Zero-phase corrector for moving-coil geophone based on state variable shaper

Abstract

The invention discloses a moving-coil geophone zero-phase corrector based on a state variable shaper. The zero-phase corrector comprises a state variable shaper, a differential-to-single-ended module and a single-ended-to-differential module. After a moving-coil geophone signal is input into a differential signal, the signal is converted into a single-ended signal suitable for filtering through the differential-to-single-ended module, and a high-pass filter, a band-pass filter and a low-pass filter in the state variable shaper correct the phase characteristic of the frequency response of the geophone to a zero-phase attribute. And finally, the single-ended to differential module converts the single-ended signal into a differential signal again and outputs the differential signal. The phase characteristic correction method can be used for phase characteristic correction of differential signals of the moving-coil geophone, low-frequency response can be expanded while the phase is corrected by changing resistance value adjustment, gain stability in the original bandwidth is kept, phase characteristic correction is provided for output of the moving-coil geophone with different frequencies and amplitudes, and the correction precision of the moving-coil geophone is improved. And the accuracy of the detector signal phase is improved.

Description

Technical Field

[0001] The present invention relates to the field of geophysical signal processing, and in particular to a zero phase correction method for a moving coil seismic detector. The invention is specifically applied to the field of analog signal processing of a moving coil seismic detector, and can perform zero phase correction on the output signal of a moving coil seismic detector with different phase characteristics. Background Art

[0002] Seismic sensors are the core components of seismic exploration, mainly including moving coil, MEMS, piezoelectric geophones and pendulum broadband seismometers. Moving coil seismic geophones are widely used in geophysical exploration due to their high sensitivity and low mechanical noise. As shown. The moving coil seismic detector uses the relative movement between the inertial body and the shell to make the coil cut the magnetic flux lines in the magnetic field, generate electromotive force at both ends of the coil, and thus convert the ground vibration into an electrical signal. Therefore, it has extremely high sensitivity and can detect tiny ground vibrations. The output signal is a differential voltage signal, and the signal frequency band is mainly distributed in 5~300Hz. However, due to the different response characteristics of electronic components to different frequencies, the output voltage signal of the moving coil seismic detector has a phase delay. Because it has the characteristics of a second-order high-pass filter, such as Figure 2 As shown in the figure, the lower the frequency, the greater the phase delay, which can exceed 100°, or even approach phase reversal. In seismic data acquisition and processing, the phase delay of seismic data often seriously affects the data processing effect, and avoiding phase distortion through software correction cannot effectively remove the phase delay, thus affecting the acquisition quality and reliability of seismic data.

[0003] The state variable shaper is a zero phase correction circuit composed of an adder and two integrators. It can output the effects of high-pass, band-pass and low-pass filters at different output ports. Corresponding to different phase changes, it forms a linear combination by summing products of different multiples to compensate for the phase delay of the output signal, thereby correcting the phase of the output signal. Through the dynamic adjustment of the state variable, a filter with a specific frequency domain response can be designed to achieve accurate phase correction, and it has a certain robustness to changes in component parameters and non-ideal characteristics of the circuit. It is suitable for processing analog signals of moving coil seismic detectors, and provides a possibility for solving the output phase delay of moving coil seismic detectors. Summary of the invention

[0004] In response to the problem of phase delay in the output of a moving coil geophone, the present invention proposes a moving coil geophone zero phase corrector based on a state variable shaper, which aims to correct the phase of the moving coil geophone signal to 0°, and achieve zero phase correction of the frequency response of the moving coil geophone with different phase characteristics by adjusting circuit parameters such as resistance value. At the same time, considering the power consumption requirements, single and dual power supply modes are selectable.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A zero-phase corrector for a moving coil seismic detector based on a state variable shaper is formed by connecting a differential to single-end module, a state variable shaper module, a single-end to differential module and a single-double power supply selection module.

[0007] Among them, the frequency characteristics of the state variable shaper module system only consider 5~300Hz, and it includes three parts: high-pass filter, band-pass filter and low-pass filter. The high-pass filter includes a first adder U1, the band-pass filter includes a first integrator U2 and a first inverter U4, and the low-pass filter includes a second integrator U3.

[0008] The first adder U1 of the high-pass filter is composed of a first adder operational amplifier, a first resistor R1 and a second resistor R2. The first resistor R1 is used as a feedback resistor to connect the negative input terminal of the first adder operational amplifier and the output terminal of the second integrator U3. The second resistor R2 is connected to the negative input terminal of the first adder U1 and the output terminal of the first adder operational amplifier. The output terminal of the first adder operational amplifier is the output port of the high-pass filter, and the phase is substantially zero.

[0009] The first integrator U2 in the bandpass filter is composed of a first integrator operational amplifier, a third resistor R3, a fourth resistor R4 and a capacitor C1. The third resistor R3 connects the output end of the first adder U1 and the negative input end of the operational amplifier. The fourth resistor R4 and the first capacitor C1 are the feedback resistor and feedback capacitor of the first integrator operational amplifier, which are connected in parallel to the negative input end and the output end of the first integrator operational amplifier to form an inverting integrator. The output end of the first integrator U2 has the frequency characteristics of the bandpass filter and provides a phase leading by about 90°. The output end of the first integrator U2 is connected to the first Inverter U4, the first inverter U4 is composed of a first inverter operational amplifier, a seventh resistor R7, an eighth resistor R8 and a twenty-fourth resistor R24, the seventh resistor R7 is connected to the negative input terminal of the first inverter operational amplifier and the output terminal of the first integrator U2, the twenty-fourth resistor R24 ​​is connected to the positive input terminal of the first inverter operational amplifier and the input reference voltage or ground, the eighth resistor R8 is a feedback resistor of the first inverter operational amplifier connected to the negative input terminal and the output terminal of the first inverter operational amplifier, the first inverter U4 constituted by the bandpass filter does not change the phase characteristic;

[0010] The second integrator U3 in the low-pass filter is composed of a second integrator operational amplifier, a fifth resistor R5, a sixth resistor R6 and a second capacitor C2. The fifth resistor R5 connects the output end of the first integrator U2 and the negative input end of the second integrator operational amplifier. The sixth resistor R6 and the second capacitor C2 are the feedback resistor and feedback capacitor of the second integrator operational amplifier, which are connected in parallel to the negative input end and the output end of the second integrator operational amplifier. The output end of the second integrator U3 has the frequency characteristics of a low-pass filter, providing a phase advance of about 180°.

[0011] The outputs of the high-pass filter, the band-pass filter and the low-pass filter are respectively connected to the ninth resistor R9, the tenth resistor R10 and the eleventh resistor R11, which are respectively used as the resistors of the summation coefficients of the low-pass, band-pass and high-pass filters to determine the multiples of the filter for summation; the ninth resistor R9, the tenth resistor R10 and the eleventh resistor R11 are connected to the second adder U5 and the second inverter U6;

[0012] The twelfth resistor R12 in the second adder U5 is connected to the output end and the negative input end of the second adder operational amplifier in the second adder U5 as a feedback resistor of the second adder U5, so as to determine the amplification factor during summation. The twenty-first resistor R21 is connected to the positive input end of the operational amplifier and the input reference voltage or ground.

[0013] The second inverter U6 can ensure that the phase will not change due to the existence of the adder. The second inverter U6 is composed of a second inverter operational amplifier, a thirteenth resistor R13, a fourteenth resistor R14 and a twenty-second resistor R22. The thirteenth resistor R13 is connected to the negative input terminal of the second inverter operational amplifier and the output terminal of the second adder U5. The twenty-second resistor R22 is connected to the positive input terminal of the second inverter operational amplifier and the input reference voltage or ground. The fourteenth resistor R14 is a feedback resistor of the second inverter operational amplifier and is connected to the negative input terminal and the output terminal of the operational amplifier.

[0014] The state variable shaper module transfer function is as follows:

[0015]

[0016] In formula (1), s represents the frequency in the Laplace transform domain, K1, K2, K3 are the summation coefficients of high pass, band pass, and low pass. Different summation coefficients correspond to different linear combinations. By changing the summation coefficients, the transfer function of the circuit construction can be changed to achieve phase characteristic correction of different detector output frequency responses. The summation coefficients K1, K2, K3 follow the following relationship:

[0017]

[0018] Where R9 represents the resistance value of the ninth resistor R9, R 10 Represents the resistance value of the tenth resistor R10, R 11 represents the resistance value of the eleventh resistor R11;

[0019] In formula (1), , , They are the transfer functions of high-pass, band-pass, and low-pass filters, respectively, and their expressions are as follows:

[0020]

[0021]

[0022]

[0023] In the above transfer functions (3) to (5), C1 represents the capacitance of the first capacitor C1, C2 represents the capacitance of the second capacitor C2, R1 represents the resistance of the first resistor R1, R2 represents the resistance of the resistor R2, R3 represents the resistance of the third resistor R3, R4 represents the resistance of the fourth resistor R4, R5 represents the resistance of the fifth resistor R5, and R6 represents the resistance of the sixth resistor R6;

[0024] set up represents the target transfer function used for zero phase correction, and the transfer function H2(s) of the moving coil geophone zero phase corrector after series connection, respectively:

[0025]

[0026]

[0027] In formula (6) , are the cutoff frequency and damping ratio of the transfer function of the moving coil geophone, , are the cutoff frequency and damping ratio of the transfer function of the zero-phase correction circuit respectively; in formula (7) is the gain of the transfer function of the moving coil geophone;

[0028] make , combined with reasonable design and selection of resistor and capacitor parameters, the parameters C1, C2, R1, R2, R3, R4, R5, R6, R9, R 10 , R 11 , K1, K2 and K3 can be solved, and the zero phase correction of the detector can be performed based on the solved circuit parameters;

[0029] That is, the transfer function of the detector connected in series with the zero phase correction circuit is Phase characteristics The phase magnitude at 5 Hz is , as follows:

[0030]

[0031] , Knowing that, we can solve To determine the target transfer function for zero phase correction .

[0032] The differential-to-single-ended module includes a differential-to-single-ended operational amplifier, a fifteenth resistor R15, a sixteenth resistor R16, a seventeenth resistor R17 and an eighteenth resistor R18; wherein the fifteenth resistor R15 is connected to the positive end of the input signal, and is connected in parallel with the sixteenth resistor R16 to the positive end of the differential-to-single-ended operational amplifier input, and the sixteenth resistor R16 is grounded or connected to a reference voltage; the seventeenth resistor R17 is connected to the negative end of the input signal, and is connected in parallel with the eighteenth resistor R18 to the negative end of the differential-to-single-ended operational amplifier input, and the single-ended signal is input to the state variable shaper module; the fifteenth resistor R15, the sixteenth resistor R16, the seventeenth resistor R17 and the eighteenth resistor R18 have equal resistance values.

[0033] The single-ended to differential module includes an inverting proportional amplifier. One path of the single-ended output signal is directly connected to the positive output terminal, and the other path is connected to the negative output terminal through the inverting proportional amplifier. The amplification factor of the inverting proportional amplifier is 1; the subtraction of the two signals eliminates the DC component, and the AC part is twice the original AC signal.

[0034] The inverting proportional amplifier is composed of an inverting proportional amplifier operational amplifier and a nineteenth resistor R19, a twentieth resistor R20 and a twenty-third resistor R23. The nineteenth resistor R19 is connected to the negative input terminal of the inverting proportional amplifier operational amplifier, the twentieth resistor R20 is connected to the output terminal and the negative input terminal of the inverting proportional amplifier operational amplifier as a feedback resistor, and the twenty-third resistor R23 is connected to the positive input terminal of the inverting proportional amplifier operational amplifier and the input reference voltage or ground; wherein the nineteenth resistor R19 and the twentieth resistor R20 have equal resistance values.

[0035] The moving coil seismic detector zero phase corrector based on the state variable shaper in the present invention also includes a single power supply and dual power supply mode selection module, which provides single power supply and dual power supply modes for selection. The differential-to-single-ended operational amplifier, the first integrator operational amplifier, the first inverter operational amplifier, the second integrator operational amplifier, the second adder operational amplifier, the second inverter operational amplifier and the single-ended-to-differential operational amplifier can select a single power supply or a dual power supply circuit structure through a jumper cap. When the single power supply is used, the negative voltage terminal of the operational amplifier is connected to the ground, and the positive input terminal is connected to the reference voltage, that is, half of the positive power supply voltage; when the dual power supply is used, the negative voltage terminal of the operational amplifier is connected to the negative power supply, and the positive input terminal is grounded.

[0036] Beneficial effects of the present invention:

[0037] Compared with the prior art, the zero phase correction method of the present invention can correct the phase characteristics of the frequency response with different phase characteristics by constructing a state variable shaper circuit. In addition, the circuit expands the low-frequency response of the detector by constructing a linear combination of high-pass, band-pass, and low-pass filter circuits, thereby improving the acquisition quality and reliability of seismic data.

[0038] After correction by the phase correction circuit, the phase delay of the moving coil geophone can be effectively compensated, so that the phase is corrected to zero phase, especially the phase delay in the low-frequency band is effectively controlled, while keeping the original frequency band gain unchanged, the low-frequency response of the geophone is expanded, which significantly expands the application prospects of moving coil geophones in data processing and further improves the application accuracy of moving coil geophones. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] This is a schematic diagram of a moving coil seismic detector, 1-housing, 2-spring sheet, 3-coil, 4-coil frame, 5-permanent magnet.

[0040] is the Bode plot of the transfer function of the detector output.

[0041] It is the overall block diagram of phase correction.

[0042] This is the circuit schematic of the differential to single-ended module.

[0043] It is the circuit schematic diagram of the state variable shaper.

[0044] is the Bode plot of the state variable shaper circuit.

[0045] This is the circuit schematic of the single-ended to differential module.

[0046] Figure 8 It is a single or dual power mode selection structure. DETAILED DESCRIPTION

[0047] The technical solution of the present invention is further explained and illustrated in the form of specific embodiments below.

[0048] like Figure 3 As shown, the present invention is a zero-phase corrector for a moving coil seismic detector based on a state variable shaper, which is formed by connecting a differential to single-ended module, a state variable shaper module and a single-ended to differential module. The following are the detailed steps and methods for implementing these modules:

[0049] 1. Differential to single-ended module

[0050] The circuit diagram of the differential to single-ended module is as follows As shown, it is mainly a subtractor, which consists of an operational amplifier, a fifteenth resistor R15, a sixteenth resistor R16, a seventeenth resistor R17 and an eighteenth resistor R18; wherein the fifteenth resistor R15 is connected to the positive end of the input signal, and is connected in parallel with the sixteenth resistor R16 to the positive end of the operational amplifier input, and the sixteenth resistor R16 is grounded or connected to a reference voltage; the seventeenth resistor R17 is connected to the negative end of the input signal, and is connected in parallel with the eighteenth resistor R18 to the negative end of the operational amplifier input, and the single-ended signal is input to the state variable shaper module.

[0051] In order to simplify the calculation and balance the circuit, the resistance values ​​of the fifteenth resistor R15, the sixteenth resistor R16, the seventeenth resistor R17 and the eighteenth resistor R18 in the circuit have the following relationship: R18 / R17=R16 / R15. At this time, the expression of the circuit can be calculated.

[0052] Assume the positive terminal of the differential signal is , the negative terminal is , then the converted single-ended signal for

[0053]

[0054] The subtractor pre-processes the differential signal and converts it into a single-ended signal suitable for the state variable shaper.

[0055] If the resistance values ​​of the fifteenth resistor R15, the sixteenth resistor R16, the seventeenth resistor R17 and the eighteenth resistor R18 are equal, the output single-ended signal is a differential signal. and difference.

[0056] 2. State variable shaper module design

[0057] The state variable shaper is an important part of the present invention, which includes high-pass, band-pass and low-pass filters. The phase correction of the moving coil seismic detector output is realized by linearly combining the high-pass, band-pass and low-pass filters. The system mainly corrects the phase in the 5~300Hz frequency band to solve the phase delay problem of the moving coil seismic detector. The core idea of ​​the state variable shaper is to construct a transfer function through variable feedback control to compensate for the phase delay of the detector frequency response, so that its phase output is always at zero phase.

[0058] The circuit diagram of the state variable shaper is as follows: As shown in the figure, the circuit corrects the phase of the output signal of the moving coil seismic detector through an adder, an integrator, an inverting circuit, etc., and constructs a transfer function with different requirements according to different summation coefficients to make its phase meet the preset standard. Through this linear combination, the system can effectively correct the signal phase delay problem output by the moving coil seismic detector.

[0059] Phase correction is achieved by summing different multiples of high pass, band pass, and low pass. The process is designed to be completed by the following steps:

[0060] Firstly, the detector's transfer function is fitted from the frequency domain characteristics of the detector's output signal. According to the transfer function characteristics, the target transfer function of the phase corrector is designed based on the zero-pole compensation method. Secondly, the circuit structure and circuit parameters are designed according to the target transfer function.

[0061] The design of circuit parameters should be based on the target transfer function. The single-ended signal first enters the positive end of the adder, and forms a high-pass filter characteristic at the output end of the adder. The signal is integrated once by the primary integrator to form a band-pass filter characteristic, and then integrated twice by the secondary integrator to form a low-pass filter characteristic. The three output ends with different characteristics output signals and connect resistors of different resistance values. The new adder is used to amplify and sum different multiples, thus realizing a linear combination of high-pass, band-pass, and low-pass filters. Finally, the signal is passed through an inverter to offset the phase change caused by the adder. The transfer function of the circuit This can be calculated using the amplifier current and voltage laws.

[0062] The following describes how to design the target transfer function of the state variable shaper based on the detector transfer function, such as Figure 3 shown.

[0063] According to the characteristics of the moving coil seismic detector as a second-order high-pass filter, the transfer function of the detector is for

[0064]

[0065] The phase characteristic of the detector is for

[0066]

[0067] Where s represents the frequency in the Laplace transform domain and is a complex variable, , is the gain of the transfer function of the moving coil geophone, is the cutoff frequency of the transfer function of the moving coil geophone, is the damping ratio. To compensate the transfer function, it is necessary to reconfigure the zero poles based on the zero pole configuration method. Suppose the target transfer function of zero phase correction is for

[0068]

[0069] Where A, B, C, and D are the unknown parameters of the transfer function of the constructed second-order system.

[0070] The final system transfer function is for

[0071]

[0072] In order to achieve the reconfiguration of zeros and poles and the simplicity of the system, we make , , , Then the target transfer function of zero phase correction is for

[0073]

[0074] in is the cutoff frequency of the transfer function of the zero phase correction circuit, is the damping ratio.

[0075] Transfer function of the detector and correction circuit in series for

[0076]

[0077] So the target transfer function only needs to confirm and The two unknowns immediately determine the final transfer function. After the detector is compensated in series, the system is still a second-order system. However, the denominator of the detector transfer function and the numerator of the target transfer function cancel each other out, and the new system formed has a different natural frequency and damping ratio from the original detector. When the phase of the detector is distorted, a target transfer function and a phase correction circuit are designed to correct the phase to zero within the required frequency band. After series compensation, the new system achieves zero phase correction of the detector signal while maintaining the original gain within the bandwidth, thereby widening the effective frequency band of the detector. This method is highly theoretical, easy to design, intuitive in expected results, and has a variety of implementation methods. It is a relatively ideal phase correction solution.

[0078] We define the phase of the system at 5Hz after phase correction is the performance index of the correction effect, called the correction error. When it is less than a certain range, the phase correction requirement is met.

[0079] That is, the transfer function of the final system is Phase characteristics Phase size at 5Hz ≤ , as follows, where .

[0080]

[0081] Since the system gain is related to the pole configuration of the transfer function, it will change with The gain increases with the decrease of gain. Too large gain often brings greater noise in the hardware circuit. Therefore, if , If the phase correction target transfer function and the final system transfer function are known, the phase correction target transfer function and the final system transfer function can be solved. Therefore, the phase corrector based on the invention can perform phase correction on detector signals with different transfer functions, and has certain practicality.

[0082] The circuit connection of the phase corrector of the present invention is described in detail below. The frequency characteristics of the state variable shaper module system only consider 5~300Hz, which includes three parts: high-pass filter, band-pass filter and low-pass filter. The high-pass filter includes a first adder U1, the band-pass filter includes a first integrator U2 and a first inverter U4, and the low-pass filter includes a second integrator U3.

[0083] The first adder U1 of the high-pass filter is composed of an operational amplifier, a first resistor R1 and a second resistor R2. The first resistor R1 is used as a feedback resistor to connect the negative input terminal of the operational amplifier and the output terminal of the second integrator U3. The second resistor R2 is used to connect the negative input terminal of the first adder U1 and the output terminal of the operational amplifier. The output terminal of the operational amplifier is the output port of the high-pass filter, and the phase is basically zero.

[0084] The first integrator U2 in the bandpass filter is composed of an operational amplifier, a third resistor R3, a fourth resistor R4 and a first capacitor C1. The third resistor R3 is connected to the output end of the first adder U1 and the negative input end of the operational amplifier. The fourth resistor R4 and the first capacitor C1 are the feedback resistors and feedback capacitors of the operational amplifier and are connected in parallel to the negative input end and the output end of the operational amplifier to form an inverting integrator. The output end of the first integrator U2 has the frequency characteristics of the bandpass filter and provides a phase leading by about 90°. The output end of the first integrator U2 is connected to the first inverter U4, which is composed of an operational amplifier, a seventh resistor R7, an eighth resistor R8 and a twenty-fourth resistor R24. The seventh resistor R7 is connected to the negative input end of the operational amplifier and the output end of the first integrator U2. The twenty-fourth resistor R24 ​​is connected to the positive input end of the operational amplifier and the input reference voltage or grounding. The eighth resistor R8 is the feedback resistor of the operational amplifier and is connected to the negative input end and the output end of the operational amplifier. The first inverter U4 formed by the eighth resistor R8 ensures that the phase characteristics of the bandpass filter will not be changed.

[0085] The second integrator U3 in the low-pass filter is composed of an operational amplifier, a fifth resistor R5, a sixth resistor R6 and a second capacitor C2. The fifth resistor R5 connects the output end of the first integrator U2 and the negative input end of the operational amplifier. The sixth resistor R6 and the second capacitor C2 are the feedback resistor and feedback capacitor of the operational amplifier, which are connected in parallel to the negative input end and the output end of the operational amplifier. The output end of the second integrator U3 has the frequency characteristics of a low-pass filter, providing a phase advance of about 180°.

[0086] The outputs of the high-pass filter, the band-pass filter and the low-pass filter are respectively connected to the ninth resistor R9, the tenth resistor R10 and the eleventh resistor R11, which are respectively used as the resistors of the summation coefficients of the low-pass, band-pass and high-pass filters to determine the multiples of the filter for summation; the ninth resistor R9, the tenth resistor R10 and the eleventh resistor R11 are connected to the second adder U5 and the second inverter U6;

[0087] The twelfth resistor R12 in the second adder U5 is connected to the output end and the negative input end of the operational amplifier in the second adder U5 as a feedback resistor of the second adder U5 to determine the amplification factor during summation. The twenty-first resistor R21 is connected to the positive input end of the operational amplifier and the input reference voltage or ground.

[0088] The second inverter U6 can ensure that the phase will not change due to the existence of the adder. The second inverter U6 is composed of an operational amplifier, a thirteenth resistor R13, a fourteenth resistor R14 and a twenty-second resistor R22. The thirteenth resistor R13 is connected to the negative input terminal of the operational amplifier and the output terminal of the second adder U5. The twenty-second resistor R22 is connected to the positive input terminal of the operational amplifier and the input reference voltage or ground. The fourteenth resistor R14 is a feedback resistor of the operational amplifier and is connected to the negative input terminal and the output terminal of the operational amplifier.

[0089] The following describes how to calculate the circuit parameters of the state variable shaper based on the target transfer function.

[0090] According to the circuit structure of the state variable shaper, the formula can be listed as follows:

[0091]

[0092] in is the output signal after differential conversion to single-ended. is the output of the high-pass filter, is the output of the bandpass filter, is the output of the low pass filter.

[0093] The above formula can be used to obtain the relationship between the output of the high-pass filter and the input single-ended signal.

[0094]

[0095] make , then the above formula can be written as the transfer function of the high-pass filter :

[0096]

[0097] Similarly, the transfer functions of bandpass and lowpass filters are as follows.

[0098]

[0099]

[0100] The transfer function of the bandpass filter is negative, which is inconsistent with the transfer functions of other filters. Therefore, an inverter is added to convert the negative transfer function into a positive transfer function. The parameters remain unchanged to ensure the accuracy of the transfer function phase.

[0101] Assume that the sum coefficients of the high-pass, band-pass and low-pass filters are K1, K2, K3 respectively, and their relationship with the ninth resistor R9, R10, R11, R12 is as follows.

[0102]

[0103] So the final circuit transfer function is

[0104]

[0105]

[0106] The transfer function Cut-off frequency .

[0107] make , then the circuit parameters can be solved, and the zero-phase correction of the detector can be performed based on the solved circuit parameters.

[0108] The Bode plot of the state variable shaper is shown in As shown, HPF represents the frequency domain characteristic curve of high-pass output, BPF represents the frequency domain characteristic curve of band-pass output, LPF represents the frequency domain characteristic curve of low-pass output, and SYSTEM represents the Bode diagram of the target transfer function when the summation coefficients are all 1.

[0109] The design of the transfer function is based on the zero-pole configuration method. The dynamic response characteristics of the system are adjusted by reconfiguring the zero poles. The denominator of the transfer function of the original moving-coil seismic detector is set as the numerator, and then the new damping ratio and cutoff frequency are redesigned as the poles for phase correction.

[0110] In fact, the design idea of ​​the target transfer function is to approximate the phase inversion of the original moving-coil seismic detector transfer function, so that the sum of the two is zero phase and meets the requirements. Therefore, the zero-phase correction based on the zero-pole configuration method is to use the pole to offset the zero point. The frequency response within 5~300Hz increases with the increase of frequency, and the phase is always negative within the frequency band, which is opposite to the phase delay of the detector, and can be used to correct the phase delay problem of the detector.

[0111] Target transfer function Phase characteristics The formula is as follows:

[0112]

[0113] From the formula, we can see that the phase characteristic is always less than zero within 5~300Hz, and is infinitely close to zero when the frequency is high, and the phase gradually decreases when the frequency is low. If known, just determine the appropriate By adjusting the parameters, the phase of the target transfer function can be made opposite to the output phase of the moving coil geophone, and the phase characteristic of the geophone can be effectively corrected.

[0114] The zero-phase correction circuit based on the state variable shaper we designed can achieve the inversion of the original moving-coil seismic detector output, so that the circuit and the detector are connected in series. After the phases of the two are added, the final phase correction is zero. Finally, the zero point of the transfer function of the system remains unchanged while the pole changes. At the same time, no additional gain is generated on the output of the moving-coil seismic detector, the gain within the frequency band is kept unchanged, and the low-frequency response of the detector is expanded.

[0115] In the highly complex and precise frontier scientific field of modern signal processing, high-pass, band-pass and low-pass filters serve as the basic key architectures and provide a solid support for the entire signal processing system. It should be emphasized that the transfer functions of high-pass, band-pass and low-pass filters have the same cut-off frequency, and the overall phase-corrected transfer function phase has a phase-lead characteristic in the 5~300Hz frequency band. When the circuit is connected in series with the detector, the two second-order systems are connected in series, and the result is still a second-order system. The denominator of the moving coil seismic detector transfer function and the numerator of the phase correction transfer function cancel each other out, and the new system formed has a different natural frequency and damping ratio from the original detector, which can correct the phase characteristics of the second-order high-pass filter in the detector output frequency response, and because the target transfer function The coefficients of the high-order terms in the numerator and denominator are both 1, so while the phase correction is being performed, the band gain within the band will not be affected, and the gain of the original detector can be kept unchanged. At the same time, it has a low-frequency compensation characteristic in the amplitude diagram, which can expand the low-frequency response of the detector. After series compensation, the damping ratio is improved, the equivalent natural frequency is reduced, and the low-frequency characteristic compensation is achieved, thereby widening the effective frequency band of the moving coil seismic detector, and the internal structure of the moving coil seismic detector is not changed.

[0116] For different moving coil geophone outputs, by determining different target transfer functions, different K1, K2, and K3 values ​​can be changed to construct different transfer functions for correcting different phase characteristics, thereby realizing correction of the moving coil geophone output phase characteristics. When the summation coefficient is different, the phase correction characteristics in the circuit will change, which is opposite to the moving coil geophone output phase, thereby achieving the purpose of correction. Also because of the change in the summation coefficient, the circuit can flexibly construct different transfer functions according to different summation coefficients. , suitable for moving coil seismic detectors with different phase characteristics.

[0117] 3. Single-ended to differential module

[0118] The circuit diagram of the single-ended to differential module is as follows As shown, the single-ended to differential module includes an inverting proportional amplifier. One path of the single-ended output signal is directly connected to the positive output terminal, and the other path is connected to the negative output terminal through the inverting proportional amplifier. The amplification factor of the inverting proportional amplifier is 1; the DC component is eliminated by subtracting the two signals, and the AC part is twice the original AC signal.

[0119] The inverting proportional amplifier is composed of an operational amplifier and a nineteenth resistor R19, a twentieth resistor R20 and a twenty-third resistor R23. The nineteenth resistor R19 is connected to the negative input terminal of the operational amplifier, the twentieth resistor R20 is connected to the output terminal and the negative input terminal of the operational amplifier as a feedback resistor, and the twenty-third resistor R23 is connected to the positive input terminal of the operational amplifier and the input reference voltage or ground.

[0120] In order to simplify the calculation and balance the circuit, the resistance values ​​of the nineteenth resistor R19 and the twentieth resistor R20 in the circuit are equal. At this time, the expression of the circuit can be obtained. Assume that the single-ended signal output by the circuit is , then the positive end of the output differential signal is , the negative terminal is They are

[0121]

[0122] The inverter inverts the single-ended signal so that the positive end of the differential signal is the single-ended signal itself, and the negative end is the inverted single-ended signal. The difference between the two is twice the original output signal.

[0123] 4. Single and dual power supply selection module

[0124] Single and dual power supply selection module circuit As shown, a jumper is used for selection. Port represents the reference voltage of the operational amplifier. When a single power supply is selected, the VEE terminal of the operational amplifier is grounded, the jumper is placed on P4, and the reference voltage is selected as Vref; when a dual power supply is selected, the VEE terminal of the operational amplifier is connected to the negative power supply, the jumper is placed on P5, and the reference voltage is selected as ground.

[0125] Through the above method, we have achieved zero-phase correction of the phase delay of the moving coil geophone, improved the phase stability of the system output, and significantly improved the acquisition quality and reliability of seismic data. It is worth emphasizing that our method can effectively correct the delay problem of the output phase of the moving coil geophone while compensating for the low-frequency response. For different types of moving coil geophones with different phase delays, the circuit transfer function can be changed by changing the summation coefficient. It can be applied to moving coil geophones with different transfer functions to correct the phase characteristics in the 5~300Hz frequency band. This zero-phase correction method for moving coil geophones based on state variable shaper is real-time and reliable, can effectively correct the phase delay, improve the performance indicators of moving coil geophones, and expand the application range of moving coil geophones.

Claims

1. A zero-phase corrector for a moving coil seismic detector based on a state variable shaper, which is formed by connecting a differential-to-single-ended module, a state variable shaper module and a single-ended-to-differential module; in, The frequency characteristic of the state variable shaper module system only considers 5 to 300 Hz, and it includes three parts: a high-pass filter, a band-pass filter and a low-pass filter. The high-pass filter includes a first adder (U1), the band-pass filter includes a first integrator (U2) and a first inverter (U4), and the low-pass filter includes a second integrator (U3); The first adder (U1) of the high-pass filter is composed of a first adder operational amplifier, a first resistor (R1) and a second resistor (R2); the first resistor (R1) is used as a feedback resistor to connect the negative input terminal of the first adder operational amplifier and the output terminal of the second integrator (U3); the second resistor (R2) is connected between the negative input terminal of the first adder (U1) and the output terminal of the first adder operational amplifier; the output terminal of the first adder operational amplifier is the output port of the high-pass filter; The first integrator (U2) in the bandpass filter is composed of a first integrator operational amplifier, a third resistor (R3), a fourth resistor (R4) and a first capacitor (C1), the third resistor (R3) is connected to the output end of the first adder (U1) and the negative input end of the first integrator operational amplifier, the fourth resistor (R4) and the first capacitor (C1) are the feedback resistor and feedback capacitor of the first integrator operational amplifier, and are connected in parallel to the negative input end and the output end of the first integrator operational amplifier; the output end of the first integrator (U2) is connected to the first inverter (U4), the first inverter (U4) is composed of the first inverter operational amplifier, a seventh resistor (R7), an eighth resistor (R8) and a twenty-fourth resistor (R24), the seventh resistor (R7) is connected to the negative input end of the operational amplifier and the output end of the first integrator (U2), the twenty-fourth resistor (R24) is connected to the positive input end of the first inverter operational amplifier and the input reference voltage or ground, and the eighth resistor (R8) is the feedback resistor of the first inverter operational amplifier and is connected to the negative input end and the output end of the operational amplifier; The second integrator (U3) in the low-pass filter is composed of a second integrator operational amplifier, a fifth resistor (R5), a sixth resistor (R6) and a second capacitor (C2), the fifth resistor (R5) is connected to the output end of the first integrator (U2) and the negative input end of the second integrator operational amplifier, the sixth resistor (R6) and the second capacitor (C2) are the feedback resistor and feedback capacitor of the second integrator operational amplifier and are connected in parallel to the negative input end and the output end of the second integrator operational amplifier; The outputs of the high-pass filter, the band-pass filter and the low-pass filter are connected to the ninth resistor (R9), the tenth resistor (R10) and the eleventh resistor (R11) respectively, and the ninth resistor (R9), the tenth resistor (R10) and the eleventh resistor (R11) are respectively used as the resistors of the summation coefficients of the low-pass, band-pass and high-pass filters to determine the multiples of the filter for summation; A ninth resistor (R9), a tenth resistor (R10) and an eleventh resistor (R11) are connected to the second adder (U5) and the second inverter (U6); The twelfth resistor (R12) in the second adder (U5) is connected to the output terminal and the negative input terminal of the second adder operational amplifier in the second adder (U5) as a feedback resistor of the second adder (U5) to determine the amplification factor during summing, and the twenty-first resistor (R21) is connected to the positive input terminal of the second adder operational amplifier and the input reference voltage or ground; The second inverter (U6) is composed of a second inverter operational amplifier, a thirteenth resistor (R13), a fourteenth resistor (R14) and a twenty-second resistor (R22), the thirteenth resistor (R13) is connected to the negative input terminal of the operational amplifier and the output terminal of the second adder (U5), the twenty-second resistor (R22) is connected to the positive input terminal of the second inverter operational amplifier and the input reference voltage or ground, and the fourteenth resistor (R14) is a feedback resistor of the second inverter operational amplifier connected to the negative input terminal and the output terminal of the operational amplifier; The state variable shaper module transfer function is as follows: （1） In formula (1), s represents the frequency in the Laplace transform domain, K1, K2, K3 are the summation coefficients of high pass, band pass, and low pass. Different summation coefficients correspond to different linear combinations. By changing the summation coefficients, the transfer function of the circuit construction can be changed to achieve phase characteristic correction of different detector output frequency responses. The summation coefficients K1, K2, K3 follow the following relationship: （2） Where R9 represents the resistance of the ninth resistor (R9), R 10 Represents the resistance of the tenth resistor (R10), R 11 Represents the resistance value of the eleventh resistor (R11); In formula (1), , , They are the transfer functions of high-pass, band-pass, and low-pass filters, respectively, and their expressions are as follows: （3） （4） （5） In the above transfer functions (3) to (5), C1 represents the capacitance of the first capacitor (C1), C2 represents the capacitance of the second capacitor (C2), R1 represents the resistance of the first resistor (R1), R2 represents the resistance of the second resistor (R2), R3 represents the resistance of the third resistor (R3), R4 represents the resistance of the fourth resistor (R4), R5 represents the resistance of the fifth resistor (R5), and R6 represents the resistance of the sixth resistor (R6); set up represents the target transfer function used for zero phase correction, and the transfer function H2(s) of the moving coil geophone zero phase corrector after series connection, respectively, is expressed as: （6） （7） In formula (6) , are the cutoff frequency and damping ratio of the transfer function of the moving coil geophone, , are the cutoff frequency and damping ratio of the transfer function of the zero-phase correction circuit respectively; in formula (7) is the gain of the transfer function of the moving coil geophone; make , combined with reasonable design and selection of resistor and capacitor parameters, the parameters C1, C2, R1, R2, R3, R4, R5, R6, R9, R 10 , R 11 , K1, K2 and K3 can be solved, and the zero phase correction of the detector can be performed based on the solved circuit parameters; That is, the transfer function of the detector connected in series with the zero phase correction circuit is Phase characteristics The phase magnitude at 5 Hz is , as follows: ； , Known, we can solve To determine the target transfer function for zero phase correction .

2. The zero phase corrector for a moving coil geophone based on a state variable shaper according to claim 1, characterized in that: The differential-to-single-ended module comprises a differential-to-single-ended operational amplifier, a fifteenth resistor (R15), a sixteenth resistor (R16), a seventeenth resistor (R17) and an eighteenth resistor (R18); wherein the fifteenth resistor (R15) is connected to the positive end of the input signal and is connected in parallel with the sixteenth resistor (R16) to the positive end of the differential-to-single-ended operational amplifier input, and the sixteenth resistor (R16) is grounded or connected to a reference voltage; the seventeenth resistor (R17) is connected to the negative end of the input signal and is connected in parallel with the eighteenth resistor (R18) to the negative end of the differential-to-single-ended operational amplifier input, and the single-ended signal is input to the state variable shaper module; the fifteenth resistor (R15), the sixteenth resistor (R16), the seventeenth resistor (R17) and the eighteenth resistor (R18) have equal resistance values.

3. The zero phase corrector for a moving coil geophone based on a state variable shaper according to claim 1, characterized in that: The single-ended to differential module includes an inverting proportional amplifier. One path of the single-ended output signal is directly connected to the positive output terminal, and the other path is connected to the negative output terminal through the inverting proportional amplifier. The amplification factor of the inverting proportional amplifier is 1; the subtraction of the two signals eliminates the DC component, and the AC part is twice the original AC signal.

4. The zero phase corrector for a moving coil geophone based on a state variable shaper according to claim 3, characterized in that: The inverting proportional amplifier is composed of an inverting proportional amplifier operational amplifier and a nineteenth resistor (R19), a twentieth resistor (R20) and a twenty-third resistor (R23), wherein the nineteenth resistor (R19) is connected to the negative input terminal of the inverting proportional amplifier operational amplifier, the twentieth resistor (R20) is connected to the output terminal and the negative input terminal of the inverting proportional amplifier operational amplifier as a feedback resistor, and the twenty-third resistor (R23) is connected to the positive input terminal and the input reference voltage or ground of the inverting proportional amplifier operational amplifier; wherein the nineteenth resistor (R19) and the twentieth resistor (R20) have equal resistance values.

5. The zero phase corrector for a moving coil geophone based on a state variable shaper according to claim 3, characterized in that: The moving coil seismic detector zero phase corrector based on the state variable shaper also includes a single power supply and dual power supply mode selection module, which provides selectable single power supply and dual power supply modes for the differential to single-ended module, the state variable shaper module and the single-ended to differential module. The differential to single-ended operational amplifier, the first integrator operational amplifier, the first inverter operational amplifier, the second integrator operational amplifier, the second adder operational amplifier, the second inverter operational amplifier and the single-ended to differential operational amplifier select the circuit structure of single power supply or dual power supply through jumpers; when the single power supply is used, the negative voltage terminal of the above-mentioned operational amplifier is connected to the ground, and the positive input terminal is connected to the reference voltage, that is, half of the positive power supply voltage; when the dual power supply is used, the negative voltage terminal of the above-mentioned operational amplifier is connected to the negative power supply, and the positive input terminal is grounded.

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