A multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method

Abstract

The present invention belongs to the field of magnetic source frequency domain electromagnetic detection in geophysical exploration, and in particular to a multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method. The frequency spectra, amplitude spectra and phase spectra of multi-frequency SPWM excitation signals and multi-frequency excitation current signals are designed, and the multi-frequency sine modulation signal u m is used. Based on the regular sampling method, the multi-frequency sine modulation signal u m modulates the bipolar triangular carrier wave u c , and the drive control circuit outputs the drive control signals s1 and s2 of the H-bridge transmitting circuit. Under the action of the drive control signals s1 and s2, the transmitting voltage of the H-bridge transmitting circuit is a multi-frequency SPWM excitation signal, and the transmitting current in the transmitting coil is a multi-frequency excitation current signal. The transmitting current contains each required main frequency point, and high-precision electromagnetic sounding of the target investigation area can be completed, overcoming the defects of fixed main frequency point intervals and low detection efficiency of multi-frequency pseudo-random excitation signals, as well as the disadvantages of large computational amount of electromagnetic sounding excitation signals based on SHEPWM and inability to perform real-time control at the exploration site.

Description

Technical Field

[0001] The present invention belongs to the field of magnetic source frequency domain electromagnetic exploration in geophysical exploration, and particularly relates to a multi-frequency SPWM high-precision frequency domain electromagnetic sounding excitation method suitable for high-precision magnetic source frequency domain electromagnetic sounding. Background Art

[0002] With the continuous development of energy and mineral resources, the resources that are easy to exploit and explore are decreasing year by year. High-efficiency and high-precision detection methods for extremely harsh environments have become an important research direction in the field of geophysical exploration. The magnetic source frequency domain electromagnetic method is an important geophysical detection method and has been widely used in geological surveys, environmental assessments, etc. in China. In the detection experiment, a high-frequency excitation current signal is injected into the transmitting coil through the transmitting system as the excitation source. According to the electromagnetic induction principle, the earth induces an electromagnetic field response signal, which is collected by the receiving system. By analyzing the electromagnetic response signal generated by the earth to a specific excitation signal source, the resistivity distribution of the earth can be obtained, and then the geological structure can be deduced and the position of the abnormal body can be determined. As the source of electromagnetic method detection, the waveform quality of the excitation signal plays a crucial role in the success or failure of the detection experiment. According to the principle of frequency domain electromagnetic exploration and the skin effect, excitation current signals of different frequencies can detect the electrical information of different depth strata. By transmitting excitation current signals of different frequencies within a certain range, electromagnetic exploration of the corresponding depth range of the earth can be completed. In high-precision electromagnetic sounding experiments, in order to ensure high vertical detection resolution of the target investigation area, it is necessary to complete the spectrum design of the excitation current signal so that the main frequency points of the excitation signal are all distributed within the effective frequency band corresponding to the depth range of the target investigation area, meeting the desired frequency point distribution. In addition, on the premise that the total energy of the excitation signal is certain, the energy should be concentrated on the effective main frequency points, and the energy between the main frequency points is evenly distributed to improve the resolution ability of the abnormal body.

[0003] In high-precision frequency-domain electromagnetic sounding experiments, the traditional detection method uses a single-frequency excitation current signal as the excitation source, and completes the one-by-one test of the required frequency points within the effective frequency band through frequency sweeping. However, multiple experimental tests will reduce the detection efficiency, increase the detection cost, and due to the different test times of different frequency points, there may be differences in the magnetotelluric characteristics and environmental noise, resulting in a decrease in detection accuracy. The multi-frequency electromagnetic excitation method can effectively solve the problem of low detection efficiency of the single-frequency point frequency sweeping method. The most commonly used method in China is the multi-frequency pseudo-random method proposed by Academician He Jishan of Central South University. The multi-frequency pseudo-random signal contains multiple available frequency points with high energy. Each frequency point is evenly distributed on the logarithmic coordinate, and the frequency point interval is fixed. When detecting, transmitting one excitation signal can obtain the geoelectric response information of multiple effective main frequency points, improving the detection efficiency. In high-precision electromagnetic sounding experiments, resistivity imaging is required for the longitudinal section of a specific depth range in the target investigation area. It is required that the main frequency points of the transmission are distributed in an effective narrow frequency band and in a specific manner. However, since the main frequency points of the multi-frequency pseudo-random signal have a fixed interval, in order to completely cover all the required frequency points in the narrow frequency band, different pseudo-random signal base frequencies usually need to be set for multiple experiments, resulting in low detection efficiency. In addition, there are low-order harmonics near each main frequency point in the pseudo-random signal, increasing the difficulty of analyzing and processing the subsequent geoelectric response information. In the patent CN108427145A, a ground-air frequency-domain electromagnetic sounding excitation method based on SHEPWM is proposed. By calculating the switching moments of each switching device in the transmitting circuit, a multi-frequency excitation voltage signal containing the desired main frequency is obtained, realizing the arbitrary distribution of the frequency, amplitude, and phase parameters of each main frequency point, with relatively high flexibility. However, since it is necessary to solve a complex non-linear transcendental equation set by a computer, it will consume a large amount of time. When the required main frequency parameters change, it is necessary to recalculate. Since it cannot be implemented in a single-chip microcomputer controller, in the field exploration site, it is impossible to adjust the parameters of each main frequency point in real time according to the detection environment, and it is difficult to adapt to the harsh exploration environment where geoelectric parameters such as medium resistivity change with time, and its practicability is limited to a certain extent. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method. The multi-frequency SPWM excitation signal contains multiple effective frequency points, and can realize the arbitrary setting of the number, amplitude, and distribution of main frequency points within a specific frequency band. The calculation amount is small, and in field exploration experiments, the parameters of the main frequency points can be adjusted in real time in the controller according to the changing environment, realizing high-efficiency and high-precision electromagnetic sounding experiments. It overcomes the defects of the fixed interval of the main frequency points of the multi-frequency pseudo-random excitation signal and low detection efficiency, as well as the large calculation amount of the electromagnetic sounding excitation signal based on SHEPWM and the inability to perform real-time control at the exploration site.

[0005] The present invention is implemented as follows.

[0006] A multi - frequency SPWM high - precision frequency - domain electromagnetic sounding excitation method, which includes:

[0007] Step 1: Determine the expression of the multi - frequency SPWM excitation signal according to the structure of the multi - frequency SPWM electromagnetic sounding transmitting system and the principle of multi - frequency sinusoidal pulse - width modulation;

[0008] Step 2: According to the depth range D H ~D L of the surveyed target area and the skin - depth formula, determine the frequency - band range f L ~f H of the effective main - frequency points of the multi - frequency excitation current signal. According to the requirement for the longitudinal detection resolution of the surveyed target area, determine the number N of the main frequencies of the transmitted current and the distribution of the main - frequency points, and complete the frequency - spectrum design of the multi - frequency SPWM excitation signal and the multi - frequency excitation current signal;

[0009] Step 3: Make the amplitudes B i of each main - frequency point of the multi - frequency excitation current equal. Combining the law of conservation of energy and the requirement for the signal - to - noise ratio in the electromagnetic sounding experiment, calculate the amplitudes A i of each component of the multi - frequency sinusoidal composite signal, and determine the amplitudes MEA i of each main - frequency point of the multi - frequency SPWM excitation signal and the amplitudes B i of each main - frequency point of the multi - frequency excitation current signal, and complete the amplitude - spectrum design of the multi - frequency SPWM excitation signal and the multi - frequency excitation current signal;

[0010] Step 4: Taking the phase combination θ = [θ1 θ2 … θ N T of the multi - frequency excitation current signal as the independent variable, and aiming at minimizing the crest factor CF of the multi - frequency excitation current signal, determine the optimal solution θ′ = [θ′1 θ′2 … θ′ N T of the phase combination through the iterative method, and calculate the phases of each required main - frequency point of the multi - frequency SPWM excitation signal to complete the phase - spectrum design of the multi - frequency SPWM excitation signal and the multi - frequency excitation current signal;

[0011] Step 5: Determine the expression of the multi - frequency sinusoidal modulation signal u N according to the frequency - spectrum f1,f2,…,f N , amplitude - spectrum MEA1,MEA2,…,MEA and phase - spectrum m of the multi - frequency SPWM excitation signal;

[0012] Step 6: Inside the drive control circuit, based on the regular sampling method, use the multi - frequency sinusoidal modulation signal u m to modulate the bipolar triangular carrier wave u c ​​For modulation, the drive control circuit outputs drive control signals s1 and s2 for the H-bridge transmitting circuit;

[0013] Step 7: Under the action of drive control signals s1 and s2, the transmitting voltage of the H-bridge transmitting circuit is a multi-frequency SPWM excitation signal, and the transmitting current in the transmitting coil is a multi-frequency excitation current signal. The transmitting current contains each required main frequency point, and high-precision electromagnetic sounding of the investigation target area can be completed.

[0014] Further, step 2 specifically includes: According to the depth range of the investigation target area, use the skin depth formula (1) to determine the frequency band range of the effective main frequency points of the multi-frequency excitation current signal:

[0015]

[0016] where δ represents the exploration depth, ρ represents the resistivity of the medium in the measurement area, and f represents the frequency of the excitation signal.

[0017] Suppose the depth range of the investigation target is the area from the shallow depth D L to the deep depth D H According to the skin depth formula, the shallow depth D L corresponds to the high-frequency point f H and the shallow depth D H corresponds to the low-frequency point f L Then the required effective frequency band for the exploration target area is f L ~f H Combined with the requirements of the investigation target area for the longitudinal detection resolution, determine the number N of required main frequencies and the distribution of main frequency points within the effective frequency band.

[0018] Further, step 3 specifically includes:

[0019] After applying a multi-frequency SPWM excitation voltage signal across the transmitting coil, a multi-frequency excitation current is generated in the coil. The equivalent impedance expression of the transmitting coil is:

[0020] Z(ω) = R + jωL

[0021] where R and L are the equivalent resistance and equivalent inductance of the transmitting coil respectively;

[0022] In the frequency domain, the relationship between the transmitting voltage U out and the transmitting current I out is:

[0023]

[0024] The time-domain expression of the multi-frequency excitation current signal is:

[0025]

[0026] Wherein, B i and θ i are respectively the amplitude and phase of the i-th main frequency component in the multi-frequency excitation current signal. The amplitude B i and the phase θ i are respectively expressed as:

[0027]

[0028]

[0029] Let the amplitudes B i of all main frequency points of the multi-frequency excitation current be equal, that is, B1 = B2 = … = B N , then the amplitudes of the sine components in the multi-frequency sine composite signal satisfy:

[0030]

[0031] For the i-th main frequency point in the multi-frequency excitation current signal, if ω i L ≥ 10R, it is considered that this main frequency point is high frequency, and the high-frequency angular frequency ω H = 10R / L. When ω i ≥ ω H , the inductive reactance ω i L in the impedance of the transmitting coil plays a major role, and the resistance R of the transmitting coil impedance is ignored; when ω i < ω H , the resistance R in the impedance of the transmitting coil plays a major role, and the inductive reactance ω i L of the transmitting coil impedance can be ignored. Combining with the formula for the amplitudes of the sine components in the multi-frequency sine composite signal, the amplitude relationship of the sine components in the multi-frequency sine composite signal is expressed as

[0032]

[0033] According to the conditions that the amplitudes of the main frequency voltages in the multi-frequency SPWM excitation signal should satisfy, the amplitudes of the multi-frequency sine composite signal u s satisfy the constraint conditions, and the requirements of the electromagnetic sounding experiment for the detection accuracy, determine the amplitudes A i of the sine components in the multi-frequency sine composite signal. At this time, from the expression of the multi-frequency SPWM excitation signal and the constraint conditions satisfied by the amplitude of the multi-frequency sine composite signal u s , the amplitudes MEA i of the main frequency points of the multi-frequency SPWM excitation signal and the amplitudes B i

[0034] Furthermore,

[0035] In step 4, an iterative method is used to solve for the phase combination θ, with the goal of minimizing the crest factor CF. First, N angular values are evenly taken within [0, 2π] as the initial value of the phase combination θ Use the fminsearch function in Matlab to solve for the phase combination, and obtain the initial value of the phase combination as θ (0) The optimal solution and the crest factor CF (1) . Take the phase combination θ (1) after one solution as the new initial value, and call the fminsearch function again to solve for the phase combination. Solve for the phase combination θ in this iterative manner. After calling the fminsearch function S times, obtain the phase combination and the crest factor CF (S) . When the number of times S of calling the fminsearch function is greater than 50 or the crest factor CF (S) converges below the set value, the optimal solution θ′ = [θ′1 θ′2 … θ′ N T is the final solution result. According to the phase combination θ′ = [θ′1 θ′2 … θ′ N T , combined with the expression of the phase θ i , the phases of each main frequency point of the multi-frequency SPWM excitation signal can be obtained Complete the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal.

[0036] Furthermore, the expression of the multi-frequency SPWM excitation signal is:

[0037] where u out is the transmitted voltage, M is the modulation depth, E is the DC power supply voltage, A i is the amplitude of each component of the multi-frequency sine synthesis signal, f i is the frequency of each component of the multi-frequency sine synthesis signal, is the phase of each component of the multi-frequency sine synthesis signal.

[0038] Furthermore, the expression of the multi-frequency sine modulation signal u m is:

[0039]

[0040] ​​Compared with the prior art, the beneficial effects of the present invention are as follows: Based on the Sinusoidal Pulse Width Modulation (SPWM) technology, the present invention proposes a multi-frequency SPWM electromagnetic sounding excitation method. The multi-frequency SPWM excitation signal contains multiple effective frequency points, and arbitrary settings of the number, amplitude, and distribution of the main frequency points within a specific frequency band can be achieved. The calculation amount is small, and in field exploration experiments, the main frequency point parameters can be adjusted in real time in the controller according to the changing environment, realizing high-efficiency and high-precision electromagnetic sounding experiments. It overcomes the defects of the multi-frequency pseudo-random excitation signal with a fixed frequency interval and low detection efficiency, as well as the large calculation amount of the electromagnetic sounding excitation signal based on SHEPWM and the inability to perform real-time control at the exploration site. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of the structure of the multi-frequency SPWM electromagnetic sounding transmitting system provided by an embodiment of the present invention;

[0042] Figure 2 Schematic diagram of the principle of multi-frequency sinusoidal pulse width modulation provided by an embodiment of the present invention;

[0043] Figure 3 Schematic diagram of the principle of multi-frequency sinusoidal modulation symmetric rule sampling method provided by an embodiment of the present invention;

[0044] Figure 4 Double-resistance anomaly body homogeneous earth model provided by an embodiment of the present invention;

[0045] Figure 5a Waveform diagram of multi-frequency sinusoidal modulation wave and triangular carrier wave; Figure 5b Waveform diagram of drive control signal s1; Figure 5c Waveform diagram of drive control signal s2;

[0046] Figure 6a Time-domain information of multi-frequency SPWM excitation signal; Figure 6b Time-domain information of multi-frequency excitation current signal; Figure 6c Frequency-domain information of multi-frequency excitation current signal. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0048] A multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method, the method includes:

[0049] Step 1: Determine the expression of the multi-frequency SPWM excitation signal according to the structure of the multi-frequency SPWM electromagnetic sounding emission system and the principle of multi-frequency sinusoidal pulse width modulation;

[0050] Step 2: According to the depth range D H ~D L of the target investigation area and the skin depth formula, determine the frequency band range f L ~f H of the effective main frequency points of the multi-frequency excitation current signal. According to the requirement for the longitudinal detection resolution of the target investigation area, determine the number N of the main frequencies of the transmitted current and the distribution of the main frequency points, and complete the frequency spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;

[0051] Step 3: Make the amplitudes B i of the main frequency points of the multi-frequency excitation current equal. Combining the law of conservation of energy and the requirement for the signal-to-noise ratio in the electromagnetic sounding experiment, calculate the amplitudes A i of the components of the multi-frequency sine composite signal, and determine the amplitudes MEA i of the main frequency points of the multi-frequency SPWM excitation signal and the amplitudes B i of the main frequency points of the multi-frequency excitation current signal, and complete the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;

[0052] Step 4: According to the determined frequency spectrum and amplitude spectrum of the multi-frequency excitation current signal, with the phase combination θ = [θ1 θ2 … θ N T of the sine components of the multi-frequency excitation current as the independent variable and the goal of minimizing the crest factor CF of the multi-frequency excitation current signal, determine the optimal solution θ′ = [θ′1 θ′2 … θ′ N T of the phase combination through the iterative method, and calculate the phases of the required main frequency points of the multi-frequency SPWM excitation signal Complete the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;

[0053] Step 5: Determine the expression of the multi-frequency sine modulation signal u N according to the frequency spectrum f1, f2, …, f N , amplitude spectrum MEA1, MEA2, …, MEA and phase spectrum m of the multi-frequency SPWM excitation signal;

[0054] Step 6: Inside the drive control circuit, based on the regular sampling method, modulate the bipolar triangular carrier wave u m with the multi-frequency sine modulation signal u c , and the drive control circuit outputs the drive control signals s1 and s2 of the H-bridge transmitting circuit; ​​

[0055] Step 7: Under the action of the drive control signals s1 and s2, the emission voltage of the H-bridge emission circuit is a multi-frequency SPWM excitation signal, and the emission current in the emission coil is a multi-frequency excitation current signal. The emission current contains each required main frequency point, and high-precision electromagnetic sounding of the investigated target area can be completed.

[0056] Among them, Step 1: The structural schematic diagram of the multi-frequency SPWM electromagnetic sounding emission system is as Figure 1 shown, including a DC power supply, an H-bridge emission circuit, an emission coil, and a drive control circuit. The voltage of the DC power supply is E, which is responsible for supplying power to the emission circuit. The H-bridge emission circuit includes two bridge arms. The left bridge arm includes switching devices V1 and V2, and the right bridge arm includes switching devices V3 and V4. The connection point of the switching devices V1 and V2 in the left bridge arm is U, and the connection point of the switching devices V3 and V4 in the right bridge arm is V. The emission voltage u out of the emission circuit is the potential difference between point U and point V. The emission coil is a series connection of an equivalent inductance L and an equivalent resistance R, and the current in the emission coil is the emission current. Let the emission voltage u out and the emission current i out both be positive in the direction from U to V. The drive control circuit is responsible for generating drive control signals s1 and s2 that can control the normal operation of each switching device in the H-bridge emission circuit. The drive control signals of the switching devices V1 and V4 are the same as s1, and the drive control signals of the switching devices V2 and V3 are the same as s2. The drive control signals s1 and s2 are complementary signals (without considering the dead time). When the drive control signal s1 = 1 and s2 = 0, the switching devices V1 and V4 are turned on, and the switching devices V2 and V3 are turned off. The emission voltage u out is +E; when the drive control signal s1 = 0 and s2 = 1, the switching devices V1 and V4 are turned off, and the switching devices V2 and V3 are turned on. The emission voltage u out is -E. Inside the drive control circuit, after the multi-frequency sine modulation signal and the triangular carrier wave pass through the multi-frequency sine modulation drive circuit, the drive control signals s1 and s2 are generated. Under the action of the drive control signals s1 and s2, the emission voltage u out at the output end of the H-bridge emission circuit is a multi-frequency SPWM excitation signal, and a multi-frequency excitation current is generated in the emission coil. Let the frequencies required for the electromagnetic sounding experiment in the investigated target area be f1, f2,..., f N . Define the multi-frequency sine synthesis signal u s as the combination of sine signals of these N frequencies, and its expression is:

[0057]

[0058] where, A i , f i , ω iare respectively the amplitude, frequency, phase and angular frequency of the i-th component in the multi-frequency sine composite signal, and the angular frequency ω i = 2πf i , where t is the time variable.

[0059] The multi-frequency sine composite signal u s has an amplitude that satisfies the constraint

[0060] |u s (t)| ≤ 1 (2)

[0061] The multi-frequency sine modulation signal u m is the product of the modulation depth M and the multi-frequency sine composite signal u s , that is, u m = Mu s . The value range of the modulation depth M is between 0 and 1. By changing the modulation depth M, the amplitude of the multi-frequency sine modulation signal u m can be adjusted.

[0062] The triangular carrier wave u c is a bipolar isosceles triangular wave with a positive peak value of 1, a negative peak value of -1, and an angular frequency of ω c . To ensure the waveform quality of the multi-frequency excitation current signal, the carrier angular frequency ω c needs to satisfy ω c ≥ 10ω i , where i = 1, 2,..., N.

[0063] A schematic diagram of the multi-frequency sine pulse width modulation principle is as shown in Figure 2 . During multi-frequency sine pulse width modulation, the multi-frequency sine modulation signal u m performs bipolar modulation on the triangular carrier wave u c . Based on the symmetric rule sampling method, within each carrier period T c , the multi-frequency sine modulation signal u m is sampled at the negative peak moment of the triangular carrier wave, and a horizontal line is drawn with the sampling value of the multi-frequency sine modulation signal as the center, intersecting with the triangular carrier waves on both sides. The left and right intersection points are respectively used as the front and rear edges of the square wave pulse of the drive control signal s1 within one carrier period T c . By inverting the waveform of the drive control signal s1, the drive control signal s2 can be obtained. At this time, the drive control signals s1 and s2 of the H-bridge transmitting circuit can be obtained in the time domain. Under the action of the drive control signals s1 and s2, the transmitted voltage u out at the output end of the H-bridge transmitting circuit is a multi-frequency SPWM excitation signal, and the transmitted current i out generated in the transmitting coil is a multi-frequency excitation current. By designing the modulation signal u m , a multi-frequency SPWM excitation signal and a multi-frequency excitation current containing the required main frequency information can be obtained.

[0064] Under the multi - frequency sinusoidal modulation method, the Fourier analysis of the output voltage is carried out. The schematic diagram of the principle of the multi - frequency sinusoidal modulation symmetric regular sampling method is as shown in Figure 3 Figure. For simplicity of analysis, assume that the sampling point time ω c t = 0, within one sampling period T s , α1 and α2 are the abscissas of the intersection points of the horizontal lines where the sampling values of the multi - frequency sinusoidal modulation wave u m are located and the left and right intersections of the triangular carrier wave. The expressions of the intersection points α1 and α2 are

[0065]

[0066] Within one sampling period T s , the expression of the transmitted voltage u out is

[0067]

[0068] According to the definition of the Fourier transform formula, within [-π, π], with the angular frequency ω c of the triangular carrier wave as the reference, the Fourier series expansion of the transmitted voltage u out is as follows

[0069]

[0070] In the formula, n is the harmonic order of the angular frequency ω c of the carrier wave, a0, a n and b n are the Fourier coefficients of the fundamental wave and the n - th harmonic. According to the definition of the Fourier coefficients and formula (4), the Fourier coefficients of each harmonic can be obtained as

[0071]

[0072] Substitute the expression (1) of the multi - frequency sinusoidal composite signal u s and the expressions (3) of the intersection points α1 and α2 into the Fourier coefficient expression (6), and we can get:

[0073]

[0074] Furthermore, substitute the Fourier coefficient expression (7) into the Fourier series expression (5), and the Fourier series expansion of the transmitted voltage u out can be further simplified to

[0075]

[0076] In Equation (8), the first term on the right side of the equation is the main frequency component, which includes each desired main frequency point; the second term is the high-frequency harmonic component, which is generated by modulating the triangular carrier with a multi-frequency sine modulation signal, denoted as Equation H. Expanding Equation H gives the following expression

[0077]

[0078] (1) When the carrier harmonic order n is odd, that is, when n = 1, 3, 5, …, cos(nπ / 2) = 0. Equation H can be simplified to

[0079]

[0080] According to the Bessel function of the first kind, the identity (11) can be obtained

[0081]

[0082] where x and β are variables, j is the imaginary unit, and J m is the Bessel function of the first kind of order m, and m is an integer.

[0083] Substituting the multi-frequency sine composite signal expression (1) into the identity (11), we can get

[0084]

[0085] According to the properties of the Bessel function, when m is an integer order, the Bessel function of the first kind of order m, J m satisfies

[0086] J -m (x) = (-1) m J m (x) (13)

[0087] Therefore, Equation (12) can be simplified to

[0088]

[0089] According to Euler's identity, we can get

[0090]

[0091] Combining Equation (14) and Equation (15), making the real and imaginary parts of both sides of the equation equal respectively, and substituting Equation (10), ignoring the phases of each harmonic, the high-frequency harmonic expression H can be further simplified

[0092]

[0093] where n = 1, 3, 5, …, k i = 0, 2, 4, …, k iis the k-th harmonic of the i-th expected main frequency point.

[0094] (2) When the carrier harmonic order n is even, i.e., n = 2, 4, 6, …, sin(nπ / 2) = 0. Ignoring the phases of each harmonic, the high-frequency harmonic expression H can be simplified to

[0095]

[0096] where n = 2, 4, 6, …, k i = 1, 3, 5, ….

[0097] According to equations (8), (16), and (17), the angular frequencies of the high-frequency harmonics generated by the multi-frequency sinusoidal modulation signal modulating the triangular carrier are The amplitude is When n = 1, 3, 5, …, k i = 0, 2, 4, …; when n = 2, 4, 6, …, k i = 1, 3, 5, ….

[0098] It can be seen from the Fourier series expansion formula (8) of the multi-frequency SPWM excitation signal and the high-frequency harmonic expressions (16) and (17) that the multi-frequency SPWM excitation signal contains each expected main frequency point. In the effective frequency band corresponding to the detection target area, except for each expected main frequency point, the amplitudes of the remaining frequency components are all 0. By multi-frequency sinusoidal modulation, the low-order harmonics near each expected main frequency point are eliminated, and the longitudinal resolution of the electromagnetic sounding experiment can be improved. The high-frequency harmonics generated by the multi-frequency sinusoidal modulation signal modulating the carrier are distributed at odd multiples of the carrier frequency and the upper and lower sidebands near the integer multiples of the carrier frequency. Compared with the required main frequency points, the frequencies of the high-frequency harmonic components are very high and the amplitudes are very low. And because the transmitting coil is inductive, it has a good suppression effect on the high-frequency harmonics, and the influence of the high-frequency harmonics on the electromagnetic sounding experiment can be almost ignored. Therefore, the expression of the multi-frequency SPWM excitation signal can be simplified to

[0099]

[0100] According to equation (18), in the multi-frequency SPWM excitation signal, the phases of each main frequency point are the same as those of the multi-frequency sinusoidal modulation signal, and the voltage amplitudes of each main frequency point are MEA i .

[0101] According to the law of conservation of energy, the total energy of the multi-frequency SPWM excitation signal is the sum of the energies of each main frequency point and the high-frequency harmonic energy. Therefore, the voltage amplitudes of each main frequency in the multi-frequency SPWM excitation signal should satisfy

[0102]

[0103] On the premise of satisfying Equation (19) and Constraint (2), in the electromagnetic sounding experiment, the DC power supply voltage E, modulation depth M, and the amplitudes A of the components of the multi-frequency sine composite signal can be increased according to the detection accuracy requirements i , to improve the energy of each main frequency point of the multi-frequency SPWM excitation signal, and thus improve the signal-to-noise ratio.

[0104] Step 2: In the electromagnetic sounding experiment, according to the depth range of the surveyed target area, use the skin depth formula (20) to determine the frequency band range of the effective main frequency points of the multi-frequency excitation current signal

[0105]

[0106] Among them, δ represents the exploration depth, ρ represents the resistivity of the medium in the measurement area, and f represents the frequency of the excitation signal.

[0107] Let the depth range of the surveyed target be from the shallow depth D L to the deep depth D H area. According to the skin depth formula, the shallow depth D L corresponds to the high-frequency point f H , and the shallow depth D H corresponds to the low-frequency point f L , then the required effective frequency band for the exploration target area is f L ~f H . Combining the requirements of the surveyed target area for the longitudinal detection resolution, the required number of main frequencies N and the distribution of the main frequency points within the effective frequency band can be determined.

[0108] Step 3:

[0109] After applying a multi-frequency SPWM excitation voltage signal across the two ends of the transmitting coil, a multi-frequency excitation current is generated in the transmitting coil. The equivalent impedance expression of the transmitting coil is:

[0110] Z(ω) = R + jωL (21)

[0111] In the formula, R and L are the equivalent resistance and equivalent inductance of the transmitting coil respectively.

[0112] In the frequency domain, the relationship between the transmitted voltage U out and the transmitted current I out is

[0113]

[0114] According to Equation (22), the multi-frequency excitation current has the same frequency as each main frequency point in the multi-frequency SPWM excitation signal, but different amplitudes and phases. Therefore, the time-domain expression of the multi-frequency excitation current signal is

[0115]

[0116] wherein, B i and θ i are respectively the amplitude and phase of the i-th main frequency component in the multi-frequency excitation current signal. The amplitude B i and the phase θ i are respectively expressed as

[0117]

[0118]

[0119] According to Equation (24), when the voltage amplitudes MEA i of each main frequency point in the multi-frequency SPWM excitation signal are the same, for the main frequency component with a higher angular frequency ω i , the current amplitude B i is lower; for the main frequency component with a lower angular frequency ω i , the current amplitude B i is higher. It can be seen that since the transmitting coil is inductive, the transmitting coil has an inhibitory effect on high-frequency components. In order to accurately measure the geo-electric response information of each required main frequency point and ensure the same detection accuracy for each main frequency point, it is necessary to control the current amplitudes B i of each desired main frequency point of the multi-frequency excitation current signal to be approximately equal, so that the energy distribution among the main frequency points of the multi-frequency excitation current signal in the frequency domain is more uniform.

[0120] Let the amplitudes B i of each main frequency point of the multi-frequency excitation current be equal, that is, B1 = B2 =... = B N . Combining Equation (21) and Equation (22), it can be obtained that the amplitudes of the sine components in the multi-frequency sine synthesis signal satisfy

[0121]

[0122] For the i-th main frequency point in the multi-frequency excitation current signal, if ω i L ≥ 10R, then this main frequency point is considered to be high-frequency, and the high-frequency angular frequency ω H = 10R / L. When ω i ≥ ω H , the inductive reactance ω i L in the impedance of the transmitting coil plays a major role, and the resistance R of the impedance of the transmitting coil can be ignored; when ω i <ω H , the resistance R in the impedance of the transmitting coil plays a major role, and the inductive reactance ω i L of the impedance of the transmitting coil can be ignored. Combining Equation (26), the amplitude relationship of the sine components in the multi-frequency sine synthesis signal can be expressed as

[0123]

[0124] According to Equation (2), Equation (19), and the requirements for detection accuracy in electromagnetic sounding experiments, the amplitude A of each sine component in the multi-frequency sine composite signal can be determined. i At this time, according to Equation (18) and Equation (24), the amplitude MEA of each main frequency point of the multi-frequency SPWM excitation signal can be determined. i And the amplitude B of each main frequency point of the multi-frequency excitation current. i That is, the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal is completed.

[0125] Step 4: To avoid the aliasing of the geoelectric response signals generated by the excitation of multiple main frequency points, which may cause a decrease in detection accuracy, and to reduce the requirements for the acquisition accuracy of the geoelectric response signals by the receiving system, the multi-frequency excitation current signal should have a uniform amplitude distribution and few spike pulses in the time domain. The crest factor (CF) is used to measure the uniformity of the amplitude distribution of the multi-frequency excitation current signal. The definition of the crest factor CF is

[0126]

[0127] where i max , i min are the maximum and minimum values of the transmitted current i out respectively, and I eff is the effective value of the transmitted current i out . The lower the crest factor CF, the more uniform the amplitude distribution of the multi-frequency excitation current signal, which can effectively improve the signal-to-noise ratio.

[0128] Since the frequency spectrum f1, f2, …, f N and the amplitude spectrum B1, B2, …, B N of the multi-frequency excitation current signal have been determined, according to Equation (23) and Equation (28), the crest factor CF is a function of the phase combination θ = [θ1 θ2 … θ N T of each main frequency point of the multi-frequency excitation current signal. The present invention uses an iterative method to solve the phase combination θ, and the solution target is the minimum crest factor CF. First, N angular values are equally spaced in [0, 2π] as the initial value of the phase combination θ According to Equation (23) and Equation (28), the fminsearch function in Matlab is used to solve the phase combination, and the optimal solution (0) and the crest factor CF when the initial value of the phase combination is θ (1) are obtained. Since using the fminsearch function may obtain a local optimal solution, the phase combination θ (1)As a new initial value, the fminsearch function is called again to solve the phase combination. In this way, the phase combination θ is iteratively solved. After calling the fminsearch function S times, the phase combination and the crest factor CF (S) can be obtained. When the number of times S of calling the fminsearch function is greater than 50 or the crest factor CF (S) converges below the set value, it is considered that the optimal solution θ′ = [θ′1 θ′2 … θ′ N at this time T is the final solution result. At this time, the crest factor of the multi-frequency excitation current signal is low, and the current amplitude is evenly distributed in the time domain, which is beneficial to improving the signal-to-noise ratio. According to the phase combination θ′ = [θ′1 θ′2 … θ′ N , combined with Equation (25), the phases of the main frequency points of the multi-frequency SPWM excitation signal can be obtained T , that is, the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal is completed.

[0129] Step 5: According to the designed frequency spectrum f1, f2, …, f N and amplitude spectrum MEA1, MEA2, …, MEA N of the multi-frequency SPWM excitation signal and the phase spectrum , the multi-frequency sine modulation signal

[0130]

[0131] can be determined m Step 7: Inside the drive control circuit, based on the regular sampling method, the designed multi-frequency sine modulation signal u c is used to perform bipolar modulation on the bipolar triangular carrier wave u

[0132] . The drive control circuit outputs the drive control signals s1 and s2 of the H-bridge transmitting circuit. out Under the action of the drive control signals s1 and s2, the transmitted voltage u out output at the output end of the H-bridge transmitting circuit is the multi-frequency SPWM excitation signal, and the transmitted current i i generated in the transmitting coil is the multi-frequency excitation current. The multi-frequency SPWM excitation signal satisfies the expected frequency spectrum, amplitude spectrum, and phase spectrum. The multi-frequency excitation current contains each required main frequency point, the current amplitude is evenly distributed in the time domain, and the energy between each main frequency point is very close, which is beneficial to improving the longitudinal detection resolution of the electromagnetic sounding experiment and ensuring the normal implementation of the high-precision electromagnetic sounding experiment. When the detection requirements change, according to the number, amplitude, and distribution of the main frequency points required for the actual detection, the modulation depth M, amplitude A i , frequency f ​Parameters are used to obtain the required multi - frequency SPWM excitation signal and multi - frequency excitation current. It has a small amount of calculation, easy parameter adjustment, and can achieve real - time control at the exploration site.

[0133] Specific embodiment: To test the performance of the multi - frequency SPWM high - precision electromagnetic sounding excitation source, the present invention selects a uniform earth double - anomaly model for simulation verification. The burial depths of anomaly 1 and anomaly 2 are 125m and 200m respectively. The sizes of the anomalies are both 50m×50m, and the resistivity is 300Ω·m. The area within 250m below the surface is uniform earth with a resistivity of 50Ω·m.

[0134] The implementation method of the multi - frequency SPWM high - precision electromagnetic sounding excitation source of the present invention specifically includes the following steps:

[0135] Step 1: According to the structure of the multi - frequency SPWM electromagnetic sounding transmitting system and the principle of multi - frequency sinusoidal pulse width modulation, determine the expression of the multi - frequency SPWM excitation signal;

[0136] Step 2: According to the depth range D H ~D L of the surveyed target area and the skin - depth formula, determine the frequency band range f L ~f H of the effective main frequency points of the multi - frequency excitation current signal. According to the requirements for the longitudinal detection resolution of the surveyed target area, determine the number N of the main frequencies of the transmitted current and the distribution of the main frequency points, and complete the frequency spectrum design of the multi - frequency SPWM excitation signal and the multi - frequency excitation current signal;

[0137] Step 3: Make the amplitudes B i of each main frequency point of the multi - frequency excitation current equal. Combining the law of conservation of energy and the requirements for the signal - to - noise ratio in the electromagnetic sounding experiment, calculate the amplitudes A i of each component of the multi - frequency sine synthesis signal, and determine the amplitudes MEA i of each main frequency point of the multi - frequency SPWM excitation signal and the amplitudes B i of each main frequency point of the multi - frequency excitation current signal, and complete the amplitude spectrum design of the multi - frequency SPWM excitation signal and the multi - frequency excitation current signal;

[0138] Step 4: According to the determined frequency spectrum and amplitude spectrum of the multi - frequency excitation current signal, with the phase combination θ = [θ1 θ2 … θ N T as the independent variable and minimizing the crest factor CF of the multi - frequency excitation current signal as the goal, determine the optimal solution θ′ = [θ′1 θ′2 … θ′ N T of the phase combination through the iterative method, and calculate the phases of each required main frequency point of the multi - frequency SPWM excitation signal ​​Complete the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;

[0139] Step 5: According to the frequency spectrum f1, f2, …, f of the multi-frequency SPWM excitation signal N , amplitude spectrum MEA1, MEA2, …, MEA N and phase spectrum to determine the expression of the multi-frequency sine modulation signal u m ;

[0140] Step 6: Inside the drive control circuit, based on the regular sampling method, modulate the bipolar triangular carrier wave u m with the multi-frequency sine modulation signal u c to output the drive control signals s1 and s2 of the H-bridge transmitting circuit;

[0141] Step 7: Under the action of the drive control signals s1 and s2, the transmitting voltage of the H-bridge transmitting circuit is the multi-frequency SPWM excitation signal, and the transmitting current in the transmitting coil is the multi-frequency excitation current signal. The transmitting current contains each required main frequency point. Except for the expected main frequencies, there are no low-frequency harmonics, and the energy distribution among the main frequency points of the transmitting current is uniform, and the high-precision sounding experiment of the investigated target area can be completed.

[0142] In the above-mentioned Step 1, according to the multi-frequency SPWM modulation principle, the expression of the multi-frequency SPWM excitation signal is

[0143]

[0144] In the above-mentioned Step 2, as Figure 4 shown, determine the frequency band range, the number of main frequencies N and the distribution of main frequency points of the multi-frequency excitation current signal of the uniform earth double anomaly model, and complete the frequency spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal. The depth of anomaly 1 is 125m, and the depth of anomaly 2 is 250m. Then, according to the skin depth formula, determine that the transmitting current frequency point required to detect anomaly 1 is 400Hz (corresponding to a depth of 125m); to detect anomaly 2, the required transmitting current frequency point is 128Hz (corresponding to a depth of 225m), and the effective frequency band range is 128Hz to 400Hz. Combining the requirements of the electromagnetic sounding experiment for the longitudinal detection resolution, determine that the transmitting current frequency point required to distinguish anomaly 1 and anomaly 2 is 256Hz (corresponding to a depth of 157m). The number of main frequencies N is 3, and the expected main frequencies are f1 = 128Hz, f2 = 256Hz, and f3 = 400Hz respectively.

[0145] In the above-mentioned Step 3, according to the determined frequency spectrum of the multi-frequency excitation current signal, let the amplitudes B of the main frequency points of the multi-frequency excitation current iEqual, combined with the law of conservation of energy and the requirements for the signal-to-noise ratio in electromagnetic sounding experiments, the amplitude spectra of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal are designed. The impedance of the transmitting coil is Z(ω) = R + jωL, the equivalent inductance L of the coil is 2 mH, and the equivalent resistance R is 0.02 Ω. For the desired main frequency points f1 = 128 Hz, f2 = 256 Hz, and f3 = 400 Hz, the inductive reactances of the transmitting coil are ω1L = 1.61 Ω, ω2L = 3.22 Ω, and ω3L = 5.03 Ω, respectively, and in all cases ω i L ≥ 10R = 0.2 Ω (i = 1, 2, 3). The inductive reactance ω i L in the impedance Z(ω) of the transmitting coil plays a major role, and the resistance R can be ignored. In the multi-frequency sine synthesis signal, the amplitude relationship of each sine component is

[0146]

[0147]

[0148] According to the law of conservation of energy, the amplitudes of each sine component satisfy

[0149]

[0150] Combined with the amplitude constraint of the multi-frequency sine synthesis signal and the requirements for the detection accuracy in the sounding experiment, taking the modulation depth M as 0.8, the amplitudes of the main frequencies of each sine component are determined: A1 = 0.2057, A2 = 0.4115, A3 = 0.6429. The DC power supply voltage E is 10 V. The amplitudes of the main frequencies of the multi-frequency SPWM excitation voltage signal are determined as MEA1 = 1.6459 V, MEA2 = 3.2918 V, MEA3 = 5.1434 V, and the amplitudes of the main frequencies of the multi-frequency excitation current signal are B1 = B2 = B3 = 1.0232 A.

[0151] Step 4: Based on the determined frequency spectrum and amplitude spectrum of the multi-frequency excitation current signal, with the goal of minimizing the crest factor CF of the multi-frequency excitation current, iteratively solve the phase combination θ = [θ1 θ2 θ3] T . Let the initial value of the phase combination be θ (0) = [0 2π / 3 4π / 3] T , and take the phase combination obtained after 50 iterations or when the crest factor CF is less than 10 as the optimal solution. Determine the phases of the main frequency components of the multi-frequency excitation current: θ1 = 2.5133 rad, θ2 = 6.2832 rad, θ3 = 5.0266 rad. Determine the phases of the main frequency components of the multi-frequency SPWM excitation signal

[0152] Step 5: According to the frequency spectrum of the multi-frequency SPWM excitation signal f1 = 128 Hz, f2 = 256 Hz, f3 = 400 Hz; amplitude spectrum MEA1 = 1.6459 V, MEA2 = 3.2918 V, MEA3 = 5.1434 V; phase spectrum Determine the multi-frequency sine modulation signal u m :

[0153] u m (t) = 0.1646sin(256πt + 4.0716) + 0.3292sin(512πt + 1.5646) + 0.5143sin(800πt + 0.3102)(33)

[0154] Step 6: Figure 5a Waveform diagram of the multi-frequency sine modulation wave and the triangular carrier wave; Figure 5b Waveform diagram of the drive control signal s1; Figure 5c Waveform diagram of the drive control signal s2. Based on the regular sampling method, the multi-frequency sine modulation signal u m modulates the bipolar triangular carrier wave u c . The triangular carrier wave u c is a bipolar isosceles triangular wave with a positive peak value of 1 and a negative peak value of -1, and the carrier angular frequency ω c = 20π rad·s -1 . The drive control circuit outputs the drive control signals s1 and s2 of the H-bridge transmitting circuit.

[0155] Step 7: Figure 6a Time-domain information of the multi-frequency SPWM excitation signal; Figure 6b Time-domain information of the multi-frequency excitation current signal; Figure 6c Frequency-domain information of the multi-frequency excitation current signal. Under the control of the drive control signals s1 and s2, the transmission voltage of the H-bridge transmitting circuit is the waveform of the multi-frequency SPWM excitation signal, and the transmission current is the waveform of the multi-frequency excitation current. The current amplitude is evenly distributed in the time domain. The multi-frequency excitation current contains each required main frequency point in the frequency domain. Except for the main frequency points, the low-frequency harmonic components are 0, and the energy distribution between the main frequency points is uniform, with good spectral characteristics, which can effectively improve the detection accuracy.

[0156] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method, characterized in that The method includes: Step 1: Determine the expression of the multi-frequency SPWM excitation signal according to the structure of the multi-frequency SPWM electromagnetic sounding emission system and the principle of multi-frequency sinusoidal pulse width modulation; Step 2: Determine the frequency band range f of the effective main frequency points of the multi-frequency excitation current signal according to the depth range D of the investigation target area H ~D L and the skin depth formula, and determine the number N of the main frequencies of the transmitted current and the distribution of the main frequency points according to the requirements for the longitudinal detection resolution of the investigation target area, and complete the frequency spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal; L ~f H ​ Step 3: Let the amplitudes B of the main frequency points of the multi-frequency excitation current i be equal. Combining the law of conservation of energy and the requirements for the signal-to-noise ratio in electromagnetic sounding experiments, calculate the amplitudes A of the components of the multi-frequency sine composite signal i , and determine the amplitudes MEA of the main frequency points of the multi-frequency SPWM excitation signal i and the amplitudes B of the main frequency points of the multi-frequency excitation current signal i , and complete the amplitude spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal; Step 4: According to the determined frequency spectrum and amplitude spectrum of the multi-frequency excitation current signal, with the phase combination θ = [θ1 θ2 … θ N T of each sine component of the multi-frequency excitation current as the independent variable, aiming to minimize the crest factor CF of the multi-frequency excitation current signal, the optimal solution θ′ = [θ1′ θ2′ … θ′ N T of the phase combination is determined by the iterative method, and the phases of the required main frequency points of the multi-frequency SPWM excitation signal are calculated to complete the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal;​​ Step 5: Determine the expression of the multi-frequency sine modulation signal u N according to the frequency spectra f1, f2, …, f N , amplitude spectra MEA1, MEA2, …, MEA and phase spectrum m of the multi-frequency SPWM excitation signal; Step 6: Inside the drive control circuit, based on the regular sampling method, through the modulation of the multi-frequency sine modulation signal u m on the bipolar triangular carrier wave u c , the drive control circuit outputs the drive control signals s1 and s2 of the H-bridge emission circuit; Step 7: Under the action of the drive control signals s1 and s2, the emission voltage of the H-bridge emission circuit is the multi-frequency SPWM excitation signal, and the emission current in the emission coil is the multi-frequency excitation current signal. The emission current contains each required main frequency point, and high-precision electromagnetic sounding of the target area can be completed.

2. The multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method according to claim 1, wherein Step 2 specifically includes: According to the depth range of the target area to be investigated, use the skin depth formula to determine the frequency band range of the effective main frequency points of the multi-frequency excitation current signal. The skin depth formula is: where δ represents the exploration depth, ρ represents the medium resistivity of the measurement area, and f represents the frequency of the excitation signal. Set the depth range of the investigation target to the shallow depth D L to the deep depth D H In the area, according to the skin depth formula, the shallow depth D L corresponds to the high-frequency frequency point f H , the deep depth D H corresponds to the low-frequency frequency point f L , then the effective frequency band required for the exploration target area is f L ~f H . Combining the requirements of the investigation target area for the longitudinal detection resolution, determine the number N of required main frequencies and the distribution of main frequency points within the effective frequency band.

3. The multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method according to claim 1, characterized in that, Step 3 specifically includes: After applying a multi-frequency SPWM excitation voltage signal across the two ends of the emission coil, a multi-frequency excitation current is generated in the coil. The expression of the equivalent impedance of the emission coil is: Z(ω) = R + jωL In the formula, R and L are the equivalent resistance and equivalent inductance of the emission coil respectively; The relationship between the transmitted voltage U out and the transmitted current I out is as follows: The time-domain expression of the multi-frequency excitation current signal is: where B i and θ i are respectively the amplitude and phase of the i-th main frequency component in the multi-frequency excitation current signal. The expressions for the amplitude B i and the phase θ i are respectively: Let the amplitudes B of the main frequency points of the multi-frequency excitation current i be all equal, i.e., B1 = B2 = … = B N , then the amplitudes of the sine components in the multi-frequency sine composite signal satisfy: For the i-th main frequency point in the multi-frequency excitation current signal, if ω i L ≥ 10R, then this main frequency point is considered high-frequency, and the high-frequency angular frequency ω H = 10R / L. When ω i ≥ ω H , the inductive reactance ω i L in the impedance of the transmitting coil plays a major role, and the resistance R of the transmitting coil impedance is ignored; when ω i <ω H , the resistance R in the impedance of the transmitting coil plays a major role, and the inductive reactance ω i L of the transmitting coil impedance is ignored. Combining with the formula for the amplitudes of the sine components in the multi-frequency sine synthesis signal, the amplitude relationship of the sine components in the multi-frequency sine synthesis signal is expressed as According to the conditions that the main frequency voltage amplitudes in the multi-frequency SPWM excitation signal should satisfy, the amplitude of the multi-frequency sine synthesis signal u s satisfies the constraint condition, and the requirements for detection accuracy in the electromagnetic sounding experiment, determine the amplitudes A i of each sine component in the multi-frequency sine synthesis signal. At this time, from the expression of the multi-frequency SPWM excitation signal and the fact that the amplitude of the multi-frequency sine synthesis signal u s satisfies the constraint condition, determine the main frequency point amplitudes MEA i of the multi-frequency SPWM excitation signal and the main frequency point amplitudes B i of the multi-frequency excitation current. M is the transmitting voltage, E is the DC power supply voltage, and f i is the frequency of each component of the multi-frequency sine synthesis signal.

4. The multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method according to claim 3, characterized in that Step 4 uses the iterative method to solve for the phase combination θ, with the goal of minimizing the crest factor CF. First, N angular values are evenly taken within [0, 2π] as the initial value of the phase combination θ Use the fminsearch function in Matlab to solve for the phase combination, and obtain the initial value of the phase combination as θ (0) The optimal solution when and the crest factor CF (1) Take the phase combination θ (1) after one solution as the new initial value, and call the fminsearch function again to solve for the phase combination. Solve for the phase combination θ in this iterative manner. After calling the fminsearch function S times, obtain the phase combination and the crest factor CF (S) When the number of times S of calling the fminsearch function is greater than 50 or the crest factor CF (S) converges below the set value, the optimal solution θ′ = [θ′1 θ′2 … θ′ N T is the final solution result. According to the phase combination θ′ = [θ′1 θ′2 … θ′ N T and combined with the expression of the phase θ i , the phases of the main frequency points of the multi-frequency SPWM excitation signal can be obtained Complete the phase spectrum design of the multi-frequency SPWM excitation signal and the multi-frequency excitation current signal.​​ 5. The multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method according to claim 1, wherein The expression of the multi-frequency SPWM excitation signal is: Among them, u out is the modulation depth of the emission voltage M, E is the DC power supply voltage, A i is the amplitude of each component of the multi-frequency sine composite signal, f i is the frequency of each component of the multi-frequency sine composite signal, and is the phase of each component of the multi-frequency sine composite signal.

6. The multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method according to claim 5, characterized in that Multi-frequency sine modulation signal u m The expression is:

7. The multi-frequency SPWM high-precision frequency-domain electromagnetic sounding excitation method according to claim 1, characterized in that, The regular sampling method is to sample the multi-frequency sine modulation signal u at the negative peak moment of the triangular carrier within each carrier period T c . Draw a horizontal line centered on the sampled value of the multi-frequency sine modulation signal, which intersects the triangular carrier on both sides. The left and right intersection points are respectively used as the front and rear edges of the square wave pulse of the drive control signal s1 within one carrier period T m . c ​

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