CN115857011B - Method for solving seismometer transfer function based on region optimization fitting - Google Patents
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Abstract
The invention provides a method for solving a seismometer transfer function based on region optimization fitting, which comprises the following steps: acquiring a transfer function to be solved of a target seismometer; preliminarily calibrating the transfer function to be solved based on the step response to obtain a preliminarily solved transfer function; performing Fourier inverse transformation on the preliminarily solved transfer function to obtain a theoretical impulse response function of the target seismometer; loading pulse signals at the input end of the target seismometer to obtain an actual pulse response waveform of the target seismometer; constructing a region optimization objective function according to the theoretical impulse response function and the actual impulse response waveform; and solving the regional optimization objective function to obtain a transfer function with completed calibration. The invention constructs the region optimization objective function by utilizing the theoretical impulse response function and the actual impulse response waveform and solves the region optimization objective function, thereby not only greatly reducing the operation amount of the transfer function calibration work, but also improving the calibration precision of the transfer function on the basis.
Description
Technical Field
The invention relates to the technical field of seismic exploration, in particular to a method for solving a transfer function of a seismometer based on region optimization fitting.
Background
The seismometer is used as a core element of seismic exploration, and the calculation of a transfer function directly influences the accuracy of seismic exploration data. The transfer function calibration methods widely used at present are a step response calibration method and a sine wave calibration method.
The step response method is mainly based on response curve fitting, and on one hand, the convergence algorithm used by the method is large in calculation amount; on the other hand, the influence of environmental noise cannot be removed, so that the calculation accuracy is low. The sine wave calibration method has higher calibration precision, but in order to ensure the precision, the density of frequency points must be increased, and the lower the frequency is, the longer the period is. Long-time testing may cause two problems, namely, environmental noise changes occur, and the testing accuracy is reduced; secondly, for the test of the ultra wide band and ultra wide band seismometers, the calibration workload is extremely huge.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a method for solving the transfer function of a seismometer based on region optimization fitting so as to solve the problem of low calibration precision of the transfer function of the seismometer.
In order to achieve the above object, the present invention provides the following solutions:
a method for solving for a seismometer transfer function based on a region optimization fit, comprising:
acquiring a transfer function to be solved of a target seismometer;
preliminarily calibrating the transfer function to be solved based on the step response to obtain a preliminarily solved transfer function;
performing Fourier inverse transformation on the preliminarily solved transfer function to obtain a theoretical impulse response function of the target seismometer;
loading pulse signals at the input end of the target seismometer to obtain an actual pulse response waveform of the target seismometer;
constructing a region optimization objective function according to the theoretical impulse response function and the actual impulse response waveform;
and solving the regional optimization objective function to obtain a transfer function with completed calibration.
Preferably, the transfer function to be solved is:
wherein H(s) is a transfer function to be solved, ζ is a damping coefficient, ω n For natural frequency, a is a constant coefficient, a=ki 0 M, K is seismometer sensitivity, I 0 For the direct current applied to the seismometer, m is the seismometer moving coil mass.
Preferably, the step response-based preliminary calibration of the transfer function to be solved to obtain a preliminary solved transfer function includes:
carrying out inverse Laplace transformation on the transfer function to be solved to obtain a seismometer step response curve;
constructing a transfer function preliminary solving formula by utilizing extreme points and inflection points on the step response curve of the seismometer;
and obtaining the preliminarily solved transfer function according to the transfer function preliminarily solving formula.
Preferably, the seismometer step response curve is:
where e (t) is the seismometer step response curve.
Preferably, the transfer function preliminary solution formula is:
wherein T is 1 T is the inflection point of the step response curve of the seismometer 0 Is the extreme point of the seismometer step response curve.
Preferably, said constructing a region optimization objective function from said theoretical impulse response function and said actual impulse response waveform comprises:
the formula is adopted:
constructing a region optimization objective function; where Δ is the region optimization objective function, B i (t) is the actual impulse response waveform, b i (t) is a theoretical impulse response function, N is B i Length of (t).
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
compared with the prior art, the method for solving the transfer function of the seismometer based on the area optimization fitting has the advantages that the area optimization objective function is constructed by utilizing the theoretical impulse response function and the actual impulse response waveform, and is solved, so that the calculation amount of the transfer function calibration work can be greatly reduced, and the calibration precision of the transfer function can be improved on the basis.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for determining a seismometer transfer function based on a region optimization fit in an embodiment provided by the invention;
FIG. 2 is a schematic diagram of a method for determining a seismometer transfer function based on a region optimization fit in an embodiment provided by the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the present application. The appearances of such phrases in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Those of skill in the art will explicitly and implicitly appreciate that the embodiments described herein may be combined with other embodiments.
The terms "first," "second," "third," and "fourth" and the like in the description and in the claims of this application and in the drawings, are used for distinguishing between different objects and not for describing a particular sequential order. Furthermore, the terms "comprise" and "have," as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, inclusion of a list of steps, processes, methods, etc. is not limited to the listed steps but may alternatively include steps not listed or may alternatively include other steps inherent to such processes, methods, products, or apparatus.
The invention aims to provide a method for solving a seismometer transfer function based on region optimization fitting so as to solve the problem of low calibration precision of the seismometer transfer function.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Referring also to fig. 1-2, a method for determining a seismometer transfer function based on a region optimization fit includes:
step 1: acquiring a transfer function to be solved of a target seismometer;
in practical applications, the transfer function of the seismometer in the low frequency band can be described by a second order system:
wherein, xi is the damping coefficient, omega n Is the natural frequency, A is a constant coefficient,
A＝KI 0 /m
k is seismometer sensitivity, I 0 For the direct current applied to the seismometer, m is the seismometer moving coil mass.
Step 2: preliminarily calibrating the transfer function to be solved based on the step response to obtain a preliminarily solved transfer function;
further, step 2 includes:
carrying out inverse Laplace transformation on the transfer function to be solved to obtain a seismometer step response curve;
constructing a transfer function preliminary solving formula by utilizing extreme points and inflection points on the step response curve of the seismometer;
and obtaining the preliminarily solved transfer function according to the transfer function preliminarily solving formula.
The above preliminary solution of the present invention is further described below with reference to specific examples:
and (3) carrying out inverse Lawster transformation on the (1), and obtaining according to a seismometer motion equation:
equation (2) is the curve of the step response of the seismometer.
Deriving e (T), let e '(T) =0, and obtaining extreme point of response curve, and setting e' (T) 0 ) =0, have
Maximum output voltage
Equivalent to
In the formula (5), T 0 The extreme point of the response curve is measurable, only xi is unknown quantity, and the ω can be obtained by solving xi n 。
Derivative e '(t) and let e' (t) =0, to obtain
From formula (6), T 1 ＝2T 0 .T 1 Is the inflection point of the response curve.
Will T 0 、T 1 Substitution formula (2), division, has:
substituting formula (4) into formula (7) has:
solving (8) to obtain ζ and ω n 。
Will be xi, omega n And T 0 The value is substituted into (2) to obtain the sensitivity
From this, the seismometer transfer function is preliminarily found.
Step 3: performing Fourier inverse transformation on the preliminarily solved transfer function to obtain a theoretical impulse response function of the target seismometer;
step 4: loading pulse signals at the input end of the target seismometer to obtain an actual pulse response waveform of the target seismometer;
step 5: constructing a region optimization objective function according to the theoretical impulse response function and the actual impulse response waveform; the area optimization objective function of the invention is as follows:
constructing a region optimization objective function; where Δ is the region optimization objective function, B i (t) is the actual impulse response waveform, b i (t) is a theoretical impulse response function, N is B i Length of (t).
Step 6: and solving the regional optimization objective function to obtain a transfer function with completed calibration.
The following description is made of the construction process of the objective function and the solving process thereof in combination with specific embodiments:
and (3) performing Fourier inverse transformation on the transfer function H(s) obtained in the step to obtain a theoretical impulse response function b (t) of the seismometer.
And loading pulse signals at the input end of the seismometer to be measured, recording the impulse response waveform B (t) of the seismometer, wherein the length of B (t) is N, and substituting the abscissa of each point B (t) into B (t).
The area optimization objective function to be solved is:
each coefficient of the theoretical transfer function obtained in the above step is set as an independent variable vector (x), and a parameter that minimizes the objective function Δ is obtained in the vicinity of x.
The invention adopts a region optimization algorithm, namely a Nelder-Mead simplex algorithm to solve a region optimization objective function. This algorithm uses a simplex consisting of n+1 points for the n-dimensional vector x. First to x 0 Adding the components x 0 (i) To surround the initial estimate x by 5% 0 A simplex is generated. Then using two of the above n vectors as simplex divided by x 0 Other elements, the simplex is modified repeatedly according to the following process:
the point list i=1, … …, n+1 in the current simplex is denoted by x (i).
The points in the simplex are ordered in the order of the minimum function value Δ (x (1)) to the maximum function value Δ (x (n+1)). At each step of the iteration, the algorithm discards the current worst point x (n+1) and accepts another point in the simplex.
Generating reflection points
r＝2m-x(n+1)，
Wherein the method comprises the steps of
And delta (r) is calculated.
If delta (x (1)). Ltoreq.delta (r) < delta (x (n)), r is accepted and the iteration is terminated.
If delta (r) < delta (x (1)), the extension point s is calculated
s＝m+2(m-x(n+1))
And calculates delta(s).
If delta(s) < delta (r), s is accepted and the iteration is terminated.
Otherwise, accept r and terminate the iteration.
If ΔR.gtoreq.ΔX (n), then execution is between m and either x (n+1) or r.
If delta (r) < delta (x (n+1)), then calculate
c＝m+(r-m)/2
And calculates delta (c) if delta (c) < delta (r), then c is accepted and the iteration is terminated.
Otherwise, go on to step 7.
If Δ (r). Gtoreq.Δ (x (n+1)), then calculation is performed
cc＝m+(x(n+1)-m)/2
And delta (cc) was calculated. If delta (cc) < delta (x (n+1)), then cc is accepted and the iteration is terminated.
Otherwise, go on to step 7.
Calculating n points
v(i)＝x(1)+(x(i)-x(1))/2
And calculates Δ (v (i)), i=2, …, n+1. The simplex in the next iteration is x (1), v (2), …, v (n+1).
The following description is further made on the calibration process of the transfer function by combining with a specific application scene:
step one, primarily calibrating a transfer function of a seismometer according to a step response:
the seismic data collector of the embodiment adopts EDAS-24GN, and the error is smaller than 1/10000. And loading +1V step voltage at the input end of the seismometer to be tested, setting the sampling rate to 800sps, and recording the voltage signal at the input end of the seismometer and the step response waveform of the seismometer.
Reading peak time T according to step response waveform 0 T is obtainable from formulae (4) and (6) 1 E (T) of the read response curve E (T) 0 ) And E (T) 1 ) Value, E (T) 0 ) And E (T) 1 ) Substituting formula (8) and solving a nonlinear unitary function about xi. The book is provided withExamples the zeta was solved by the bisection method, defined above and below as [1.001, 10]. Will be xi and T 0 Substituting (5) to obtain the natural frequency ω n 。
Will be xi, omega n And T 0 The value is substituted into equation (2) to obtain sensitivity K.
From this, the coefficients a of the seismometer transfer function H(s) are initially determined 1 ,b 1 ,b 2 ,b 3 Is a theoretical value of (a).
Second, the precise transfer function of the seismometer is calculated by using the area optimization algorithm
And loading a unit pulse signal at the input end of the seismometer to be measured, setting the sampling rate to 800sps, and recording the impulse response waveform B (t) of the seismometer.
And using a region optimization algorithm to obtain an accurate transfer function according to the theoretical transfer function obtained in the steps and the actually measured impulse response function.
First, the matlab calls an inpulse function, and the theoretical impulse response curve b (t) can be obtained directly from the coefficients in equation (11).
Then, let the argument x= [ a ] of the optimization algorithm 1 ,b 1 ,b 2 ,b 3 ]The measured value B (t) is introduced into matlab. Initial value of independent variable x 0 Setting the theoretical value obtained in the first step, wherein the objective function of the optimization algorithm is the sum of squares of errors delta of the theoretical response curve and the actually measured response curve, and the sum is shown in a formula (10).
Finally, performing region optimization fitting on the objective function delta, and calling an fminearch function to perform optimization calculation in the embodiment, wherein the calculation result is used as each coefficient of the formula (10), namely the accurate transfer function of the seismometer.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention constructs the region optimization objective function by utilizing the theoretical impulse response function and the actual impulse response waveform and solves the region optimization objective function, thereby not only greatly reducing the operation amount of the transfer function calibration work, but also improving the calibration precision of the transfer function on the basis.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the method disclosed in the embodiment, since it corresponds to the device disclosed in the embodiment, the description is relatively simple, and the relevant points are referred to the device part description.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (2)
1. A method for determining a seismometer transfer function based on a region optimization fit, comprising:
acquiring a transfer function to be solved of a target seismometer;
preliminarily calibrating the transfer function to be solved based on the step response to obtain a preliminarily solved transfer function;
the transfer function to be solved is as follows:
wherein H(s) is a transfer function to be solved, ζ is a damping coefficient, ω n For natural frequency, a is a constant coefficient, a=ki 0 M, K is seismometer sensitivity, I 0 For the direct current applied to the seismometer, m is the mass of the seismometer moving coil;
the step response-based preliminary calibration of the transfer function to be solved to obtain a preliminary solved transfer function comprises the following steps:
carrying out inverse Laplace transformation on the transfer function to be solved to obtain a seismometer step response curve;
constructing a transfer function preliminary solving formula by utilizing extreme points and inflection points on the step response curve of the seismometer;
obtaining a preliminarily solved transfer function according to the transfer function preliminarily solving formula;
specifically, for the inverse Lawster transform (1), according to the seismometer motion equation, it is possible to obtain:
equation (2) is the curve of the step response of the seismometer;
deriving e (T), let e '(T) =0, and obtaining extreme point of response curve, and setting e' (T) 0 ) =0, have
Maximum output voltage
Equivalent to
In the formula (5), T 0 The extreme point of the response curve is measurable, only xi is unknown quantity, and the ω can be obtained by solving xi n ；
Derivative e '(t) and let e' (t) =0, to obtain
From formula (6), T 1 ＝2T 0 .T 1 Is the inflection point of the response curve;
will T 0 、T 1 Substitution formula (2), division, has:
substituting formula (4) into formula (7) has:
solving (8) to obtain ζ and ω n ；
Will be xi, omega n And T 0 The value is substituted into (2) to obtain the sensitivity
Thus, the transfer function of the seismometer is preliminarily obtained;
performing Fourier inverse transformation on the preliminarily solved transfer function to obtain a theoretical impulse response function of the target seismometer;
loading pulse signals at the input end of the target seismometer to obtain an actual pulse response waveform of the target seismometer;
constructing a region optimization objective function according to the theoretical impulse response function and the actual impulse response waveform;
and solving the regional optimization objective function to obtain a transfer function with completed calibration.
2. A method of deriving a seismometer transfer function based on a region-optimized fit according to claim 1, characterized in that said constructing a region-optimized objective function from said theoretical impulse response function and said actual impulse response waveform comprises:
the formula is adopted:
constructing a region optimization objective function; where Δ is the region optimization objective function, B i (t) is the actual impulse response waveform, b i (t) is a theoretical impulse response function, N is B i Length of (t).
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