CN110609323B - Simplified calculation method for site excellent period based on stratum information - Google Patents

Abstract

The invention discloses a simplified calculation method of a site excellent period based on stratum information, which is characterized in that an estimated value of the excellent period is obtained by applying an excellent period simple algorithm, and all calculation parameters except the site stratum information are set according to the value; taking the field soil as a seismic wave signal filter, calculating a ground seismic time course under the action of pulse waves, and performing Fourier transform on the ground seismic time course to obtain an amplitude spectrum; by judging the relation between the maximum value of the amplitude spectrum and the time (or frequency), a high-precision excellent period calculation value is obtained. The simplified calculation method for the site excellent period based on the stratum information is simple in calculation process and high in calculation precision.

Description

Simplified calculation method for site excellent period based on stratum information

Technical Field

The invention belongs to the technical field of geotechnical engineering investigation, and particularly relates to a simplified calculation method for a site excellent period based on stratum information.

Background

The excellent period refers to a harmonic component of seismic waves which have resonance action with the foundation soil layer. At present, methods for determining the excellent period of a field are roughly classified into two major types, namely a direct measurement method and a wave velocity method. In any method, calculation parameters except formation information need to be input, and even the calculation parameters need to be debugged, so that a proper calculation result can be obtained; and the calculation precision is not high, or the calculation process is complicated.

Disclosure of Invention

The invention aims to provide a simplified calculation method of a site excellent period based on stratum information, which is simple in calculation process and high in calculation precision.

The technical scheme adopted by the invention is that a simplified calculation method of the site excellent period based on stratum information is implemented according to the following steps:

step 1, determining the number n of the site and the stratum density rho according to the investigation result of geotechnical engineering_iShear velocity v_iAnd the thickness h of the formation_i(ii) a Wherein, i is 1, 2.. said., n;

step 2, calculating a site excellent period estimated value t₀；

Step 3, calculating the seismic wave duration t_lAnd a time sampling interval Δ t;

step 4, calculatingSampling point number nt of ground seismic wave holding time and sampling point number nt of seismic wave propagation time in stratum i_iThe number nT of sampling points of the Fourier periodic spectrum of the ground seismic wave;

step 5, calculating the reflection coefficient R of the seismic waves at the boundary interface of the stratum i and the stratum i +1_i；

Step 6, calculating the time course u of the ground seismic wave₀ ^d；

Step 7, seismic wave time course u₀ ^dCarrying out attenuation treatment according to time;

step 8, performing discrete Fourier transform on the seismic wave time course u (j) to obtain Fu (k);

step 9, judging whether the amplitude spectrum | Fu (k) | has a maximum value, if not, expanding nT by 20%, and returning to the step 8; if yes, determining the site excellent period T₀。

The invention is also characterized in that:

in step 2, site excellent period estimated value t₀The formula is as follows:

t₀＝4(h₁/v₁+h₂/v₂+……+h_n/v_n) (1)。

in step 3, the seismic wave duration t_lThe formula is as follows:

t_l≥10 t₀ (2)

the time sampling interval Δ t is calculated by the following equation (3):

Δt<0.02min(h₁/v₁，h₂/v₂，……，h_n/v_n) (3)。

in step 4, sampling point number nt of ground seismic wave holding time and sampling point number nt of seismic wave propagation time in stratum i_iThe sampling point number nT of the Fourier cycle spectrum of the ground seismic wave is calculated by the following formula:

nt＝Int(t_l/Δt) (4)

nt_i＝Int(h_i/v_i/Δt) (5)

nT＝Int(t₀/Δt) (6)

wherein Int is an integer function, i is 1, 2.

In step 5, the reflection coefficient R_iThe formula is as follows:

R_i＝(ρ_i+1v_i+1-ρ_iv_i)/(ρ_i+1v_i+1+ρ_iv_i) Wherein, i is 1, 2, a. (7)

R _n1, wherein i ═ n; (8).

In step 6, seismic wave time course u₀ ^dThe formula is as follows:

u₀ ^d(j)＝-u₁ ^p(j-nt₁)

u₁ ^d(j)＝(1+R₁)u₀ ^d(j-nt₁)-R₁u₂ ^p(j-nt₂)

u₁ ^p(j)＝R₁u₀ ^d(j-nt₁)+(1-R₁)u₂ ^p(j-nt₂)

u₂ ^d(j)＝(1+R₂)u₁ ^d(j-nt₂)-R₂u₃ ^p(j-nt₃)

u₂ ^p(j)＝R₂u₁ ^d(j-nt₂)+(1-R₂)u₃ ^p(j-nt₃)

......

u_i ^d(j)＝(1+R_i)u_i-1 ^d(j-nt_i)-R_iu_i+1 ^p(j-nt_i+1)

u_i ^p(j)＝R_iu_i-1 ^d(j-nt_i)+(1-R_i)u_i+1 ^p(j-nt_i+1)

......

u_n-1 ^d(j)＝(1+R_n-1)u_n-2 ^d(j-nt_n-1)-R_n-1u_n ^p(j-nt_n)

u_n-1 ^p(j)＝R_n-1u_n-2 ^d(j-nt_n-1)+(1-R_n-1)u_n ^p(j-nt_n)

u_n ^p(j)＝u_n ^d(j-nt_n)

wherein u is₀ ^dIs the ground seismic wave time course; u. of_i ^d、u_i ^pThe seismic wave time courses of the lower interface and the upper interface of the formation i are respectively, wherein i is 1, 2. u. of₀ ^d、u_i ^d、u_i ^pAre time series, j denotes a time sample number, j 0, 1.

In step 7, the seismic wave time travel u is calculated according to the following formula₀ ^dCarrying out attenuation treatment according to time:

u(j)＝u₀ ^d(j)exp[-βjΔt] (9)

wherein the attenuation coefficient beta is-ln delta/t_l(ii) a Delta is a calculation precision value for controlling the attenuation coefficient and satisfies 0<δ<0.01；j＝0，1，......，nt-1。

In step 8, performing Discrete Fourier Transform (DFT) on the seismic time interval u (j) according to the following formula:

wherein i is an imaginary unit; k is 0, 1,.. cnt-1.

In step 9, whether the amplitude spectrum | fu (k) | has a maximum value is determined according to the following formula:

| Fu (k) | > | Fu (k-1) | and | Fu (k) | > | Fu (k +1) | (11)

|Fu(k)|>0.5max(|Fu(1)|，|Fu(2)|，......，|Fu(nT-1)|) (12)

If | Fu (k) | satisfies the above condition, the site excellent period is calculated by the following formula:

T₀＝0.5t₀+kΔt (13)。

the invention has the beneficial effects that: the method adopts a simple algorithm with an excellent period to obtain an estimated value of the excellent period, and sets all calculation parameters except the field stratum information according to the value; taking the field soil as a seismic wave signal filter, calculating a ground seismic time course under the action of pulse waves, and performing Fourier transform on the ground seismic time course to obtain an amplitude spectrum; by judging the relation between the maximum value of the amplitude spectrum and the time (or frequency), a high-precision excellent period calculation value is obtained.

Drawings

FIG. 1 is a field stratum model in the method for simplifying calculation of excellent period of field based on stratum information;

FIG. 2 is a simplified calculation method of a distinguished period of a field based on stratum information, which is disclosed by embodiment 1, of an original ground earthquake time course;

FIG. 3 is a simplified calculation method of a distinguished period of a field based on stratum information, which is used for embodiment 1 of the invention, and the earthquake time course after attenuation processing is carried out;

FIG. 4 is a Fourier amplitude spectrum of seismic time course of embodiment 1 of the method for simplifying calculation of excellent period of field based on stratum information;

FIG. 5 is a simplified calculation method of excellent period of field based on stratum information, in accordance with embodiment 2, the time course of original ground earthquake;

FIG. 6 is a simplified calculation method of a site excellent period based on stratum information according to the invention, and the seismic time course after attenuation processing is performed in embodiment 2;

FIG. 7 is a Fourier amplitude spectrum of seismic time course of embodiment 2 of the method for simplifying calculation of excellent period of field based on formation information;

FIG. 8 is a simplified calculation method of excellent period of field based on stratum information in accordance with embodiment 3 of the present invention;

FIG. 9 is a simplified calculation method of a distinguished period of a field based on stratum information, which is shown in embodiment 3, and the seismic time course after attenuation processing;

FIG. 10 is a Fourier amplitude spectrum of seismic time course according to embodiment 3 of the method for simplifying calculation of excellent period of field based on formation information;

FIG. 11 is a simplified calculation method of excellent period of field based on stratum information, embodiment 4 of the invention is an original ground earthquake time course;

FIG. 12 is a simplified calculation method of a distinguished period of a field based on formation information, which is shown in FIG. 4, and the seismic time course after attenuation processing;

FIG. 13 is a Fourier amplitude spectrum of seismic time interval according to embodiment 4 of the method for simplifying calculation of excellent period of field based on formation information;

FIG. 14 is a simplified calculation method of excellent period of field based on stratum information, embodiment 5 of the invention is an original ground earthquake time course;

FIG. 15 is a simplified calculation method of a distinguished period of a field based on formation information, which is shown in FIG. 5, and shows a seismic time course after attenuation processing;

fig. 16 is a fourier amplitude spectrum of seismic time course of embodiment 5 of the method for simplifying calculation of the excellent period of the field based on the formation information.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

The invention relates to a simplified calculation method of a site excellent period based on stratum information, which is implemented according to the following steps:

step 1, determining the number n of the site and the stratum density rho according to the investigation result of geotechnical engineering_iShear velocity v_iAnd the thickness h of the formation_i(ii) a Wherein, i is 1, 2.

Step 2, calculating a site excellent period estimated value t₀；

Site excellent period estimation value t₀The formula is as follows:

t₀＝4(h₁/v₁+h₂/v₂+……+h_n/v_n) (1)。

step 3, calculating the seismic wave duration t_lAnd a time sampling interval Δ t;

earthquakeDuration of wave t_lThe formula is as follows:

t_l≥10 t₀ (2)

the time sampling interval Δ t is calculated by the following equation (3):

Δt<0.02min(h₁/v₁，h₂/v₂，……，h_n/v_n) (3)。

step 4, calculating the sampling point number nt of the ground seismic wave holding time and the sampling point number nt of the seismic wave propagation time in the stratum i_iThe number nT of sampling points of the Fourier periodic spectrum of the ground seismic wave;

sampling point number nt of ground seismic wave holding time and sampling point number nt of seismic wave propagation time in stratum i_iThe sampling point number nT of the Fourier cycle spectrum of the ground seismic wave is calculated by the following formula:

nt＝Int(t_l/Δt) (4)

nt_i＝Int(h_i/v_i/Δt) (5)

nT＝Int(t₀/Δt) (6)

wherein Int is an integer function, i is 1, 2.

Step 5, calculating the reflection coefficient R of the seismic waves at the boundary interface of the stratum i and the stratum i +1_i；

Reflection coefficient R_iThe formula is as follows:

R_i＝(ρ_i+1v_i+1-ρ_iv_i)/(ρ_i+1v_i+1+ρ_iv_i) Wherein, i is 1, 2, a. (7)

R _n1, wherein i ═ n; (8).

Step 6, calculating the time course u of the ground seismic wave₀ ^d；

Seismic time-path u₀ ^dThe formula is as follows:

u₀ ^d(j)＝-u₁ ^p(j-nt₁)

u₁ ^d(j)＝(1+R₁)u₀ ^d(j-nt₁)-R₁u₂ ^p(j-nt₂)

u₁ ^p(j)＝R₁u₀ ^d(j-nt₁)+(1-R₁)u₂ ^p(j-nt₂)

u₂ ^d(j)＝(1+R₂)u₁ ^d(j-nt₂)-R₂u₃ ^p(j-nt₃)

u₂ ^p(j)＝R₂u₁ ^d(j-nt₂)+(1-R₂)u₃ ^p(j-nt₃)

......

u_i ^d(j)＝(1+R_i)u_i-1 ^d(j-nt_i)-R_iu_i+1 ^p(j-nt_i+1)

u_i ^p(j)＝R_iu_i-1 ^d(j-nt_i)+(1-R_i)u_i+1 ^p(j-nt_i+1)

......

u_n-1 ^d(j)＝(1+R_n-1)u_n-2 ^d(j-nt_n-1)-R_n-1u_n ^p(j-nt_n)

u_n-1 ^p(j)＝R_n-1u_n-2 ^d(j-nt_n-1)+(1-R_n-1)u_n ^p(j-nt_n)

u_n ^p(j)＝u_n ^d(j-nt_n)

wherein u is₀ ^dIs the ground seismic wave time course; u. of_i ^d、u_i ^pThe seismic wave time courses of the lower interface and the upper interface of the formation i are respectively, wherein i is 1, 2. u. of₀ ^d、u_i ^d、u_i ^pAre time series, j represents a time sample point serial number, j is 0, 1,.. multidot.nt-1,j-0 means that the time is equal to zero.

Step 7, seismic wave time course u₀ ^dCarrying out attenuation treatment according to time;

the seismic wave time course u is processed according to the following formula₀ ^dCarrying out attenuation treatment according to time:

u(j)＝u₀ ^d(j)exp[-βjΔt] (9)

wherein the attenuation coefficient beta is-ln delta/t_l(ii) a Delta is a calculation precision value for controlling the attenuation coefficient and satisfies 0<δ<0.01；j＝0，1，......，nt-1。

Step 8, performing Discrete Fourier Transform (DFT) on the seismic wave time interval u (j) to obtain Fu (k);

performing Discrete Fourier Transform (DFT) on the seismic wave time interval u (j) according to the following formula:

wherein i is an imaginary unit; k is 0, 1,.. cnt-1.

Step 9, judging whether the amplitude spectrum | Fu (k) | has a maximum value, if not, expanding nT by 20%, and returning to the step 8; if yes, determining the site excellent period T₀；

Whether the amplitude spectrum | fu (k) | has a maximum value is judged according to the following formula:

| Fu (k) | > | Fu (k-1) | and | Fu (k) | > | Fu (k +1) | (11)

|Fu(k)|>0.5max(|Fu(1)|，|Fu(2)|，......，|Fu(nT-1)|) (12)

If | Fu (k) | satisfies the above condition, the site excellent period is calculated by the following formula:

T₀＝0.5t₀+kΔt (13)。

example 1

Step 1, determining the number n of the site and the stratum density rho according to the investigation result of geotechnical engineering_iShear velocity v_iAnd the thickness h of the formation_i(ii) a Wherein, i is 1, 2.. said., n; the site stratigraphic model is shown in figure 1(ii) a The formation parameters are shown in table 1;

n＝3

ρ₁＝2041 v₁＝200 h₁＝4

ρ₂＝2143 v₂＝300 h₂＝4

ρ₃＝2041 v₃＝200 h₃＝12

step 2, calculating a site excellent period estimated value t₀；

t₀＝4×(4/200+4/300+12/200)＝0.3733

Step 3, calculating the seismic wave duration t_lAnd a time sampling interval Δ t;

t_l＝10t₀＝10×0.3733＝3.7333

Δt＝0.0001<0.02min(4/200，4/300，12/200)＝0.01333

step 4, calculating the sampling point number nt of the ground seismic wave holding time and the sampling point number nt of the seismic wave propagation time in the stratum i_iThe number nT of sampling points of the Fourier periodic spectrum of the ground seismic wave;

nt＝Int(t_l/Δt)＝Int(3.733/0.0001)＝37333

nt₁＝Int(h_i/v_i/Δt)＝Int(4/200/0.0001)＝200

nt₂＝Int(h_i/v_i/Δt)＝Int(4/300/0.0001)＝133

nt₃＝Int(h_i/v_i/Δt)＝Int(12/200/0.0001)＝600

nT＝Int(t₀/Δt)＝Int(0.3733/0.0001)＝3733

step 5, calculating the reflection coefficient R of the seismic waves at the boundary interface of the stratum i and the stratum i +1_i；

R₁＝(2143×300－2041×200)/(2143×300+2041×200)＝0.2233

R₂＝(2041×200－2143×300)/(2041×200+2143×300)＝-0.2233

R₃＝1

Step 6, calculating the time course u of the ground seismic wave₀ ^d；

Let nt, nt₁，nt₂，nt₃And R₁，R₂，R₃Substituting the correlated parameters into a time recurrence equation to obtain a ground seismic time course u₀ ^d(j) J is 0, 1, a.

Step 7, seismic wave time course u₀ ^dCarrying out attenuation treatment according to time;

taking δ to be 0.005, the attenuation coefficient is calculated:

β＝－lnδ/t_l＝－ln0.005/3.7333＝1.4192

according to the formula u₀ ^d(j)exp[-βjΔt]And (3) carrying out attenuation treatment to obtain the earthquake time course u (j), wherein j is 0, 1. (as shown in FIG. 3)

Step 8, performing Discrete Fourier Transform (DFT) on the seismic wave time interval u to obtain Fu (k);

discrete Fourier Transform (DFT) is performed on the seismic time interval u to obtain Fourier spectrum Fu (k), k being 0, 1.

Step 9, judging whether the amplitude spectrum | Fu (k) | has a maximum value, if not, expanding nT by 20%, and returning to the step 8; if yes, determining the site excellent period T₀；

In descending order, the maxima of the amplitude spectrum | fu (k) | are found, in 3731, 3730, 3729. According to calculation, k is 2069, and the site excellent period can be calculated as follows:

T₀＝0.5t₀+kΔt＝0.5×0.3733+2069×0.0001＝0.3935

the excellent cycle estimates, excellent cycle calculations and the main calculation parameters are detailed in table 2.

Example 2

The formation parameters of a 2-layer soil field of 20m are shown in Table 3. The original ground seismic time interval, the seismic time interval after attenuation processing and the fourier amplitude spectrum thereof calculated according to the procedure of example 1 are shown in fig. 5, 6 and 7, and the estimated excellent period value, the calculated excellent period value and the main calculation parameters are detailed in table 4. As can be seen from the table, although the excellent cycle estimates, the main calculation parameters, are the same as in example 2, the excellent cycle calculations are not the same, 0.3935s and 0.4027s, respectively.

Example 3

The formation parameters of a certain 5-layer soil field are 10.7m, and are shown in Table 5. The original ground seismic time interval, the seismic time interval after attenuation processing and the fourier amplitude spectrum thereof calculated according to the procedure of example 1 are shown in fig. 8, 9 and 10, and the estimated excellent period value, the calculated excellent period value and the main calculation parameters are detailed in table 6. As can be seen, the calculated values for the excellent cycle are close to the estimated values, 0.2092s and 0.2345, respectively.

Example 4

The soil thickness of a certain site is 126m, the number of strata is more, the total number of the strata is 12, and the parameters of each stratum are shown in the table 7. The original ground seismic time interval, the seismic time interval after attenuation processing and the fourier amplitude spectrum thereof calculated according to the procedure of example 1 are shown in fig. 11, 12 and 13, and the estimated excellent period value, the calculated excellent period value and the main calculation parameters are detailed in table 8. The ground earthquake time course is complex (see fig. 11), and the excellent period reaches 1.3195 s.

Example 5

The soil thickness of a certain site is 250m, the stratum can reach up to 20 layers, and the parameters of each soil layer are shown in a table 9. The original ground seismic time interval, the seismic time interval after attenuation processing and the fourier amplitude spectrum thereof calculated according to the procedure of example 1 are shown in fig. 14, 15 and 16, and the estimated excellent period value, the calculated excellent period value and the main calculation parameters are shown in table 10. Due to the fact that the field is layered and thick, the ground earthquake time course is very complex (see fig. 14), the excellent period is large, and the value reaches 2.0319 s.

The simplified calculation method of the site excellent period based on the stratum information has the advantages that: the method adopts a simple algorithm with an excellent period to obtain an estimated value of the excellent period, and sets all calculation parameters except the field stratum information according to the value; taking the field soil as a seismic wave signal filter, calculating a ground seismic time course under the action of pulse waves, and performing Fourier transform on the ground seismic time course to obtain an amplitude spectrum; by judging the relation between the maximum value of the amplitude spectrum and the time (or frequency), a high-precision excellent period calculation value is obtained.

Table 1 example 1 formation parameters

Table 2 example 1 calculation of parameters

Table 3 example 2 formation parameters

Table 4 example 2 calculation of parameters

Table 5 example 3 formation parameters

Table 6 example 3 calculation of parameters

Table 7 example 4 formation parameters

Table 8 example 4 calculation of parameters

Table 9 example 5 formation parameters

Table 10 example 5 calculation of parameters

。

Claims (1)

1. A simplified calculation method for a site excellent period based on stratum information is characterized by comprising the following steps:

step 1, determining the number n of the site and the stratum density rho according to the investigation result of geotechnical engineering_iShear velocity v_iAnd the thickness h of the formation_i(ii) a Wherein, i is 1, 2.. said., n;

step 2, calculating a site excellent period estimated value t₀；

In the step 2, the site excellent period estimated value t₀The formula is as follows:

t₀＝4(h₁/v₁+h₂/v₂+……+h_n/v_n) (1)；

step 3, calculating the seismic wave duration t_lAnd a time sampling interval Δ t;

in the step 3, the seismic wave duration t_lThe formula is as follows:

t_l≥10t₀ (2)

the time sampling interval Δ t is calculated by the following equation (3):

Δt<0.02min(h₁/v₁，h₂/v₂，……，h_n/v_n) (3)；

step 4, calculating the sampling point number nt of the ground seismic wave holding time and the sampling point number nt of the seismic wave propagation time in the stratum i_iThe number nT of sampling points of the Fourier periodic spectrum of the ground seismic wave;

in the step 4, the number of sampling points nt of the ground seismic wave holding time and the number of sampling points nt of the seismic wave propagation time in the stratum i_iThe sampling point number nT of the Fourier cycle spectrum of the ground seismic wave is calculated by the following formula:

nt＝Int(t_l/Δt) (4)

nt_i＝Int(h_i/v_i/Δt) (5)

nT＝Int(t₀/Δt) (6)

wherein Int is an integer function, i is 1, 2.

Step 5, calculating the reflection coefficient R of the seismic waves at the boundary interface of the stratum i and the stratum i +1_i；

In the step 5, the reflection coefficient R_iThe formula is as follows:

R_i＝(ρ_i+1v_i+1-ρ_iv_i)/(ρ_i+1v_i+1+ρ_iv_i) Wherein, i is 1, 2, a. (7)

R_n1, wherein i ═ n; (8);

step 6, calculating the time course u of the ground seismic wave₀ ^d；

In step 6, seismic wave time course u₀ ^dThe formula is as follows:

u₀ ^d(j)＝-u₁ ^p(j-nt₁)

u₁ ^d(j)＝(1+R₁)u₀ ^d(j-nt₁)-R₁u₂ ^p(j-nt₂)

u₁ ^p(j)＝R₁u₀ ^d(j-nt₁)+(1-R₁)u₂ ^p(j-nt₂)

u₂ ^d(j)＝(1+R₂)u₁ ^d(j-nt₂)-R₂u₃ ^p(j-nt₃)

u₂ ^p(j)＝R₂u₁ ^d(j-nt₂)+(1-R₂)u₃ ^p(j-nt₃)

......

u_i ^d(j)＝(1+R_i)u_i-1 ^d(j-nt_i)-R_iu_i+1 ^p(j-nt_i+1)

u_i ^p(j)＝R_iu_i-1 ^d(j-nt_i)+(1-R_i)u_i+1 ^p(j-nt_i+1)

......

u_n-1 ^d(j)＝(1+R_n-1)u_n-2 ^d(j-nt_n-1)-R_n-1u_n ^p(j-nt_n)

u_n-1 ^p(j)＝R_n-1u_n-2 ^d(j-nt_n-1)+(1-R_n-1)u_n ^p(j-nt_n)

u_n ^p(j)＝u_n ^d(j-nt_n)

wherein u is₀ ^dIs the ground seismic wave time course; u. of_i ^d、u_i ^pThe seismic wave time courses of the lower interface and the upper interface of the formation i are respectively, wherein i is 1, 2. u. of₀ ^d、u_i ^d、u_i ^pAre time series, j represents a time sample serial number, j is 0, 1,.. said, nt-1, j is 0 represents that the time is equal to zero;

step 7, seismic wave time course u₀ ^dCarrying out attenuation treatment according to time;

in the step 7, the seismic wave time travel u is processed according to the following formula₀ ^dCarrying out attenuation treatment according to time:

u(j)＝u₀ ^d(j)exp[-βjΔt] (9)

wherein the attenuation coefficient beta is-ln delta/t_l(ii) a Delta is a calculation precision value for controlling the attenuation coefficient and satisfies 0<δ<0.01；j＝0，1，......，nt-1；

Step 8, performing discrete Fourier transform on the seismic wave time course u (j) to obtain Fu (k);

in the step 8, the seismic wave time interval u (j) is subjected to discrete fourier transform according to the following formula:

wherein i is an imaginary unit; k is 0, 1,.. cnt-1;

step 9, judging whether the amplitude spectrum | Fu (k) | has a maximum value, if not, expanding nT by 20%, and returning to the step 8; if yes, determining the site excellent period T₀；

In step 9, it is determined whether the amplitude spectrum | fu (k) | has a maximum value according to the following formula:

| Fu (k) | > | Fu (k-1) | and | Fu (k) | > | Fu (k +1) | (11)

|Fu(k)|>0.5max(|Fu(1)|，|Fu(2)|，......，|Fu(nT-1)|) (12)

If | Fu (k) | satisfies the above condition, the site excellent period is calculated by the following formula:

T₀＝0.5t₀+kΔt (13)。

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