and displacement time histories.

[0024] According to the baseline correction method of the present application, the baseline drift of near-fault ground motions can be effectively corrected, the permanent displacement of near-fault ground motions can be reasonably characterized, and the correction results are in good agreement with the coseismic displacements observed by, for example, GPS devices. Brief Description of the Drawings

[0025] Figure 1 It is a comparison diagram of the acceleration, velocity, and displacement time history curves of a certain station in the Chi-Chi earthquake before and after correction.

[0026] Figure 2 It is a flowchart of the steps of the baseline correction method of the present application.

[0027] Figure 3 It is a model diagram of the smooth ramp displacement function used in the baseline correction method of the present application.

[0028] Figure 4 It is the correction result in the UD direction of a certain station in the Chi-Chi earthquake. Detailed Description of the Embodiments

[0029] To make the objectives, technical solutions, and advantages of the present application clearer and more understandable, the embodiments of the present application will be described in detail below with reference to the accompanying drawings. It should be noted that, without conflict, the embodiments and features in the embodiments of the present application can be combined arbitrarily with each other.

[0030] Refer to Figure 1 , first define the main parameters used in the baseline correction method of the present application:

[0031] Correction parameter: t 1 is the starting point of the instantaneous offset in the strong motion segment, and t 2 is the starting point of the permanent offset;

[0032] Correction auxiliary parameter: t P is the arrival time of the P wave, that is, the moment of the P wave initial motion, and t end is the end time of the intercepted record, and t PGA is the time corresponding to the peak value of the uncorrected acceleration, and t d0 is the last zero-crossing time of the uncorrected displacement and the equilibrium position.

[0033] Specifically, the baseline correction method according to the present application includes the following steps:

[0034] (1) Use an accelerograph to record the original acceleration of ground motion and perform initialization processing on the original acceleration;

[0035] Strong motion observation is an effective means to obtain high-precision surface deformation. Strong motion instruments are easy to obtain high-resolution acceleration. However, due to the existence of acceleration baseline drift error, there are deviations in the integrated velocity and displacement.

[0036] The present application uses a strong motion instrument to record the original acceleration Acc of ground motion and calculates the arrival time t of the P wave of the original acceleration record P , subtract the acceleration mean value in the 10 - 15 s before the arrival of the P wave from the entire acceleration time history, remove the pre-event error to obtain the initialized acceleration, and then integrate to obtain the initialized velocity and initialized displacement.

[0037] (2) Select the value range of t 1 , t 2 and define the initial value;

[0038] Among them, the value range of t 2 is max(t PGA , t d0 ) ≤ t 2 ≤ t end . However, if the duration of the earthquake record far exceeds the duration of the strong motion segment, certain restrictions can also be imposed on the value of t end , for example, it can be taken as the time t 95 corresponding to 95% of the Arias intensity; the value range of t 1 satisfies t P ≤ t 1 ≤ t 2 that's all.

[0039] (3) Perform baseline correction

[0040] Use a linear function to fit the tail segment t 2 ~t end of the velocity time history, and obtain the offset a 2 ~t end section through Equation (1); f ;

[0041] V f (t) = V 0 + a f t (1)

[0042] Then determine the offset a 1 ~t 2 section through Equation (2); m ;

[0043]

[0044] Subtract a from the acceleration during the initialization period from t 1 to t 2 , and subtract a from the acceleration during the period from t m to t 2 to t end to obtain the corrected acceleration Acc_new, and integrate to obtain the corrected velocity and displacement. f

[0045] In the formula, V f is obtained by linear least-squares fitting of the velocity time history from t 2 to t end . V 0 is the velocity value V 2 corresponding to t f (t 2 ), a f is the slope of the fitted oblique line, and a m is the average value of the complex baseline drift in the strong earthquake section.

[0046] (4) Fit the displacement time history

[0047] Fit the corrected displacement Disp_new with the smooth ramp displacement function model expressed by Equation (3). The rising section of this model is represented by a smooth curve. Figure 3 As shown in the smooth ramp displacement function model, in the formula, β 1 represents the starting time when the displacement deviates from the equilibrium position, β 2 represents the time when the displacement first reaches the permanent displacement value, β 3 represents the permanent displacement value, D(t) represents the displacement time history; then calculate the error rms between the displacement model and the corrected displacement. rms is shown in Equation (4).

[0048]

[0049]

[0050] In the formula, T is the total duration, D(t) is the displacement function model, and disp(t) is the corrected displacement.

[0051] (5) Obtain the corrected acceleration, velocity, and displacement time histories

[0052] Iterate through all possible values of t 1 with δt as the time increment, and select the t 2 that minimizes the fitting error rms between the displacement function model of Equation (4) and the corrected displacement, t 1 , t 2 ​As the final value, repeat the calibration procedure in step (3) to obtain the finally calibrated acceleration, velocity, and displacement time histories. Take the mean value of the tail section of the displacement as the permanent displacement. The calibration results are as Figure 1 shown by the solid line.

[0053] As Figure 2 shown, in one embodiment, the initial value of t 2 can be selected as max(t PGA , t d0 ), the initial value of t 1 can be selected as t P , and the initial value of rms is selected as 200. If rms(i) < rms, then let rms = rms(i), save the t 1 and t 2 at this time, as well as the calibrated acceleration Acc_new, and then proceed to the next step; if rms(i) ≥ rms, then directly proceed to the next step. If t 1 < t 2 , then let t 1 = t 1 + δt, continue the loop until t 1 = t 2 , jump out of the t 1 loop, and proceed to the next step. If t 2 < t end , then let t 2 = t 2 + δt, t 1 = t P , continue the loop until t 2 = t end , jump out of the t 2 loop, and end the calculation. At this time, Acc_new in the memory is the finally calibrated acceleration time history. Integrating Acc_new can obtain the calibrated velocity and displacement time histories.

[0054] Embodiment

[0055] Taking the UD direction of a certain station in the Chi-Chi earthquake as an example, calibrate the original acceleration record according to the method proposed in this application. The calibrated acceleration, velocity, and displacement time histories are as Figure 4 shown, and the permanent displacement is about 364 cm.

Claims

1. A baseline correction method for permanent displacement of near-fault ground motion, characterized in that, it includes the following steps: (1) Use an accelerograph to record the original acceleration of ground motion and calculate the arrival time \(t\) of the P-wave of the original acceleration record. P Subtract the mean acceleration in the 10 - 15 s before the arrival of the P-wave from the entire acceleration time history to remove the pre-event error and obtain the initial acceleration, and then integrate it to obtain the initial velocity and initial displacement. (2) Select t 1 , t 2 The value range of and define t 1 , t 2 The initial value of; where t 2 ranges from max(t PGA , t d0 ) ≤ t 2 ≤ t end , and the range of t 1 satisfies t P ≤ t 1 ≤ t 2 ; t 1 is the starting point of the instantaneous offset in the strong earthquake section, t 2 is the starting point of the permanent offset, t end is the end time of the intercepted record, t PGA is the time corresponding to the peak time of the uncorrected acceleration, and t d0 is the last zero-crossing time of the uncorrected displacement and the equilibrium position; (3) Perform baseline correction; Use a linear function to fit the tail section \(t\) of the velocity time history 2 ~ \(t\) end , and obtain the offset \(a\) of the section \(t\) 2 ~ \(t\) end through Equation (1); f ; V f v(t) = V 0 + a f t(1) Determine t through formula (2) 1 ~t 2 The offset a of the segment m ; Subtract a from the t of the initial acceleration 1 ~t 2 section, and subtract a from the t m ~t 2 ~t end section to obtain the corrected acceleration Acc_new, and integrate to obtain the corrected velocity and displacement; f ​ Wherein, V f is obtained by linear least squares fitting of the velocity time history from t 2 to t end . V 0 is the velocity value V 2 corresponding to t f (t 2 ), a f is the slope of the fitting line, and a m is the average value of the complex baseline drift in the strong earthquake section; (4) Fit the displacement time history; The corrected displacement Disp_new is fitted with the smooth ramp displacement function model expressed by Equation (3), where β 1 represents the starting time when the displacement deviates from the equilibrium position, and β 2 represents the time when the displacement first reaches the permanent displacement value, and β 3 represents the permanent displacement value, D(t) represents the displacement time history; then the error rms between the displacement model and the corrected displacement is calculated, and rms is shown in Equation (4); wherein, T is the total duration, D(t) is the displacement function model, and disp(t) is the corrected displacement; (5) Obtain the corrected acceleration, velocity, and displacement time histories Iterate cyclically with δt as the time increment for t 1 , t 2 For all possible values of t, select the t that minimizes the fitting error rms between the displacement function model of Equation (4) and the corrected displacement 1 , t 2 As the final value, then repeat the correction procedure in step (3) to obtain the finally corrected acceleration, velocity, and displacement time histories, and take the mean value of the tail section of the displacement as the permanent displacement 2. The baseline correction method according to claim 1, characterized in that, t 2 The initial value of PGA t d0 is selected as max(t 1 , t P ), the initial value of t is selected as t, and the initial value of rms is selected as 200.

3. The baseline correction method according to claim 2, characterized in that, during the iteration process of step (5), If rms(i) < rms, then let rms = rms(i) and save the current t 1 and t 2 along with the corrected acceleration Acc_new, and then proceed to the next step; If rms(i) ≥ rms, proceed directly to the next step; if t 1 < t 2 , then set t 1 = t 1 + δt, and continue the loop until t 1 = t 2 , at which point the t 1 loop is exited and the next step is taken; if t 2 < t end , then set t 2 = t 2 + δt, t 1 = t P , and continue the loop until t 2 = t end , at which point the t 2 loop is exited and the calculation ends; at this time, Acc_new in memory is the finally corrected acceleration time history, and integrating Acc_new gives the corrected velocity and displacement time histories.

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