Lunar radar data diffraction-reflection joint constrained dielectric constant inversion method

Abstract

This disclosure belongs to the field of lunar subsurface material property inversion technology, and provides a method for inverting the dielectric constant of lunar radar data under joint diffraction-reflection constraints. The method includes: preprocessing the lunar radar data to obtain a radar profile; separating diffracted waves and reflected waves from the radar profile; performing dielectric background impedance inversion based on the diffracted waves to obtain the background impedance, converting the background impedance to logarithmic impedance form to obtain the logarithmic background impedance; performing dielectric impedance perturbation inversion based on the reflected waves to obtain the logarithmic impedance perturbation; matching and fusing the logarithmic background impedance and the logarithmic impedance perturbation in the frequency domain to obtain a full-band impedance model; and calculating the dielectric constant distribution based on the full-band impedance model. By comprehensively utilizing the complementary advantages of diffracted and reflected waves in dielectric constant inversion, this method achieves stable constraints on low-frequency background information of the dielectric constant and fine characterization of high-frequency variation features, thereby improving the overall reliability and resolution of the dielectric constant inversion results.

Description

Technical Field

[0001] This disclosure belongs to the field of lunar subsurface material property inversion technology, specifically a diffraction-reflection joint constrained dielectric constant inversion method for lunar exploration radar data. Background Technology

[0002] The South Pole-Aitken Basin on the far side of the Moon is the largest, deepest, and oldest impact structure on the Moon, and is the most likely area to yield deep materials such as the lunar crust and even the lunar mantle, making it an important research area for lunar evolution analysis. On January 3, 2019, the Chang'e-4 lunar probe landed at the bottom of the Von Kármán crater, located northwest of the South Pole-Aitken Basin, marking humanity's first soft landing on the far side of the Moon. Its rover, equipped with a lunar radar, can perform high-precision detection of the structure and materials of the lunar subsurface using in-situ detection methods, providing new opportunities for studying the structure, composition, and evolution of the lunar crust.

[0003] The lunar penetrating radar consists of dual-channel antennas with center frequencies of 60MHz and 500MHz. The 60MHz antenna has a deeper detection range (greater than 100 meters) but lower vertical resolution (less than 10 meters), while the 500MHz antenna has a shallower detection depth (greater than 30 meters) but higher vertical resolution (less than 0.3 meters). Both antennas have their advantages for detecting targets at different depths and are currently widely used in the detection of lunar subsurface structure and material properties. In particular, the dielectric constant, as a key physical parameter describing the electromagnetic properties of a medium, is crucial for accurate spatial distribution inversion, which is of great significance for lunar scientific research and engineering applications and has always been one of the key research focuses in lunar property inversion.

[0004] Existing methods for retrieving the dielectric constant of lunar radar mostly rely solely on reflection or diffraction information. Because the response mechanisms of electromagnetic waves to the dielectric constant differ during reflection and diffraction, the content and accuracy of the dielectric constant retrieval also differ between the two types of wave fields. Specifically: 1) The principle of dielectric constant inversion based on diffracted waves is: Point targets diffract radar signals, exhibiting a distinct hyperbolic shape on the radar profile. This hyperbolic shape is determined by both the target's depth and the wave velocity. Therefore, the wave velocity can be determined by fitting the hyperbola, superimposing velocity spectra, and performing migration velocity analysis, thereby inverting the dielectric constant. Although the resolution of the results is limited by the number of diffracted waves, the numerical range is stable and accurate, and it is currently mainly used for velocity analysis or interpretation of underground structures.

[0005] 2) The principle of dielectric constant inversion based on reflected waves is: When electromagnetic waves propagate at the interface of media, the difference in dielectric constant between adjacent media causes a sudden change in impedance, resulting in reflected waves. There is a definite physical relationship between the amplitude of the reflected wave and the reflection coefficient, which is uniquely determined by the impedance ratio of the media above and below the interface. Therefore, the dielectric impedance can be inverted from the reflected wave, and the dielectric constant can be further calculated. The results have high resolution, but they lack sufficient constraints on low frequencies or background information and are prone to background instability. Currently, this method is mainly used for characterizing layered media interfaces or inverting dielectric constant perturbation characteristics.

[0006] However, in actual lunar radar data, the subsurface medium has a complex structure, containing both continuous layered interfaces and widely distributed blocky, point-like, or irregular discontinuities. Radar echoes often contain both reflected and diffracted wave components. If only a single type of wave field is used for dielectric constant inversion, the inversion results are prone to significant deficiencies in terms of stability or resolution.

[0007] Therefore, how to fully utilize the ability of diffraction waves to stabilize low-frequency constraints while introducing the advantage of reflected waves in finely characterizing high-frequency changes in dielectric constant, and achieve complementary fusion of information from different wave fields, is a technical problem that urgently needs to be solved in the field of dielectric constant inversion for lunar exploration radar. Summary of the Invention

[0008] Given that existing methods for inverting the dielectric constant of lunar exploration radar mostly rely on single-type wavefield information, making it difficult to simultaneously ensure the stability and spatial resolution of the inversion results, the purpose of this disclosure is to propose a diffraction-reflection joint constraint dielectric constant inversion method for lunar exploration radar data. By comprehensively utilizing the complementary advantages of diffracted and reflected waves in dielectric constant inversion, this method achieves stable constraint of low-frequency background information of the dielectric constant and fine characterization of high-frequency variation features, thereby improving the overall reliability and resolution of the dielectric constant inversion results.

[0009] This disclosure provides a method for inverting the diffraction-reflection joint constrained dielectric constant of lunar radar data using hybrid phase deconvolution for the reflected wave. The method includes: Preprocessing of lunar radar data yields radar profiles; The diffracted wave and the reflected wave are separated from the radar profile; Based on the diffracted wave, the background impedance of the medium is inverted to obtain the background impedance. The background impedance is then converted into logarithmic impedance form to obtain the logarithmic background impedance. Based on the reflected wave, the dielectric impedance perturbation inversion is performed to obtain the logarithmic impedance perturbation; The logarithmic background impedance and the logarithmic impedance perturbation are matched and fused in the frequency domain to obtain a full-band impedance model. The dielectric constant distribution is calculated based on the full-band impedance model.

[0010] Furthermore, the preprocessing includes at least: performing time zero-point correction on the lunar exploration radar data; removing the DC component from the time zero-point corrected lunar exploration radar data; and performing time-varying gain on the data after removing the DC component.

[0011] Furthermore, separating diffracted waves and reflected waves from the radar profile includes: using a plane wave destruction method, by calculating the local tilt angle of the radar wave phase axis, suppressing the reflected wave component with an approximately constant local tilt angle, and retaining the diffracted wave component whose local tilt angle changes exceed a set threshold.

[0012] Furthermore, the dielectric impedance perturbation inversion based on the diffracted wave includes: A three-dimensional velocity spectrum based on the diffracted wave is established using the velocity continuation method. Using negative entropy as a measure of the focusing degree of diffraction waves, the focusing velocity spectrum corresponding to the three-dimensional velocity spectrum is calculated. The offset velocity is obtained from the focused velocity spectrum using an automatic picking algorithm; Convert the offset velocity into a layer velocity model; Calculate the background impedance based on the layer velocity model. Transform the background impedance into a logarithmic form of the background impedance.

[0013] Further, based on the reflected wave, dielectric impedance perturbation inversion is performed, including: For the reflected wave, the mixed-phase wavelet estimation is performed using the mixed-phase deconvolution method, and the radar profile is corrected to near-zero phase to obtain the near-zero phase reflected wave; For the near-zero phase reflected wave, the sparse reflection coefficient is solved by sparse pulse deconvolution; Based on the reflection coefficient, a finite bandwidth impedance inversion is performed to obtain the logarithmic impedance perturbation.

[0014] Furthermore, the matching and fusion of the logarithmic background impedance and the logarithmic impedance perturbation in the frequency domain includes: Determine the matching frequency band between the logarithmic background impedance and the logarithmic impedance disturbance; Within the matching frequency band, calculate the energy matching coefficient between the logarithmic background impedance and the logarithmic impedance disturbance; The amplitude of the logarithmic impedance disturbance within the matching frequency band is adjusted according to the energy matching coefficient. In the frequency domain, the adjusted logarithmic impedance perturbation is fused with the logarithmic background impedance to obtain a full-band impedance model.

[0015] Furthermore, the energy matching coefficient is calculated using the following formula: , in, The frequency domain representation of the logarithmic background impedance. This is the frequency domain representation of the logarithmic impedance perturbation. To match the lower limit of the frequency band, To match the upper limit of the frequency band, For frequency, This is the energy matching coefficient.

[0016] Furthermore, based on the energy matching coefficient, the amplitude of the logarithmic impedance disturbance within the matching frequency band is adjusted, including: Multiplying the spectrum of the logarithmic impedance perturbation by the energy matching coefficient yields the energy-corrected impedance perturbation spectrum.

[0017] Furthermore, the dielectric constant distribution is calculated based on the full-band impedance model, including: This is based on the relationship between dielectric impedance and dielectric constant, expressed as: , in, Where is the dielectric constant. For free space wave impedance, This represents the dielectric impedance.

[0018] Compared with the prior art, the advantages of this disclosure are as follows: This method effectively reduces the impact of low-frequency missing information in reflected wave inversion on the stability of dielectric constant results by inverting the propagation velocity of the medium using diffraction waves and constraining the low-frequency background of the dielectric constant. Utilizing the high-frequency response characteristics of reflected waves to changes in the medium interface and properties, it achieves fine inversion of dielectric constant perturbation information, improving the resolution of the spatial distribution of the dielectric constant. By matching and fusing low-frequency background information with high-frequency variation characteristics in the frequency domain, the inverted dielectric constant model achieves a good balance between numerical stability and spatial resolution. This method does not rely on prior borehole or external measurement data and is applicable to the dielectric constant inversion of lunar radar under complex lunar subsurface structure conditions, possessing strong versatility and engineering application value. Attached Figure Description

[0019] Figure 1 This is a flowchart of the diffraction-reflection joint constrained dielectric constant inversion method for lunar exploration radar data provided in this embodiment of the disclosure; Figure 2 This is the dielectric constant distribution model provided in the embodiments of this disclosure; Figure 3 These are radar profile comparison diagrams before and after preprocessing provided in the embodiments of this disclosure, wherein (a) is before preprocessing and (b) is after preprocessing; Figure 4This is a diagram showing the reflected wave and diffracted wave separated from the simulation model data provided in the embodiments of this disclosure, wherein (a) is the reflected wave and (b) is the diffracted wave; Figure 5 The following are logarithmic background impedance and logarithmic impedance perturbation distribution diagrams provided in the embodiments of this disclosure: (a) shows the logarithmic background impedance distribution diagram in the logarithmic domain obtained based on diffraction wave inversion, and (b) shows the logarithmic domain impedance perturbation distribution diagram in the logarithmic domain based on reflected wave inversion after amplitude correction. Figure 6 This is a logarithmic domain fusion impedance result diagram provided in the embodiments of this disclosure; Figure 7 The dielectric constant distribution result obtained by inversion is provided in the embodiments of this disclosure. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this disclosure.

[0021] This addresses the problem in the background technique that uses only a single type of wave field for dielectric constant inversion, resulting in significant deficiencies in the stability or resolution of the inversion results.

[0022] This disclosure provides a diffraction-reflection joint constrained dielectric constant inversion method for lunar exploration radar data. It fully utilizes the differences and complementarities in the dielectric constant response characteristics of diffracted and reflected waves during electromagnetic wave propagation and scattering. The two types of wave field information are used to invert the low-frequency background characteristics and high-frequency disturbance characteristics of the dielectric constant, respectively, and are matched and fused in the frequency domain, thereby achieving a synergistic improvement in dielectric constant stability and spatial resolution.

[0023] In one specific embodiment of this disclosure, to verify the effectiveness of the diffraction-reflection joint constrained dielectric constant inversion method for lunar radar data, radar data based on numerical forward modeling is selected as input data. The simulation data is generated using the finite-difference time-domain method for electromagnetic waves. Its data model parameters and radar system settings are mainly constructed with reference to the structural characteristics of the lunar subsurface medium and the operating conditions of the lunar radar, in order to simulate the propagation and scattering process of electromagnetic waves in the lunar subsurface medium under lunar radar conditions.

[0024] Specifically, referencing the distribution characteristics of the lunar subsurface medium, the numerical model has a horizontal length of 20m and a vertical depth of 14m. The model is internally structured as a layered medium, with both near-horizontal and inclined interfaces between layers. Anomalies of varying scales are distributed within and between layers to simulate potentially existing blocky materials, rock debris aggregates, and other discontinuities in the lunar subsurface. The dielectric constant of each layer gradually increases with depth to reflect the change in dielectric properties of the lunar subsurface material with increasing compaction.

[0025] Regarding the radar system parameter settings, the transmitted wavelet uses the Rick wavelet with a dominant frequency of 100MHz. This wavelet's shape is consistent with the transmitted waveform used by the lunar exploration radar, effectively characterizing the time-domain characteristics of the lunar exploration radar's electromagnetic pulses. The radar antenna adopts a common-offset configuration, with both the excitation and receiving antennas positioned 0.3m above the ground surface, and a horizontal distance of 0.3m between them. This geometric relationship is the same as the antenna layout of the lunar exploration radar.

[0026] In this embodiment of the disclosure, Figure 2 The dielectric constant distribution model provided for embodiments of this disclosure.

[0027] It should be noted that the 100MHz main frequency radar data used in this embodiment is only an example for method verification, and its purpose is to verify the applicability and effectiveness of the method disclosed herein under conditions with typical structural characteristics of the lunar subsurface. The method disclosed herein is also applicable to lunar radar data with different center frequencies, including but not limited to 60MHz or 500MHz channel data. Those skilled in the art can adjust the model scale, sampling parameters, and frequency range accordingly based on the specific radar system parameters without affecting the technical concept and implementation effect of the method disclosed herein.

[0028] See Figure 1 The diagram shows a flowchart of a method for inverting the diffraction-reflection joint constraint dielectric constant of lunar exploration radar data according to an embodiment of this disclosure. The method includes: S101, Preprocessing lunar radar data to obtain radar profile; S102, separating diffracted waves and reflected waves in the radar profile; S103, Based on the diffracted wave, perform background impedance inversion to obtain the background impedance, and convert the background impedance into logarithmic impedance form to obtain the logarithmic background impedance; S104, Based on the reflected wave, perform dielectric impedance perturbation inversion to obtain logarithmic impedance perturbation; S105, the background impedance and impedance disturbance are matched and fused in the frequency domain to obtain the full-band impedance model; S106, Calculate the dielectric constant distribution based on the full-band impedance model.

[0029] In step S101, lunar radar data is read and a high-quality radar profile is obtained through preprocessing: this includes performing time zero-point correction on the lunar radar data to eliminate the influence of the spatial distance and start-up time difference between the excitation antenna and the receiving antenna in the radar antenna; performing DC component removal processing on the data after time zero-point correction to eliminate the influence of horizontal background noise such as direct waves and ground waves; and performing time-varying gain on the data after DC component removal to recover the amplitude energy of the radar signal.

[0030] Among them: Time zero-point correction: Due to the spatial distance difference between the excitation antenna and the receiving antenna and the system startup timing deviation, it is necessary to truncate the invalid time period at the beginning of the recorded data in order to complete the time zero-point correction.

[0031] DC removal: Air waves, ground waves, and other interference from some equipment in the lunar radar system can generate horizontal background noise. This noise can be suppressed and anomaly information highlighted through processing methods such as averaging. Specifically, DC removal is achieved by calculating the average value of each radar data point along the time direction and then subtracting this average value from all sampling points of the corresponding channel. This operation effectively eliminates the DC offset component in the signal, making the horizontal phase axis in the radar profile clearer. For lunar radar data, due to the relatively flat lunar surface and uniform dielectric properties, direct waves and ground waves appear as near-horizontal, high-energy phase axes in the profile. DC removal significantly weakens the influence of this interference energy, creating favorable conditions for subsequent identification of reflected signals from the subsurface medium.

[0032] Time-varying gain: Radar waves experience loss and attenuation during propagation, with energy decreasing at depths. This is detrimental to the extraction of low-energy diffracted waves and the effective calculation of reflection coefficients based on deconvolution. Therefore, gain functions that disrupt interlayer relationships, such as exponential gain, are used to recover the amplitude energy of the radar signal and control the amplitude energy to be relatively balanced across the entire radar profile.

[0033] In this embodiment of the disclosure, Figure 3 For comparison of radar profiles before and after preprocessing, the profiles before preprocessing are as follows: Figure 3 Figure (a) is the result after preprocessing. Figure 3 Figure (b) shows that the radar profile before preprocessing has a low signal-to-noise ratio, making it difficult to identify effective signals. After preprocessing, the noise is suppressed and the effective signals are enhanced, making it possible to clearly identify the underground interface and the diffraction wave morphology.

[0034] In step S102, diffracted waves and reflected waves are separated in the preprocessed radar profile. In this embodiment, the separation of diffracted waves and reflected waves is based on the difference in their phase axis morphology in the radar profile. Reflected waves typically correspond to continuous or nearly continuous medium interfaces, and in the radar profile, they exhibit phase axis events with strong continuity and small local tilt angle changes. Diffracted waves, on the other hand, are typically generated by scattering from point-like or discontinuous bodies, and their phase axis morphology exhibits obvious curvature characteristics, with significant changes in local tilt angle with spatial position.

[0035] Based on the aforementioned differences, this embodiment employs a plane wave destruction method to process the radar profile. This method calculates the local tilt field of the in-phase axis in the radar profile to predict and suppress reflected waves with approximately constant local tilt angles, thereby effectively weakening the continuous in-phase axis components dominated by reflected waves. Simultaneously, since the local tilt angle of diffracted waves varies significantly and is difficult to accurately describe by the plane wave prediction model, it is preserved in the residual signal after plane wave destruction processing.

[0036] In one example, a plane wave destruction method is applied to perform local dip analysis on the original radar profile, calculating the local dip angle of the in-phase axis at each data point in the profile and constructing a local dip field. Based on the local dip field, an unsteady-state prediction filter is constructed. Using the unsteady-state prediction filter, reflected wave signals with approximately constant local dip angles and continuous in-phase axis characteristics are predicted, and the predicted reflected wave signals are subtracted from the original ground-penetrating radar profile data to obtain a residual signal containing information dominated by diffraction waves. Since diffraction waves exhibit drastic changes in local dip angle, their waveforms are difficult to predict by the unsteady-state prediction filter based on the assumption of constant local dip angles, and are therefore preserved in the residual signal. The filter coefficients of the unsteady-state prediction filter change with spatial location and time to adapt to variations in formation dip angle at different locations. This can be implemented using a finite difference operator based on the local plane wave equation, whose form is equivalent to a phase shift operator in the frequency domain.

[0037] Through the above processing, effective separation of reflected waves and diffracted waves can be achieved without relying on manual picking or prior models. The residual signal obtained after plane wave destruction processing serves as diffracted wave data, used for subsequent background propagation characteristic analysis based on diffracted waves. Furthermore, by combining or reconstructing the original ground-penetrating radar profile data with the diffracted wave residual signal, reflected wave data, dominated by reflected waves, can be obtained for subsequent dielectric impedance perturbation inversion.

[0038] In this embodiment of the disclosure, Figure 4 (a) schematically illustrates the separated reflected wave, and Figure 4 Figure (b) schematically shows the profile of the separated diffracted wave. It can be seen that the diffracted wave caused by the anomalous body in the original radar profile... Figure 4In (a), the continuous reflection interface in the original ground-penetrating radar profile is effectively highlighted. Figure 4 In (b), the diffracted wave is separated and the diffracted wave is significantly suppressed.

[0039] In this embodiment, the dielectric background impedance inversion based on diffraction waves is mainly used to obtain low-frequency background information of the dielectric constant. The low-frequency background impedance is indirectly calculated through the background propagation velocity or equivalent dielectric constant obtained by diffraction wave focusing analysis. It mainly reflects the smooth structural characteristics of the medium as it changes with depth and does not include high-frequency impedance disturbance information caused by the reflecting interface. The core idea is that the shape of the diffracted wave generated when a radar signal encounters an anomalous object during propagation in the medium is controlled by the depth of the anomalous object and the radar wave velocity. When the transmitter and receiver of the radar antenna... Position towards As the position moves forward, the radar waves encounter areas located at... When an abnormal object is encountered, a reflection will occur. The distance from the radar antenna to the anomalous object. For the two-layer travel time of radar waves, assume the radar wave speed is... Then the radar echo satisfies: , The equation can be rewritten as: , because and If the velocity is fixed, the shape of the diffracted wave will change due to the shift in wave velocity. Control means that only by using a diffracted wave with the correct deflection velocity can the energy of the diffracted wave be focused, i.e., its shape be restored. Therefore, the stable background propagation velocity can be inverted through diffracted wave focusing analysis, and the background impedance of the medium can be further calculated.

[0040] The specific calculation steps are as follows: For the separated diffracted wave, a three-dimensional velocity spectrum based on the diffracted wave is established using the velocity continuation method: The velocity extension refers to performing offset or equivalent propagation transformation on the diffracted wave under a series of candidate velocity conditions to construct a velocity spectrum reflecting the focusing characteristics of the diffracted wave under different offset velocity assumptions. Specifically, within a preset offset velocity range, different offset velocities are used to offset the separated diffracted wave one by one, and the focusing degree (such as amplitude intensity or similarity) of the imaging space is recorded at each offset velocity. Finally, the focusing degree is plotted as a function of the offset velocity to form a spectrum. Since the diffracted wave can achieve optimal focusing in the offset domain under the actual propagation velocity conditions, the background propagation velocity characteristics of the medium can be determined by analyzing the focusing degree of the diffracted wave under different offset velocity conditions.

[0041] Using negative entropy as a metric for the focusing degree of diffracted waves, the focusing velocity spectrum corresponding to the three-dimensional velocity spectrum is calculated. In this embodiment, the focusing degree of diffracted waves is characterized by negative entropy. Negative entropy can effectively reflect the concentration of signal energy in the spatiotemporal domain. After the diffracted wave is deflected under the correct offset velocity conditions, its energy distribution becomes more concentrated, and the corresponding negative entropy index reaches an extreme value. By calculating the negative entropy values ​​corresponding to the extension results of different offset velocities, the focusing velocity spectrum based on the diffracted wave can be obtained.

[0042] The offset velocity is obtained from the focusing velocity spectrum using an automatic picking algorithm: Furthermore, in the focused velocity spectrum, an automatic velocity picking method is used to extract the offset velocity corresponding to the negative entropy extreme value. The automatic velocity picking process requires no manual intervention and can determine the optimal offset velocity at each spatial location based on the changing characteristics of the focusing index in the velocity spectrum, thereby obtaining the offset velocity distribution that varies along the survey line direction.

[0043] For the constructed focused velocity spectrum, instead of simply selecting local maxima at each spatial location, the velocity picking problem is formulated as a global optimization process. By searching for a continuous path that maximizes the accumulation of focused energy in the time-space-velocity domain, the optimal migration velocity is automatically extracted; this process can be analogized to the selection of a propagation path in a focused energy field, where high focused energy regions exert an attractive effect on the velocity trajectory.

[0044] To avoid picking biases caused by local noise or anomalous diffraction waves, a continuity constraint along the survey line is introduced during the path search process. Utilizing prior information that the velocity of the subsurface medium typically varies slowly in space, a smoothing constraint based on variational solution or an optimal path search method is used to limit the velocity variation gradient, ensuring that the obtained velocity field has reasonable spatial continuity.

[0045] In response to the possibility of multiple local extreme value zones in the focusing velocity spectrum under complex geological conditions, this embodiment comprehensively considers the energy distribution characteristics through global path optimization, automatically avoids getting trapped in local abnormal peaks, and thus prioritizes the selection of the true velocity branch with the most significant focusing characteristics and the best spatial continuity.

[0046] Subsequently, based on the offset velocity distribution and the electromagnetic wave propagation laws, the offset velocities are converted into corresponding layer velocities, and multiple layer velocities form a layer velocity model. This layer velocity model reflects the background propagation characteristics of the medium as it varies with depth and is used for subsequent calculations of the medium's electromagnetic parameters.

[0047] To further reveal the underground physical properties of the probe medium and provide a basis for subsequent quantitative calculations of the medium's electromagnetic parameters, the migration velocity must be converted into a layer velocity model with clear geological significance.

[0048] The conversion of the offset velocity to the layer velocity is achieved based on the Dix formula. The specific steps are as follows: First, in the offset velocity field formed by the automatically acquired offset velocities, the root mean square velocity corresponding to each reflecting interface (or layer above the diffraction point) is extracted along the vertical direction. Under the assumption of a horizontal layered medium, the offset velocity is approximately equal to the root mean square velocity.

[0049] Calculate the two-way travel time difference between adjacent interfaces. According to the Dix formula, the first... Layer velocity Determined by the following formula: , in, This indicates the two-way travel time difference between adjacent interfaces. Indicates the first During a two-way vertical journey at the bottom of the floor, Table 1 Offset velocity at the bottom of the layer, Indicates the first Offset velocity at the bottom of the layer, Indicates the first During the two-way vertical travel at the bottom of the layer, the layer velocities of multiple layers constitute the layer velocity model.

[0050] The background impedance of the medium is calculated based on the layer velocity model: After obtaining the layer velocity model, the background impedance of the medium is calculated based on the correspondence between the medium propagation velocity and electromagnetic impedance. This background impedance mainly contains the low-frequency background information of the medium, which can provide stable low-frequency constraints for subsequent impedance perturbation inversion based on reflected waves.

[0051] Specifically, after obtaining the layer velocity model of the lunar subsurface medium, the background impedance at each depth point is calculated based on the propagation theory of high-frequency electromagnetic waves in low-loss media: , For depth layer velocity, The magnetic permeability is the vacuum permeability. Since lunar materials are primarily non-ferromagnetic minerals, their magnetic permeability can be approximated as the vacuum permeability. For depth Background impedance.

[0052] It should be noted that the background impedance obtained here only reflects the macroscopic low-frequency trend of the medium, and its spatial resolution is limited by the vertical sampling interval of the layer velocity model. To obtain a higher resolution dielectric constant distribution, impedance perturbation inversion based on reflected wave data is also required to recover the high-frequency details of the medium.

[0053] It should be noted that in this embodiment, the background impedance is expressed in logarithmic impedance form. The background impedance on a linear scale is converted to a logarithmic background impedance on a logarithmic scale, as shown in the formula: , in, For logarithmic background impedance, The background impedance is used as a reference impedance. If the background impedance and impedance perturbation are directly superimposed in the frequency domain within the non-logarithmic impedance domain, the significant differences in amplitude scale and spectral energy distribution between the two can easily lead to non-physical oscillations or low-frequency drift in the fusion result. This disclosure transforms the multiplicative change relationship of impedance into an additive change form by taking the natural logarithm of the background impedance, effectively compressing the dynamic range of the impedance value and thus improving the numerical stability of the inversion process. Simultaneously, in the logarithmic impedance domain, high-frequency perturbations and low-frequency background information of the dielectric properties are more easily linearly superimposed and fused in the frequency domain, which is beneficial for subsequent impedance perturbation inversion and the construction of a full-band impedance model. Furthermore, the logarithmic background impedance maintains a monotonically related relationship with the dielectric constant, facilitating stable calculation of the dielectric constant in subsequent steps. Therefore, this disclosure uses the logarithmic background impedance form in subsequent processing and result presentation.

[0054] In this embodiment of the disclosure, Figure 5 Figure (a) schematically shows the logarithmic background impedance distribution in the logarithmic domain obtained from diffraction wave inversion. It should be noted that... Figure 5 The result shown in (a) is the spatial domain representation obtained by performing an inverse Fourier transform on the logarithmic background impedance spectrum. Figure 5 As can be seen in (a), the obtained logarithmic background impedance is consistent with the actual distribution of the medium in terms of overall structure and layer depth, and the numerical variation is stable, which can effectively reflect the low-frequency structural characteristics of the lunar subsurface medium.

[0055] In step S104, dielectric impedance perturbation inversion is performed based on the reflected wave.

[0056] In this embodiment of the disclosure, the dielectric impedance perturbation inversion based on reflected waves is mainly used to obtain the high-frequency variation characteristics of the dielectric electromagnetic properties. The reflected wave is generated by the impedance abrupt change at the dielectric interface, and its amplitude is closely related to the impedance comparison between the dielectrics above and below the interface. Therefore, by performing deconvolution processing on the reflected wave, the reflection coefficient information can be extracted, and the perturbation component of the dielectric impedance can be further inverted.

[0057] The specific calculation steps are as follows: The separated reflected waves are then used to estimate the mixed-phase wavelet using the mixed-phase deconvolution method, and the radar profile is corrected to near-zero phase. Hybrid phase deconvolution refers to the process of estimating and correcting the phase of the reflected wave data without pre-setting the transmitted wavelet as the minimum phase. This process eliminates the phase distortion that may exist in the radar transmitted wavelet, making the reflection event exhibit near-zero phase characteristics on the time axis, thereby improving the time resolution and interpretability of the reflected wave.

[0058] Hybrid phase deconvolution specifically includes: Representing the reflected wave as a convolution model: , in, Recording for reflected waves, To transmit sub-waves for radar, For the medium reflection coefficient sequence, For noise, " indicates a convolution operation.

[0059] The goal of hybrid phase deconvolution is to find an inverse filter. , so that: , in, A sharp pulse with zero phase. It's a time delay. For time, the result of the convolution of the wavelet and the inverse filter is approximately a zero-phase pulse.

[0060] An inverse filter is applied to each reflected wave data to correct the radar profile to near-zero phase, thus obtaining near-zero phase reflected waves.

[0061] By using wavelet estimation and phase correction, the reflection events can be more concentrated in the time domain, providing a foundation for the stable solution of the subsequent reflection coefficient.

[0062] For near-zero phase reflected waves, the sparse reflection coefficient is solved using sparse pulse deconvolution.

[0063] The sparse pulse deconvolution refers to the process of performing sparse pulse deconvolution on near-zero phase reflected waves based on the physical characteristics of the limited number of medium reflective interfaces and the sparse distribution of reflection coefficients in the time domain. This process suppresses noise and false reflections while highlighting the reflection coefficient pulses corresponding to the real medium interfaces, thereby obtaining a stable and physically meaningful reflection coefficient sequence.

[0064] Sparse pulse deconvolution processing of near-zero phase reflected waves includes: Construct the objective function for sparse impulse deconvolution: , in, Let be the objective function to be minimized. , as well as Both represent the reflection coefficient. It is a near-zero phase reflected wave. ( ) represents the residual wavelet. For regularization parameters, This represents a measure of sparsity.

[0065] The final reflection coefficients are obtained by iteratively solving the objective function. It should be noted that the result here is a sequence of reflection coefficients. In one example, the least squares method is used for iterative solution.

[0066] Based on the aforementioned reflection coefficient, a finite-bandwidth impedance inversion is performed to obtain the logarithmic impedance perturbation: In this embodiment, the reflection coefficient reflects the relative change in impedance at the dielectric interface, and its physical meaning can be described by the comparison between the impedances of the dielectrics above and below the interface. Under the engineering assumptions that the lateral change of the dielectric is relatively gradual, the impedance changes of adjacent dielectrics are relatively small, and the reflection event is mainly near-perpendicular, an approximate correspondence can be established between the reflection coefficient and the perturbation of the logarithmic impedance of the dielectric. Based on the above approximation, and combined with the characteristic that the reflection coefficient is sparsely distributed in the time domain, the obtained reflection coefficient sequence can be mapped to the high-frequency perturbation component of the logarithmic impedance of the dielectric.

[0067] Specifically, under the constraint of a finite effective frequency band, the reflection coefficient is numerically accumulated along the time direction to obtain the logarithmic impedance perturbation of the medium, which can be expressed as: , in, Indicates time Logarithmic impedance perturbation of the medium at that point, For integration variables The reflection coefficient at a given location and the finite effective frequency band constraint mean that in actual lunar radar data processing, due to the limitations of the radar system itself and the characteristics of the underground medium, the signal energy that can be acquired and utilized is concentrated in a specific frequency range.

[0068] It should be noted that in the embodiments disclosed herein, the above integration operation is not an ideal continuous integration, but is achieved by numerical accumulation under the constraints of finite sampling interval and finite effective frequency band of radar data. The result only reflects the high-frequency impedance disturbance information corresponding to the effective frequency band of the reflected wave, and does not include low-frequency background components. It must be used in conjunction with logarithmic background impedance to construct a complete full-band impedance model.

[0069] Therefore, the logarithmic impedance perturbation of the medium can be obtained under limited effective frequency band conditions. This logarithmic impedance perturbation mainly characterizes the high-frequency impedance changes corresponding to the changes in the medium interface and local properties. To facilitate integration with the obtained low-frequency logarithmic background impedance within the same parameter domain, this embodiment uses logarithmic impedance form to describe the medium impedance perturbation.

[0070] In step S105, the logarithmic background impedance and the logarithmic impedance perturbation are matched and fused in the frequency domain to obtain the full-band impedance model: Since the logarithmic background impedance and logarithmic impedance perturbation are obtained from inversions of different wave fields, their spectral coverage, amplitude references, and energy levels differ. Direct superposition would affect the physical consistency and numerical stability of the impedance model. Therefore, this disclosure matches and fuses the logarithmic background impedance and logarithmic impedance perturbation in the frequency domain to construct a physically consistent full-band impedance model.

[0071] It should be noted that this disclosure does not simply superimpose the diffraction wave inversion results with the reflection wave inversion results. Instead, it establishes a unified parameter expression framework in the logarithmic impedance domain, so that the low-frequency background information and high-frequency disturbance information obtained from different wave field constraints can be consistently fused in the same physical quantity space, thereby avoiding the inconsistency problem of multi-wave field results in parameter scale and spectral coverage.

[0072] The specific calculation steps are as follows: Determine the matching band between the logarithmic background impedance and the logarithmic impedance disturbance: First, based on the radar system's center frequency, effective bandwidth, spectral characteristics of logarithmic background impedance, and spectral characteristics of impedance perturbation, and considering the complementary characteristics of diffraction wave inversion and reflection wave inversion in terms of spectral coverage, a frequency range in which their spectra effectively overlap is selected as the matching band. This matching band is typically located between the high-frequency end of the logarithmic background impedance and the low-frequency end of the logarithmic impedance perturbation to ensure the stability of the matching process.

[0073] Calculate the energy matching factor between the logarithmic background impedance and the logarithmic impedance disturbance: Within the matching frequency band, the spectral energy of the logarithmic background impedance and the logarithmic impedance perturbation in the frequency domain are calculated respectively, and the energy matching coefficient is determined accordingly. Its expression is: , in, The frequency domain representation of the logarithmic background impedance. This is the frequency domain representation of the logarithmic impedance perturbation. To match the lower limit of the frequency band, To match the upper limit of the frequency band, The frequency is denoted by . The energy matching coefficient is used to correct the overall energy level of impedance disturbances within the matching frequency band, ensuring it remains consistent with the logarithmic background impedance in the frequency domain.

[0074] Based on the energy matching coefficient, the amplitude of the logarithmic impedance disturbance within the matching frequency band is adjusted: In this embodiment of the disclosure, based on the energy matching coefficient The amplitude of the logarithmic impedance disturbance is corrected. The energy matching coefficient is used to characterize the overall energy ratio between the logarithmic impedance disturbance and the logarithmic background impedance within the effective frequency band.

[0075] Specifically, in the frequency domain, the spectrum of the logarithmic impedance perturbation is represented. Multiplied by the energy matching coefficient The logarithmic impedance perturbation spectrum after energy correction was obtained. Its expression is: , Through the above amplitude adjustment, the overall spectral energy level of the logarithmic impedance disturbance is kept consistent with the logarithmic background impedance.

[0076] It should be noted that the energy matching coefficient described in this disclosure... Instead of simply normalizing the average power of the full-band signal, it determines the frequency band based on the constraint of consistent spectral energy distribution. It is only used to correct the overall energy level of the impedance disturbance term within the selected matching frequency band, thereby achieving stable connection and integration with the background impedance without changing the relative amplitude structure within its spectrum.

[0077] In this embodiment of the disclosure, Figure 5 (b) schematically presents the logarithmic domain impedance perturbation distribution based on reflected wave inversion in the logarithmic domain after amplitude correction. It should be noted that... Figure 5 The result shown in (b) is the logarithmic impedance perturbation spectrum in the logarithmic domain after energy correction. The spatial domain representation obtained by performing the inverse Fourier transform. Figure 5 (b) It can be seen that the results can clearly characterize the location of the medium interface and the characteristics of local property changes, but there is still a lack of information in the low-frequency background part, and further constraints are still needed.

[0078] The adjusted impedance perturbation is fused with the background impedance in the frequency domain to obtain a full-band impedance model.

[0079] In this embodiment of the disclosure, after adjusting the amplitude of the logarithmic impedance disturbance within the matching frequency band, the logarithmic background impedance and the logarithmic impedance disturbance after energy matching correction are fused in the frequency domain to construct a physically consistent full-band impedance model.

[0080] Specifically, in the frequency domain, the spectrum of the logarithmic background impedance is represented. Compared with the corrected logarithmic impedance perturbation spectrum By superimposing the values, we obtain the frequency domain representation of the full-band logarithmic impedance. Its expression is: , Subsequently, the full-band logarithmic impedance spectrum was analyzed. Performing the inverse Fourier transform yields the full-band logarithmic impedance model in the time domain: , in, It also includes low-frequency background impedance information obtained from diffraction wave inversion and high-frequency impedance perturbation information obtained from reflected wave inversion, realizing a unified expression of different wave field constraint information in the impedance domain.

[0081] In this embodiment of the disclosure, Figure 6 The logarithmic domain impedance fusion result is presented, which is the logarithmic domain impedance fusion result after matching and fusing the logarithmic background impedance and logarithmic impedance perturbation in the frequency domain, and then undergoing inverse Fourier transform. Figure 6 It is evident that the fused logarithmic impedance model inherits the low-frequency background variation characteristics obtained from diffraction wave inversion in its overall structure. Its impedance variation trend with depth is smooth and continuous, without obvious low-frequency drift or non-physical oscillation. At the same time, at the local medium interface and the distribution location of the anomalous body, the fusion result clearly depicts the high-frequency impedance disturbance information obtained from the reflection wave inversion, with clear interface location and significantly improved spatial resolution.

[0082] By employing a matching and fusion method based on frequency domain energy consistency within the logarithmic impedance domain, the spectral discontinuities and energy imbalances that might be introduced by directly superimposing information from different frequency bands are effectively avoided. This allows for a physically consistent unified expression of low-frequency background constraints and high-frequency disturbance information within the same impedance model. The results demonstrate that the frequency domain matching and fusion strategy proposed in this disclosure can fully preserve the high-resolution information provided by the reflected wave while ensuring numerical stability, thus providing a reliable full-band impedance input model for the subsequent stable inversion of the dielectric constant.

[0083] In step S106, the dielectric constant distribution is calculated based on the full-band impedance model: In this embodiment of the disclosure, the full-band logarithmic impedance model constructed based on step S105 is... This allows for the calculation of the dielectric constant distribution of the medium. Since there is a definite physical correspondence between the wave impedance and the dielectric constant when electromagnetic waves propagate in a non-magnetic medium, a full-band logarithmic impedance model can be used to calculate this distribution. Achieve stable inversion of dielectric constant.

[0084] Dielectric impedance Determined by the full-band logarithmic impedance model, its expression is: , Based on this, assuming that the permeability of the medium is approximately equal to the permeability of free space, the dielectric wave impedance... With dielectric constant The following relationship exists between them: , in, Where is the dielectric constant. This is the free-space wave impedance; in one example, the free-space wave impedance value is 377. Therefore, the dielectric constant distribution of the medium can be obtained by inversion using the full-band logarithmic impedance model, and its expression is: , In this embodiment of the disclosure, Figure 7 The dielectric constant distribution obtained by inversion based on the method disclosed in this paper is presented. Figure 2 This serves as a reference model for the dielectric constant used in numerical forward modeling. A comparison of the two models reveals that the inversion results recover the overall spatial distribution characteristics of the dielectric constant, showing a gradual increase with depth. The tilt direction and geometry of the layer interfaces remain consistent with the reference model, without significant low-frequency drift or non-physical fluctuations. Furthermore, the range of dielectric constant values ​​obtained through inversion is largely consistent with the range in the reference model, without any systematic overestimation or underestimation, indicating that the method disclosed in this paper effectively guarantees the numerical stability of the dielectric constant inversion results. In addition, regarding local structure characterization, the inversion results can clearly identify the thin-layer structures set in the reference model, and their spatial location and geometric features are largely consistent with the reference model, demonstrating that the method disclosed in this paper possesses good local spatial resolution while maintaining overall stability.

[0085] Through the above calculation process, the dielectric constant distribution results can be obtained under the constraints of both the low-frequency background of diffracted waves and the high-frequency disturbances of reflected waves. Compared with the inversion results that rely solely on single wavefield information, this dielectric constant model achieves a good balance between overall numerical stability and local spatial resolution, and can more realistically reflect the electromagnetic property distribution characteristics of the lunar subsurface medium.

[0086] This disclosure does not simply superimpose or use in parallel the inversion results based on diffraction waves and the inversion results based on reflection waves. Instead, it establishes a unified physical parameter expression framework in the logarithmic impedance domain, matches and fuses the low-frequency background constraint information obtained from diffraction wave inversion with the high-frequency impedance perturbation information obtained from reflection wave inversion through frequency domain energy consistency constraints, thereby constructing a physically consistent full-band impedance model, and on this basis, achieving stable inversion of the dielectric constant.

[0087] This fusion strategy effectively avoids the instability of the dielectric constant background caused by the lack of low-frequency information in traditional reflected wave inversion methods. It also overcomes the spatial resolution limitations of relying solely on diffraction wave inversion, enabling a unified expression of different wavefield constraint information within the same impedance model. The resulting dielectric constant distribution exhibits good consistency in overall trend, numerical range, and local structure characterization, better reflecting the true electromagnetic properties of the lunar subsurface medium.

[0088] Those skilled in the art will understand that, without departing from the technical concept of this disclosure, this method is not only applicable to the inversion of the subsurface dielectric constant of lunar radar, but can also be extended to the inversion of electromagnetic properties of other deep space exploration or planetary radar data.

[0089] The above description is merely a preferred embodiment of this disclosure and is not intended to limit this disclosure. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for inverting the diffraction-reflection joint constrained dielectric constant of lunar radar data, characterized in that, The method includes: Preprocessing of lunar radar data yields radar profiles; The diffracted wave and the reflected wave are separated from the radar profile; Based on the diffracted wave, the background impedance of the medium is inverted to obtain the background impedance. The background impedance is then converted into logarithmic impedance form to obtain the logarithmic background impedance. Based on the reflected wave, the dielectric impedance perturbation inversion is performed to obtain the logarithmic impedance perturbation; The logarithmic background impedance and logarithmic impedance perturbation are matched and fused in the frequency domain to obtain a full-band impedance model, including: Determine the matching frequency band between the logarithmic background impedance and the logarithmic impedance disturbance; Within the matching frequency band, calculate the energy matching coefficient between the logarithmic background impedance and the logarithmic impedance disturbance; The amplitude of the logarithmic impedance disturbance within the matching frequency band is adjusted according to the energy matching coefficient. In the frequency domain, the adjusted logarithmic impedance perturbation is fused with the logarithmic background impedance to obtain a full-band impedance model; The energy matching coefficient is calculated using the following formula: ， in, The frequency domain representation of the logarithmic background impedance. This is the frequency domain representation of the logarithmic impedance perturbation. To match the lower limit of the frequency band, To match the upper limit of the frequency band, For frequency, Energy matching coefficient; The dielectric constant distribution is calculated based on the full-band impedance model, including: Multiplying the spectrum of the logarithmic impedance perturbation by the energy matching coefficient yields the energy-corrected impedance perturbation spectrum. The dielectric constant distribution is calculated based on the full-band impedance model.

2. The method for inverting the diffraction-reflection joint constrained dielectric constant of lunar radar data according to claim 1, characterized in that, The preprocessing includes at least: performing time zero-point correction on the lunar exploration radar data; removing the DC component from the time zero-point corrected lunar exploration radar data; and performing time-varying gain processing on the data after removing the DC component.

3. The method for inverting the diffraction-reflection joint constrained dielectric constant of lunar radar data according to claim 1, characterized in that, Separating diffracted and reflected waves from the radar profile includes: using a plane wave destruction method, by calculating the local tilt angle of the radar wave phase axis, suppressing the reflected wave component with an approximately constant local tilt angle, and retaining the diffracted wave component whose local tilt angle changes exceed a set threshold.

4. The method for inverting the diffraction-reflection joint constrained dielectric constant of lunar radar data according to claim 1, characterized in that, Inversion of dielectric impedance perturbation based on the diffracted wave includes: A three-dimensional velocity spectrum based on the diffracted wave is established using the velocity continuation method. Using negative entropy as a measure of the focusing degree of diffraction waves, the focusing velocity spectrum corresponding to the three-dimensional velocity spectrum is calculated. The offset velocity is obtained from the focused velocity spectrum using an automatic picking algorithm; Convert the offset velocity into a layer velocity model; Calculate the background impedance based on the layer velocity model. Transform the background impedance into a logarithmic form of the background impedance.

5. The method for inverting the diffraction-reflection joint constrained dielectric constant of lunar radar data according to claim 1, characterized in that, Based on the reflected wave, dielectric impedance perturbation inversion is performed, including: For the reflected wave, the mixed-phase wavelet estimation is performed using the mixed-phase deconvolution method, and the radar profile is corrected to near-zero phase to obtain the near-zero phase reflected wave; For the near-zero phase reflected wave, the sparse reflection coefficient is solved by sparse pulse deconvolution; Based on the reflection coefficient, a finite bandwidth impedance inversion is performed to obtain the logarithmic impedance perturbation.

6. The method for inverting the diffraction-reflection joint constrained dielectric constant of lunar radar data according to claim 1, characterized in that, This is based on the relationship between dielectric impedance and dielectric constant, expressed as: ， in, Where is the dielectric constant. For free space wave impedance, This represents the dielectric impedance.

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