CN117233863B - A transfer function calibration method and device for a three-component seismograph - Google Patents
A transfer function calibration method and device for a three-component seismograph Download PDFInfo
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Abstract
The invention discloses a transfer function calibration method and a transfer function calibration device for a three-component seismograph, which are applied to the technical field of seismic exploration and comprise the following steps: reading the response signal and the calibration signal; inputting an initial damping coefficient and an initial self-vibration period, and respectively calculating an optimal damping coefficient and an optimal self-vibration period according to different precision requirements, so that the rapid fitting of the damping coefficient and the self-vibration period is realized; substituting the optimal damping coefficient and the optimal self-vibration period into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function; calculating zero points and poles of each order of the high-frequency band transfer function through optimization fitting to obtain an optimal high-frequency band transfer function; the product of the low-band transfer function and the high-band transfer function is the complete transfer function of the whole three-component seismometer.
Description
Technical Field
The invention relates to the technical field of seismic exploration, in particular to a transfer function calibration method and device of a three-component seismometer.
Background
With the popularization of three-component digital seismometers and the deep research of seismic data analysis methods, the transfer function is used as a key parameter of the three-component seismometers, and the accuracy degree of the transfer function is also required to be higher and higher. In a second-order over-damping closed-loop system of the geophone, the self-vibration period and damping coefficient of the geophone are related to the mechanical structure, materials, suspension mode, transportation, installation, environmental temperature, humidity and other factors of the seismometer in a working state, are the most important factors reflecting the performance of the whole geophone, are also key points of low-frequency expansion of the geophone, and are required to be subjected to precise calibration and fitting.
The transfer function is divided into a low-band transfer function and a high-band transfer function. The low-frequency band transfer function mainly comprises two parameters, namely damping and self-vibration period, and the damping and self-vibration period can be obtained by fitting and calculating calibration signals. In the traditional fitting method, as two parameters are uncertain, the calculated amount is large, the time cost is obviously increased, the precious time for seismic data acquisition is occupied, and the fitting method is not suitable for being embedded in a seismic instrument acquisition system. The method and the device provided by the invention can be used for quickly realizing the fitting of two parameters, and further obtaining the high-frequency band transfer function through the optimized fitting.
The seismograph comprises a detector and a data collector, a calibration signal generator is arranged in the data collector, and a calibration coil is arranged in the detector, so that the seismograph belongs to split system design, can only calibrate the detector, cannot calibrate the whole machine comprising the data collector, and cannot reflect the whole system response of the instrument. The independent calibration coil also increases the cost of the instrument and the debugging difficulty.
In order to overcome the defects, the application provides a transfer function calibration method and a transfer function calibration device of a three-component seismometer, a calibration circuit based on a complete machine is designed, and the calibration circuit is in a structure shared by acquisition and calibration, and does not need an additional calibration coil. Considering that the damping and self-vibration period of the detector have given values when leaving the factory, the damping and self-vibration period can be used as initial values to realize the rapid fitting of the damping and self-vibration period, and further, the zero point and the pole of each order of the high-frequency band transfer function are optimally fitted to obtain the complete transfer function of the whole three-component seismometer.
Disclosure of Invention
The application aims to provide a transfer function calibration method and device of a three-component seismometer, and aims to solve the problem.
In order to achieve the above purpose, the present application provides the following technical solutions:
The application provides a transfer function calibration method of a three-component seismograph, which comprises the following specific steps:
Reading the response signal and the calibration signal;
Inputting an initial damping coefficient and an initial self-vibration period;
Respectively calculating an optimal damping coefficient and an optimal self-vibration period according to different precision requirements, substituting the optimal damping coefficient and the optimal self-vibration period into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function, and calculating zero points and poles of each order of a high-frequency band transfer function through optimal fitting to obtain an optimal high-frequency band transfer function;
And outputting the product of the optimal low-frequency band transfer function and the optimal high-frequency band transfer function as a complete transfer function of the three-component seismometer.
Further, in the step of reading the response signal and the calibration signal, the method specifically includes the following steps:
the response signal is represented as U(s) by Laplace transformation in the frequency domain, and the calibration signal is The response signal U(s) is the output signal, and the calibration signalI.e. the input signal, the response signal U(s) and the calibration signalThe relation of (2) is expressed as:
where H(s) is the transfer function, expressed as:
H(s)＝H0(s)·H1(s) (2)
Wherein H 0(s) is a low-frequency band transfer function, H 1(s) is a high-frequency band transfer function, H(s) is a complete transfer function of the whole three-component seismometer, ω is a self-vibration period, and ζ is a damping coefficient; a and b are each zero and pole of H 1(s), Z is zero order, and P is pole order.
Further, in the step of calculating the optimal damping coefficient and the optimal self-vibration period according to different precision requirements, the method specifically comprises the following steps:
calculating an optimal self-vibration period according to the accuracy requirement of alpha%;
and calculating the optimal damping coefficient according to the accuracy requirement of beta percent.
Further, in the step of calculating the optimal self-oscillation period according to the accuracy requirement of α%, the method specifically includes the following steps:
the initial damping and the initial self-vibration period are respectively marked as xi 0 and omega 0, and the self-vibration period is modified according to the accuracy requirement of alpha percent, namely omega i＝ω0 (1+/-i.alpha percent), wherein i is the number of modification times, and adjustment and increment or adjustment and subtraction can be carried out; the initial damping xi 0 is unchanged;
Calculation of H 0(s)i by ζ 0 and ω i Namely, the response signal which is theoretically output at the ith time;
Normalizing U i(s) and the response signal U(s) which is actually output, and calculating a fitting difference delta i between U i(s) and U(s); if delta i exceeds the threshold value, adding 1 to the modification times i to recalculate; if δi is smaller than the threshold value, ω i is regarded as the optimal solution, and ω k is rewritten as the optimal self-oscillation period.
Further, in the step of calculating the optimal damping coefficient according to the accuracy requirement of β%, the method specifically includes the following steps:
Modifying a damping coefficient, namely, ζ j＝ξ0 (1+/-j.beta%) according to the accuracy requirement of beta percent, wherein j is the modification times, and the adjustment and the increment or the adjustment and the subtraction can be carried out; the optimal self-vibration period omega k is unchanged;
Calculation of H 0(s)j by ω k and ζ j I.e. the response signal of the jth theoretical output;
normalizing U j(s) and the response signal U(s) which is actually output, and calculating a fitting difference delta j between U j(s) and U(s); if delta j exceeds the threshold value, adding 1 to the modification times j to recalculate; if δj is smaller than the threshold, using ζ j as the optimal solution, rewriting ζ k as the optimal damping coefficient.
Further, in the step of substituting the optimal damping coefficient and the optimal self-oscillation period into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function, the method specifically includes the following steps:
Substituting the optimal damping coefficient and the optimal self-vibration period into the formula (3) to obtain the optimal H 0(s)k, and then obtaining the optimal low-frequency band transfer function as follows:
further, in the step of calculating the zero and the pole of each order of the high-frequency band transfer function through optimization fitting to obtain the optimal high-frequency band transfer function, the method specifically comprises the following steps:
Substituting the optimal low-band transfer function H 0(s)k into equation (2) according to equation (1), the high-band transfer function H 1(s) is:
extracting at least 2 (Z+P) frequency points from the calculated H 1(s), and performing optimization fitting on a and b in the formula (4) to obtain optimal a k and b k, namely obtaining each order zero and each pole of the optimal high-frequency band transfer function;
substituting the optimal zero points and poles of each step into the step (4) to obtain a high-frequency band transfer function H 1(s)k, wherein the optimal high-frequency band transfer function is as follows:
And substituting the formulas (6) and (7) into the formula (2), namely the product of the low-frequency band transfer function and the high-frequency band transfer function, so as to obtain the complete transfer function H(s) of the whole three-component seismometer.
The application provides a transfer function calibration device of a three-component seismometer, which comprises:
and a reading module: reading the response signal and the calibration signal;
an input module: inputting an initial damping coefficient and an initial self-vibration period;
The calculation module: respectively calculating an optimal damping coefficient and an optimal self-vibration period according to different precision requirements, substituting the optimal damping coefficient and the optimal self-vibration period into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function, and calculating zero points and poles of each order of a high-frequency band transfer function through optimal fitting to obtain an optimal high-frequency band transfer function;
And an output module: and outputting the product of the optimal low-frequency band transfer function and the optimal high-frequency band transfer function as a complete transfer function of the three-component seismometer.
The application provides equipment, which comprises a processor and a memory coupled with the processor, wherein the memory stores program instructions for realizing a transfer function calibration method of a three-component seismometer; the processor is used for executing the program instructions stored in the memory to realize the transfer function calibration of the three-component seismograph.
The application provides a storage medium storing program instructions executable by a processor for performing a transfer function calibration method for a three-component seismometer.
The application provides a transfer function calibration method and a transfer function calibration device for a three-component seismograph, which have the following beneficial effects:
According to the application, given values of damping and self-vibration period of the detector are considered when the detector leaves a factory, the damping and self-vibration period can be used as initial values, the initial damping coefficient and the initial self-vibration period are substituted into the low-frequency band transfer function to calculate, so that rapid fitting of the damping coefficient and the self-vibration period is realized, and the optimal low-frequency band transfer function is obtained; calculating zero points and poles of each order of the high-frequency band transfer function by optimization fitting to obtain the high-frequency band transfer function; the product of the transfer functions of the low frequency band and the high frequency band is used as the complete transfer function of the three-component seismometer, so that the quick calibration is realized;
The application also designs a calibration circuit of the three-component seismometer, which carries out filtering according to the low-frequency characteristic of the system, firstly substitutes the initial damping of the detector into a low-frequency band transfer function formula, continuously adjusts the self-vibration period according to the required precision by taking the initial self-vibration period given by a factory as a reference, and confirms the self-vibration period at the moment, namely the optimal self-vibration period under the condition that the normalized actual measurement response and theoretical response reach the maximum fitting degree; then, the damping is confirmed by the same method according to the self-vibration period, and the optimal damping is obtained; the calibration circuit can be adapted to detectors with more models, so that the application range is increased, and the calibration circuit has larger use potential; the adaptive calibration circuit is not required to be additionally designed for the calibration coil, the circuit design is simplified, the complexity of the calibration circuit is reduced, the reliability of a calibration system is improved, the production and transformation cost of the detector is reduced, electronic components are saved, and the manufacturing cost of the instrument is reduced as a whole.
Drawings
FIG. 1 is a flow chart of a transfer function calibration method of a three-component seismometer according to embodiment 1 of the present application;
FIG. 2 is a flow chart of parameter calculation according to embodiment 1 of the present application;
FIG. 3 is a schematic diagram of a transfer function calibration device of a three-component seismometer according to embodiment 2 of the present application;
FIG. 4 is a schematic diagram of a calibration circuit according to embodiment 2 of the present application;
fig. 5 is a schematic diagram of a device structure according to embodiment 3 of the present invention;
Fig. 6 is a schematic diagram of a storage medium structure according to embodiment 4 of the present invention.
Detailed Description
It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
The following description of the embodiments of the present application will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Example 1
Referring to fig. 1, a flow chart of a transfer function calibration method of a three-component seismometer according to embodiment 1 of the present application is shown; the method comprises the following specific steps:
s1: the response signal and the calibration signal are read.
In the present embodiment, the response signal is represented as U(s) in the frequency domain by Laplace transform, and the calibration signal isThe response signal U(s) is the output signal, and the calibration signalI.e. the input signal, the response signal U(s) and the calibration signalThe relation of (2) is expressed as:
where H(s) is the transfer function, expressed as:
H(s)＝H0(s)·H1(s) (2)
wherein H 0(s) is a low-frequency band transfer function, H 1(s) is a high-frequency band transfer function, H(s) is a complete transfer function of the whole three-component seismometer, ω is a self-vibration period, and ζ is a damping coefficient; a and b are each zero and pole of H 1(s), Z is zero order, P is pole order, Z and P are both 2; the calibration of the transfer function is thus to determine four parameters: ω, ζ, a and b.
S2: an initial damping coefficient and an initial self-oscillation period are input.
S3: respectively calculating an optimal damping coefficient and an optimal self-vibration period according to different precision requirements, substituting the optimal damping coefficient and the optimal self-vibration period into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function, and calculating zero points and poles of each order of a high-frequency band transfer function through optimal fitting to obtain an optimal high-frequency band transfer function;
In this embodiment, the steps of calculating the optimal damping coefficient and the optimal self-oscillation period according to different accuracy requirements respectively include the following steps S31 to S32, and the implementation manner of each step is described in detail below.
S31: and calculating the optimal self-oscillation period according to the accuracy requirement of alpha percent.
Taking the vertical component of the three-component seismometer as an example, respectively marking the initial damping and the initial self-vibration period as xi 0 and omega 0, and modifying the self-vibration period according to the accuracy requirement of alpha percent (alpha=1), namely omega i＝ω0 (1+/-i.alpha percent), wherein i is the number of modification times, and can be adjusted, increased or reduced; the initial damping xi 0 is unchanged;
H 0(s)i is calculated by ζ 0 and ω i, and the high-band transfer function H 1(s) is temporarily disregarded, then Namely, the response signal which is theoretically output at the ith time;
Normalizing U i(s) and the response signal U(s) which is actually output, and calculating a fitting difference delta i between U i(s) and U(s); if delta i exceeds the threshold value, adding 1 to the modification times i to recalculate; if δi is smaller than the threshold value, ω i is taken as the optimal solution, rewritten into ω k and taken as the optimal self-oscillation period, wherein the threshold value is 1%.
S32: and calculating the optimal damping coefficient according to the accuracy requirement of beta percent.
Modifying a damping coefficient according to the accuracy requirement of beta% (beta=1), namely, ζ j＝ξ0 (1+/-j·beta%), wherein j is the modification times, and can be adjusted, increased or reduced; the optimal self-vibration period omega k is unchanged;
H 0(s)j is calculated by ω k and ζ j, and the high-band transfer function H 1(s) is temporarily disregarded, then (S). H 0(s)j, namely the response signal theoretically output by the jth time;
Normalizing U j(s) and the response signal U(s) which is actually output, and calculating a fitting difference delta j between U j(s) and U(s); if delta j exceeds the threshold value, adding 1 to the modification times j to recalculate; if δj is smaller than the threshold, using ζ j as the optimal solution, rewriting ζ k as the optimal damping coefficient, where the threshold is 1%.
Substituting the optimal damping coefficient and the optimal self-vibration period into the formula (3) to obtain the optimal H 0(s)k, and then obtaining the optimal low-frequency band transfer function as follows:
Substituting the optimal low-band transfer function H 0(s)k into equation (2) according to equation (1), the high-band transfer function H 1(s) is:
extracting at least 2 (Z+P) frequency points from the calculated H 1(s), and performing optimization fitting on a and b in the formula (4) to obtain optimal a k and b k, namely obtaining each order zero and each pole of the optimal high-frequency band transfer function;
substituting the optimal zero points and poles of each step into the step (4) to obtain a high-frequency band transfer function H 1(s)k, wherein the optimal high-frequency band transfer function is as follows:
s4: and outputting the product of the optimal low-frequency band transfer function and the optimal high-frequency band transfer function as a complete transfer function of the three-component seismometer.
In this embodiment, equations (6) and (7) are substituted into equation (2), i.e., the product of the low-band transfer function and the high-band transfer function, to obtain the complete transfer function H(s) of the three-component seismograph complete machine.
Referring to fig. 2, a flow chart of parameter calculation according to embodiment 1 of the present application is shown.
Firstly, reading response data U(s) of actual test, and reading calibration signalsInputting a damping coefficient xi 0 and a self-vibration period omega 0 as initial values; modifying the self-vibration period according to the accuracy requirement of alpha percent, substituting xi 0 and omega i to calculate H 0(s)i, and temporarily not considering the high-frequency band transfer function H 1(s), thenAnd normalizing U i(s) and U(s); judging whether the requirement is met or not according to the fitting difference delta i of the U i(s) and the U(s), and if the fitting difference delta i exceeds a threshold value, adding 1 to the modification times i to recalculate; if delta i is smaller than the threshold value, taking omega i as an optimal solution, and rewriting omega k as an optimal self-oscillation period; then modifying the damping coefficient according to the accuracy requirement of beta percent, substituting omega k and xi j to calculate H 0(s)j, and temporarily not considering the high-frequency band transfer function H 1(s), thenAnd normalizing U j(s) and U(s); judging whether the requirement is met or not according to the fitting difference delta j of U j(s) and U(s), if delta j exceeds the threshold value, adding 1 to the modification times j for recalculation; if δj is smaller than the threshold, using ζ j as the optimal solution, rewriting ζ k as the optimal damping coefficient, and further obtaining the optimal low-frequency band transfer function H 0(s)k, then obtaining the high-frequency band transfer functionExtracting at least 2 (Z+P) frequency points from the high-frequency band transfer function, and performing optimization fitting to obtain zero points and poles of each order of the high-frequency band transfer function, thereby obtaining an optimal high-frequency band transfer function H 1(s)k; and obtaining the complete transfer function H(s) of the whole three-component seismometer by the product of the low-frequency band transfer function and the high-frequency band transfer function.
In summary, in embodiment 1 of the present application, the damping and self-vibration periods given when the geophone leaves the factory are substituted as initial values into the low-frequency band transfer function to perform calculation, so as to realize rapid fitting of the damping coefficient and the self-vibration period, and obtain the optimal low-frequency band transfer function; calculating zero points and poles of each order of the high-frequency band transfer function by optimization fitting; the product of the low-frequency band transfer function and the high-frequency band transfer function is used as the complete transfer function of the whole three-component seismometer, so that the quick calibration is realized.
Example 2
Referring to fig. 3, a schematic structural diagram of a transfer function calibration device of a three-component seismometer according to embodiment 2 of the present application is shown; comprising the following steps:
and a reading module: reading the response signal and the calibration signal;
an input module: inputting an initial damping coefficient and an initial self-vibration period;
The calculation module: respectively calculating an optimal damping coefficient and an optimal self-vibration period according to different precision requirements, substituting the optimal damping coefficient and the optimal self-vibration period into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function, and calculating zero points and poles of each order of a high-frequency band transfer function through optimal fitting to obtain an optimal high-frequency band transfer function;
And an output module: and outputting the product of the optimal low-frequency band transfer function and the optimal high-frequency band transfer function as a complete transfer function of the three-component seismometer.
Fig. 4 is a schematic diagram of a calibration circuit according to embodiment 2 of the present application; the method specifically comprises the following steps:
and a micro control unit: for starting a calibration procedure;
a digital-to-analog converter: for generating a calibration voltage;
voltage dividing, current limiting, multiplexing circuit: matching corresponding detector components according to built-in resistors and voltage distribution to generate calibration signals of different forms, namely input signals Laplace transform of (A)
Three-component detector: generating a response signal based on the input signal;
The modulus collector: collecting the response signals, and generating output response signals U (t), wherein the Laplace transformation of U (t) is U(s);
Communication interaction port: and the response signal u (t) is generated by the micro control unit and is sent to the upper computer through the communication interaction port.
In the embodiment, a calibration circuit of the three-component seismometer is designed based on the principle of whole machine calibration, and the structure shared by acquisition and calibration is followed, so that an additional calibration coil is not needed. In a second-order over-damping closed-loop system of the geophone, the self-vibration period and damping coefficient of the geophone are related to the mechanical structure, materials, suspension mode, transportation, installation, environmental temperature, humidity and other factors of the seismometer in a working state, are the most important factors reflecting the performance of the whole geophone, are also key points of low-frequency expansion of the geophone, and are required to be subjected to precise calibration and fitting. The traditional inversion fitting method is large in calculated amount and is not suitable for being embedded into a seismic instrument acquisition system. Considering that the damping and self-vibration period of the detector have given values when leaving the factory, the detector can be used as an initial value for quick fitting calibration.
The parameter fitting thinking is as follows: firstly, substituting initial damping of a detector into a theoretical low-frequency band transfer function formula, taking a factory-set initial self-vibration period as a reference, continuously adjusting the self-vibration period according to required precision, and confirming the self-vibration period at the moment, namely the optimal self-vibration period under the condition that normalized actual measurement response and theoretical response reach maximum fitting degree; then, the damping is confirmed with the same method and the optimal self-vibration period, and the optimal damping is obtained.
In summary, in embodiment 2 of the present application, a signal is first read by a reading module, and then an initial damping coefficient and an initial self-oscillation period are input by an input module; then the calculation module carries out fine adjustment on the initial damping coefficient and the initial self-vibration period respectively according to different precision requirements, iterates to calculate a response signal which is theoretically output, calculates a fitting difference between the response signal and the response signal which is actually output until the fitting requirement is met, obtains the optimal damping coefficient and the optimal self-vibration period, and calculates optimal zero points and poles of each order in the high-frequency band transfer function through optimal fitting; finally, outputting an optimal low-frequency band transfer function and an optimal high-frequency band transfer function by an output module, and outputting the product of the optimal low-frequency band transfer function and the optimal high-frequency band transfer function as a complete transfer function of the whole three-component seismometer, so that quick calibration is realized; the calibration circuit of the three-component seismometer is designed, a structure shared by acquisition and calibration is followed, an additional calibration coil is not needed, the circuit design is simplified, the complexity of the calibration circuit is reduced, the reliability of a calibration system is improved, the production and transformation cost of the detector is reduced, electronic components are saved, and the manufacturing cost of the instrument is reduced as a whole.
Example 3
Fig. 5 is a schematic diagram of an apparatus structure according to an embodiment of the application. The device 50 includes a processor 51, a memory 52 coupled to the processor 51.
The memory 52 stores program instructions for implementing a transfer function calibration method for a three-component seismometer as described above.
The processor 51 is configured to execute program instructions stored in the memory 52 to effect transfer function calibration of the three-component seismometer.
The processor 51 may also be referred to as a CPU (Central Processing Unit ).
The processor 51 may be an integrated circuit chip with signal processing capabilities. Processor 51 may also be a general purpose processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
Example 4
Fig. 6 is a schematic structural diagram of a storage medium according to an embodiment of the application. The storage medium of the embodiment of the present application stores a program file 61 capable of implementing all the methods described above, where the program file 61 may be stored in the storage medium in the form of a software product, and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) or a processor (processor) to execute all or part of the steps of the methods of the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, an optical disk, or other various media capable of storing program codes, or a computer, a server, a mobile phone, a tablet, or other devices.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, apparatus, article, or method. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, apparatus, article, or method that comprises the element.
The foregoing description is only of the preferred embodiments of the present application and is not intended to limit the scope of the application, and all equivalent structures or equivalent processes using the descriptions and drawings of the present application or direct or indirect application in other related technical fields are included in the scope of the present application.
Although embodiments of the present application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the application, the scope of which is defined in the appended claims and their equivalents.
Of course, the present invention can be implemented in various other embodiments, and based on this embodiment, those skilled in the art can obtain other embodiments without any inventive effort, which fall within the scope of the present invention.
Claims (7)
1. A transfer function calibration method of a three-component seismometer is characterized by comprising the following specific steps:
Reading the response signal and the calibration signal;
inputting an initial self-vibration period and an initial damping coefficient;
respectively calculating an optimal self-vibration period and an optimal damping coefficient according to different precision requirements, substituting the optimal self-vibration period and the optimal damping coefficient into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function, and calculating zero points and poles of each order of a high-frequency band transfer function through optimal fitting to obtain an optimal high-frequency band transfer function;
outputting the product of the optimal low-frequency band transfer function and the optimal high-frequency band transfer function as a complete transfer function of the three-component seismometer;
The method specifically comprises the following steps of:
Calculating an optimal self-vibration period according to the accuracy requirement of alpha%; the method comprises the following steps:
the initial damping and the initial self-vibration period are respectively marked as xi 0 and omega 0, and the self-vibration period is modified according to the accuracy requirement of alpha percent, namely omega i＝ω0 (1+/-i.alpha percent), wherein i is the number of modification times, and adjustment and increment or adjustment and subtraction can be carried out; the initial damping xi 0 is unchanged;
Calculation of the modified i-th order low-band transfer function H 0(s)i by ζ 0 and ω i I.e. the response signal of the ith theoretical output, whereS is a Laplacian operator and is a calibration signal;
Normalizing U i(s) and the response signal U(s) which is actually output, and calculating a fitting difference delta i between U i(s) and U(s); if delta i exceeds the threshold value, adding 1 to the modification times i to recalculate; if delta i is smaller than the threshold value, taking omega i as an optimal solution, and rewriting omega k as an optimal self-oscillation period;
Calculating an optimal damping coefficient according to the beta percent precision requirement, wherein the optimal damping coefficient is specifically as follows:
Modifying a damping coefficient, namely, ζ j＝ξ0 (1+/-j.beta%) according to the accuracy requirement of beta percent, wherein j is the modification times, and the adjustment and the increment or the adjustment and the subtraction can be carried out; the optimal self-vibration period omega k is unchanged;
calculation of modified j times low-band transfer function H 0(s)j by ω k and ζ j I.e. the response signal of the jth theoretical output;
normalizing U j(s) and the response signal U(s) which is actually output, and calculating a fitting difference delta j between U j(s) and U(s); if delta j exceeds the threshold value, adding 1 to the modification times j to recalculate; if δj is smaller than the threshold, using ζ j as the optimal solution, rewriting ζ k as the optimal damping coefficient.
2. A method of calibrating a transfer function of a three-component seismometer according to claim 1, characterized in that in the step of reading the response signal and the calibration signal, it comprises the steps of:
the response signal is represented as U(s) by Laplace transformation in the frequency domain, and the calibration signal is The response signal U(s) is the output signal, and the calibration signalI.e. the input signal, the response signal U(s) and the calibration signalThe relation of (2) is expressed as:
Wherein H(s) is the complete transfer function of the three-component seismometer complete machine, and is expressed as:
H(s)＝H0(s)·H1(s) (2)
Wherein H 0(s) is a low-frequency band transfer function, H 1(s) is a high-frequency band transfer function, H(s) is a complete transfer function of the whole three-component seismometer, ω is a self-vibration period, and ζ is a damping coefficient; a and b are each zero and pole of H 1(s), Z is zero order, and P is pole order.
3. The method for calibrating a transfer function of a three-component seismometer according to claim 1, wherein in the step of substituting the optimal damping coefficient and the optimal self-vibration period into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function, the method specifically comprises the following steps:
Substituting the optimal damping coefficient and the optimal self-vibration period into a low-frequency band transfer function to obtain an optimal H 0(s)k, wherein the optimal low-frequency band transfer function is as follows:
4. the method for calibrating a transfer function of a three-component seismometer according to claim 1, wherein in the step of calculating the zero and the pole of each order of the high-frequency band transfer function by optimization fitting, the optimal high-frequency band transfer function is obtained, specifically comprising the steps of:
Based on the response signal U(s) and the calibration signal Substituting the optimal low-frequency band transfer function H 0(s)k into the complete transfer function of the three-component seismometer complete machine, the high-frequency band transfer function H 1(s) is:
Extracting at least 2 (Z+P) frequency points from the calculated H 1(s), and performing optimization fitting on a and b in the high-frequency band transfer function to obtain optimal a k and b k, namely obtaining the zero point and the pole of each step of the high-frequency band transfer function;
Substituting the optimal zero point and the pole of each step into the high-frequency band transfer function to obtain a high-frequency band transfer function H 1(s)k, wherein the optimal high-frequency band transfer function is as follows:
Substituting equations (6) and (7) into the complete transfer function of the three-component seismograph complete machine, namely the product of the low-frequency band transfer function and the high-frequency band transfer function, so as to obtain the complete transfer function H(s) of the three-component seismograph complete machine.
5. An apparatus for a transfer function calibration method for a three-component seismometer according to claim 1, characterized by comprising:
and a reading module: reading the response signal and the calibration signal;
an input module: inputting an initial damping coefficient and an initial self-vibration period;
The calculation module: respectively calculating an optimal damping coefficient and an optimal self-vibration period according to different precision requirements, substituting the optimal damping coefficient and the optimal self-vibration period into a low-frequency band transfer function to obtain an optimal low-frequency band transfer function, and calculating zero points and poles of each order of a high-frequency band transfer function through optimal fitting to obtain an optimal high-frequency band transfer function;
And an output module: and outputting the product of the optimal low-frequency band transfer function and the optimal high-frequency band transfer function as a complete transfer function of the three-component seismometer.
6. An apparatus comprising a processor, a memory coupled to the processor, wherein the memory stores program instructions for implementing a transfer function calibration method of a three-component seismometer of any one of claims 1-4; the processor is used for executing the program instructions stored in the memory to realize the transfer function calibration of the three-component seismograph.
7. A storage medium storing program instructions executable by a processor for performing a transfer function calibration method of a three-component seismometer according to any one of claims 1-4.
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