Rock fracture energy back-calculation method considering influence of crack energy attenuation

Abstract

The application provides a rock fracture energy back calculation method considering crack energy attenuation influence, and belongs to the technical field of rock mechanics and geotechnical engineering monitoring and analysis. The rock fracture energy back calculation method considering crack energy attenuation influence takes existing positioning results as input, extracts the density and scale parameters of cracks on the propagation path, and decouples total attenuation into matrix absorption attenuation and crack scattering additional attenuation. According to the relationship between crack scale and wavelength, a scattering model is selected to represent crack loss, and the wave number and velocity under the joint action of multiple cracks are corrected based on effective medium theory. A frequency-related compensation function containing a crack scattering term is constructed to compensate the signal by frequency and apply stability constraints, and the travel time is co-corrected according to the causal relationship between attenuation and dispersion. The fracture energy is back calculated in the effective frequency band, and the crack parameters are optimized jointly based on the measured values of attenuation and velocity. The application can reduce the energy underestimation caused by cracks, improve the back calculation accuracy, and is suitable for rock burst early warning and rock mass stability monitoring.

Description

Technical Field

[0001] This invention belongs to the field of rock mechanics and geotechnical engineering monitoring and analysis technology. Specifically, it relates to a rock fracture energy back-calculation method that considers the influence of crack energy attenuation, which can be used for rock mass damage evolution analysis, underground engineering stability evaluation, rockburst disaster early warning and safety monitoring of complex rock mass structures. Background Technology

[0002] In the fields of rock engineering and geological monitoring, acoustic emission / microseismic monitoring technology is widely used to detect internal rock fracture events. By deploying vibration sensor arrays on or inside the rock mass, elastic wave signals generated by rock fractures can be collected, allowing the location of the fracture source and estimation of its released energy. Fracture energy is a crucial parameter for evaluating the degree of rock mass damage and predicting dynamic hazards such as rockbursts; its back-calculation accuracy directly affects the reliability of engineering safety assessments.

[0003] Existing methods for back-calculating rock fracture energy typically rely on fracture source location results, estimating the energy released from the fracture source based on elastic wave propagation distance, medium attenuation characteristics, and sensor reception response. These methods often treat the propagation medium between the fracture source and the sensor as a continuous, homogeneous medium, primarily considering energy attenuation caused by factors such as internal material absorption, propagation distance, and quality factor Q. By establishing an empirical or semi-empirical relationship between propagation distance and amplitude attenuation, the energy received by the sensor is extrapolated to the fracture source location.

[0004] However, natural fractures and mining-induced fractures of different scales and orientations are commonly found in actual rock masses. When elastic waves propagate from the fracture source to the sensor and pass through the fracture region, they undergo scattering, reflection, transmission, and local energy dissipation at the fracture interface, resulting in a further reduction in the effective energy received by the sensor compared to the fracture-free condition. Therefore, even if the fracture source is accurately located, if the energy calculation does not take into account the additional energy loss caused by the fractures in the propagation path, the energy released by the fracture source may still be significantly underestimated, thus affecting the accuracy of rock fracture energy assessment. Summary of the Invention

[0005] In view of this, the present invention provides a rock fracture energy back-calculation method that considers the influence of fracture energy attenuation. This method can solve the technical problems of existing rock fracture energy back-calculation methods that treat the propagation medium as a continuous and homogeneous medium and do not consider the additional energy loss caused by fracture scattering along the propagation path, resulting in an underestimation of the energy released from the fracture source. At the same time, the methods also have problems such as the lack of decoupling between fracture scattering attenuation and matrix absorption attenuation, the lack of characterization of the combined effect of multiple fractures, the failure of energy compensation to reflect the frequency correlation characteristics of fractures, and the lack of coordinated correction of attenuation and dispersion, which affect the accuracy of the back-calculation results.

[0006] This invention is implemented as follows:

[0007] This invention provides a method for back-calculating rock fracture energy considering the influence of fracture energy attenuation, comprising the following steps:

[0008] S01 acquires existing rock fracture source location results, elastic wave waveform signals collected by multi-channel sensors, and sensor spatial arrangement parameters to determine the propagation path from the fracture source to each sensor.

[0009] S02 acquires information on crack detection inside rocks, extracts the number, size, spatial distribution and geometric morphology parameters of cracks along the propagation path, and uses crack density and equivalent crack size to characterize crack distribution features.

[0010] S03 decomposes the total energy attenuation of elastic waves along the propagation path into two independent components: rock matrix absorption attenuation and crack scattering additional attenuation. It establishes a frequency-dependent equivalent quality factor to separate the crack scattering additional attenuation from the total attenuation.

[0011] S04: Based on the relative relationship between crack density, equivalent crack size and elastic wave wavelength, select the corresponding scattering model and establish a quantitative mapping relationship between crack structural parameters and crack scattering additional attenuation.

[0012] S05: Based on the effective medium theory, the effective wave number and propagation velocity under the combined action of the crack group are corrected according to the crack density level, and the influence of multi-crack interaction and multiple scattering on the propagation characteristics of elastic waves is characterized.

[0013] S06: Construct a frequency-related compensation function that includes an additional attenuation term for crack scattering, apply differentiated energy compensation to the received signals of each channel according to the frequency components, and determine the effective compensation frequency band through compensation stability constraints to suppress high-frequency over-compensation;

[0014] S07: Based on the causal physical relationship between elastic wave attenuation and dispersion, calculate the change in propagation velocity caused by crack scattering, and correct the elastic wave propagation time along the propagation path;

[0015] S08: Based on the compensated and corrected wavefield signal, calculate the estimated energy released by the rupture source within the effective compensation frequency band, and optimize the rupture parameters jointly with the objective of minimizing the deviation between the measured values ​​and model values ​​of the rupture attenuation characteristics and propagation velocity characteristics. Output the results after iterative convergence.

[0016] The technical effects of the above technical solution are as follows:

[0017] A technical chain was constructed, encompassing fracture influence identification, attenuation mechanism decoupling, fracture energy compensation, dispersion travel time correction, and fracture energy back-calculation. By elevating fracture structure along the propagation path from a neglected background factor to an independent energy attenuation influencing factor, the total attenuation was decoupled from matrix absorption and fracture scattering. Sequentially, quantitative scattering characterization, multi-fracture correction, frequency-specific energy compensation, travel time correction, and joint optimization were performed, resolving the current problem of underestimated fracture source energy due to neglecting additional fracture attenuation. This ensures that the back-calculation results accurately reflect the energy loss characteristics of non-uniform elastic wave propagation in fractured rock masses.

[0018] Based on the above technical solution, the rock fracture energy back-calculation method of the present invention considering the influence of fracture energy attenuation can be further improved as follows:

[0019] The crack density is determined by the cube of the number of cracks per unit volume and the equivalent crack size, so as to comprehensively characterize the crack number density and spatial occupancy. For irregular three-dimensional cracks, the scales of the three principal axes are converted into equivalent crack scales by geometric mean, so that the scattering ability of irregular cracks is equivalent to that of a standard disk crack.

[0020] The technical effects of the above technical solution are as follows:

[0021] Crack density and equivalent radius The definition provides a unified quantitative characterization parameter for cracks of different scales and morphologies. Crack density integrates the number and scale of cracks into a scalar field that can be integrated along the propagation path, and the equivalent radius equates the scattering ability of irregular three-dimensional cracks to a disk model, so that subsequent scattering attenuation calculations do not depend on the specific orientation and complex geometry of the cracks, greatly improving the engineering applicability of the method.

[0022] In step S03, the absorption attenuation of the rock matrix is ​​characterized by a frequency power-law model, and the additional attenuation of fracture scattering is characterized by a frequency high-power model related to fracture density and fracture size. By utilizing the additivity of the quality factors, the inverses of the quality factors corresponding to the two types of attenuation are superimposed to obtain an equivalent quality factor that varies with frequency, so that the matrix absorption term and the fracture scattering term have identifiable different frequency dependence characteristics in the frequency domain.

[0023] The technical effects of the above technical solution are as follows:

[0024] Total Attenuation Decoupling Model And the additive relationship of quality factors, which mathematically and rigorously separates the two distinct physical mechanisms of attenuation, viscoelastic absorption of rock matrix and elastic scattering of fractures.

[0025] Frequency-dependent equivalent quality factor Matrix term The crack term changes (approximately frequency-independent when γ≈1) and... The significant difference in frequency dependence between the two allows the effects of cracks to be clearly identified, which can resolve the problem of unclear physical meaning of parameters caused by mixing crack attenuation into matrix Q value.

[0026] In step S04, the scattering model is selected based on the ratio of the equivalent crack size to the elastic wave wavelength: when the crack size is much smaller than the wavelength, the Rayleigh scattering model is used, so that the additional attenuation of crack scattering is proportional to the crack density and the fourth power of the frequency; when the crack size and the wavelength are on the same order of magnitude, the Mie scattering model is switched to and a scale correction factor is introduced to cover the range of medium-sized cracks that are not applicable to the Rayleigh model.

[0027] The technical effects of the above technical solution are as follows:

[0028] By constructing a Rayleigh scattering model, the scattering attenuation and crack density under small-scale crack conditions are given. Proportional to frequency A directly proportional quantitative relationship:

[0029] and

[0030] This analytical expression directly maps crack geometry parameters to frequency-dependent attenuation coefficients, resulting in high computational efficiency and providing accurate attenuation parameter inputs for energy compensation under the influence of cracks. The frequency dependence characteristic explains the experimental phenomenon that high-frequency signals experience more severe energy loss after passing through the crack region.

[0031] Furthermore, for non-uniform cracks, a crack aspect ratio shape correction factor is introduced into the scattering model to correct the scattering attenuation of flat or elliptical cracks; for crack groups with continuous scale distribution, the crack scale distribution function is piecewise integrated over the entire scale range to accumulate the scattering contribution of cracks at different scales.

[0032] The technical effects of the above technical solution are as follows:

[0033] By adjusting the Mie scattering correction function Non-uniform crack shape correction function The introduction of this technology expands the applicability of scattering attenuation to the small-scale Rayleigh scattering region (…). The method extends to the Mie scattering region, which is on the same order of magnitude as the crack wavelength, and covers non-disc-shaped cracks such as flat and elliptical cracks. This allows the method to accurately calculate scattering attenuation in engineering scenarios with a wide range of crack scales, such as in on-site tunnel microseismic monitoring where crack scales range from 0.1m to several meters, avoiding the limitations of the Rayleigh model. Systematic overestimation when the condition of being much less than 1 is not met.

[0034] In step S05, when the crack density is lower than a preset threshold, the effective wavenumber and equivalent propagation velocity are approximated by a first-order effective medium. When the crack density is higher than the preset threshold, the complex effective wavenumber is corrected by a multiple scattering model that considers multiple scattering and coherence effects between cracks, and the imaginary part of the complex effective wavenumber is used as the effective attenuation parameter under multiple scattering conditions, so as to realize the adaptive selection of correction strategy according to crack density level.

[0035] The technical effects of the above technical solution are as follows:

[0036] The Foldy effective medium model is used to represent discrete crack groups as homogeneous effective media, and the effective wavenumber is used to... and effective speed The systemic reduction effect of crack density on propagation velocity was characterized;

[0037] The Waterman-Truell multiple scattering model was employed to further consider the multiple scattering and coherence effects between fractures under high fracture density, and the imaginary part of the complex wavenumber was used as the effective attenuation. The two-stage correction strategy enables the method to adapt to different fracture density levels, maintaining computational simplicity at low fracture density and ensuring accuracy at high fracture density, thus improving its applicability to complex fractured rock masses.

[0038] In step S06, the compensation function includes both matrix absorption compensation term and crack scattering compensation term. The compensation amount of the crack scattering compensation term increases nonlinearly with increasing frequency, so that the high-frequency components receive greater compensation to match the crack scattering loss. The upper limit frequency of compensation is solved with the preset maximum compensation gain as a constraint condition. Compensation is only performed within the effective compensation frequency band. Frequency components outside the band are truncated or attenuated to prevent high-frequency noise from being excessively amplified.

[0039] The technical effects of the above technical solution are as follows:

[0040] A frequency-division inverse Q compensation function incorporating a crack scattering attenuation term is employed:

[0041]

[0042] The compensation amount adapts to the frequency characteristics of crack attenuation—high-frequency components receive more compensation due to greater crack scattering attenuation, while low-frequency components receive less compensation, overcoming the defect that constant Q compensation cannot characterize the frequency-selective attenuation of cracks.

[0043] Compensation stability constraint equation with maximum gain Automatically determine the cutoff frequency for the upper limit It effectively suppresses the inherent noise amplification problem of high-frequency inverse Q filtering, achieving a balance between crack attenuation compensation and numerical stability.

[0044] In step S07, based on the causal constraint relationship between attenuation and dispersion, the static velocity reduction caused by crack density and the frequency-related dynamic velocity dispersion are calculated and superimposed to obtain the velocity change of each frequency component; along the actual propagation path from the crack source to the sensor, the propagation time is integrated segment by segment with the corrected frequency-related velocity to ensure that the travel time parameters on which energy compensation is based are consistent with the crack dispersion characteristics.

[0045] The technical effects of the above technical solution are as follows:

[0046] The dispersion correction based on Kramers-Kronig causality unifies attenuation and velocity variation within the same physical framework, ensuring that the compensated wavefield satisfies causality. (Velocity variation) Medium static term and dispersion Characterizing the long-term velocity reduction and frequency-dependent transient dispersion caused by crack density, respectively, and correcting the propagation time by path integral. This ensures consistency between timekeeping and attenuation compensation, avoiding phase distortion and positioning errors caused by correcting only energy without correcting timekeeping.

[0047] Furthermore, in step S08, the compensation function is applied to the received signal spectrum to obtain the compensated wavefield. The energy spectrum of the compensated wavefield is integrated within the effective compensation frequency band to obtain the estimated value of the energy released by the rupture source. The joint optimization aims to minimize the weighted deviation between the measured attenuation characteristics and measured velocity characteristics and the model prediction values. The crack density field and crack scale parameters are updated synchronously and iteratively. When the change in crack parameters between two adjacent iterations is less than the preset convergence threshold, the iteration is terminated and the optimization result is output.

[0048] The technical effects of the above technical solution are as follows:

[0049] Frequency domain energy integration achieves a quantitative mapping from received energy to energy released from the fracture source within the effective compensation frequency band. The joint optimization objective function simultaneously constrains attenuation and velocity characteristics, utilizing redundant information from multiple channels and physical quantities to invert fracture density and scale parameters.

[0050] Closed-loop iterative convergence condition This ensures the stability of the optimization results. The dual constraint mechanism reduces the impact of multiple solutions inverted from a single observation and the uncertainty of crack parameters on the energy results.

[0051] Furthermore, the present invention also provides a rock fracture energy back-calculation system that considers the influence of fracture energy attenuation, for performing the above steps and processing data, including:

[0052] The rupture location result input and signal acquisition module is used to acquire existing rupture source location results, multi-channel elastic wave waveform signals and sensor spatial arrangement parameters, and determine the propagation path.

[0053] Crack parameter acquisition and propagation path construction module: used to extract crack structural parameters on the propagation path, characterize crack distribution with crack density and equivalent crack scale, and construct path model;

[0054] Crack attenuation decoupling calculation module: used to decompose the total energy attenuation into rock matrix absorption attenuation and crack scattering additional attenuation and establish frequency-related equivalent quality factor;

[0055] Quantitative characterization module for crack scattering attenuation: used to select a scattering model based on the relationship between crack size and wavelength, and to establish a quantitative mapping between crack structural parameters and additional scattering attenuation;

[0056] Multi-fracture effective medium correction module: used to adaptively correct effective wavenumber, propagation velocity and effective attenuation based on the effective medium theory and fracture density level;

[0057] Crack-related inverse Q energy compensation module: used to construct a frequency-dependent compensation function containing crack scattering terms and perform frequency-division energy compensation under stability constraints;

[0058] Dispersion travel time correction module: used to correct the propagation speed based on the causal relationship between attenuation and dispersion and to correct the propagation time by integrating along the path;

[0059] Rupture energy back-calculation and parameter optimization module: used to calculate the estimated value of the energy released by the rupture source within the effective compensation frequency band and jointly optimize the fracture parameters;

[0060] In this system, the modules are connected sequentially according to the data flow to form the system architecture for engineering deployment, execute the above methods, and process the data.

[0061] Compared with existing technologies, the beneficial effects of the rock fracture energy back-calculation method considering the influence of fracture energy attenuation provided by this invention are:

[0062] By rigorously decoupling the total attenuation into matrix absorption and crack scattering, a quantitative analytical relationship between crack density, scale, morphology, and frequency-dependent scattering attenuation is established using the Rayleigh / Mie scattering model. Crack structural parameters along the propagation path are transformed into calculable additional energy losses, which are then compensated for term by term using a frequency-division inverse Q-compensation function. Compared to current homogeneous medium methods, this approach significantly reduces the energy underestimation caused by crack propagation losses and improves the agreement between the back-calculated results and the actual fracture energy.

[0063] By introducing Foldy's effective medium theory and the Waterman-Truell multiple scattering model, the correction strategy can be adaptively selected according to the crack density level, covering a wide range from sparse cracks to dense crack zones. At the same time, the method is enhanced in its applicability to practical engineering rock masses by handling multi-scale and non-uniform diameter cracks through Mie correction and shape correction functions.

[0064] High-frequency compensation is automatically truncated by a maximum gain constraint to suppress noise amplification. Simultaneously, the Kramers-Kronig relationship is used to coordinate attenuation compensation and velocity dispersion correction, ensuring the causality of the compensated wavefield and the self-consistency of propagation parameters. The joint optimization mechanism utilizes both attenuation and velocity constraints to invert fracture parameters, reducing the impact of parameter uncertainties on the final energy estimate.

[0065] The fracture source release energy, fracture additional attenuation parameters, and propagation characteristic parameters output by this invention, after correction for fracture influence, can be directly used for rock mass damage evolution analysis, underground engineering stability evaluation, rockburst disaster early warning, and safety monitoring of complex fractured rock masses, and have significant engineering practical value. Attached Figure Description

[0066] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 A flowchart of a rock fracture energy back-calculation method that takes into account the effect of fracture energy attenuation;

[0068] Figure 2 This is a schematic diagram of a rock fracture scene;

[0069] Figure 3 This is a schematic diagram of the sensor array arrangement;

[0070] Figure 4 This is a schematic diagram of multi-channel elastic wave signal acquisition.

[0071] Figure 5 This is a schematic diagram of the elastic wave propagation and reception path;

[0072] Figure 6 This is a schematic diagram showing the attenuation coefficient as a function of frequency.

[0073] Figure 7 A comparison of the spectra before and after inverse Q-energy compensation for the attenuation term added to the scattering with cracks;

[0074] Figure 8A comparison curve showing the dispersion travel-time correction based on the change in crack scattering velocity; Detailed Implementation

[0075] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0076] like Figure 1 The diagram shows a flowchart of a rock fracture energy back-calculation method considering the influence of fracture energy attenuation provided by the present invention, including the following steps:

[0077] S01: Obtain existing rock fracture source location results, elastic wave waveform signals acquired by multi-channel sensors, and sensor spatial arrangement parameters to determine the propagation path from the fracture source to each sensor:

[0078] Combination Figures 2-4 As shown, the existing rock fracture source location results are obtained, including the fracture source spatial coordinates (x, y, z) and the earthquake occurrence time t0, and the elastic wave waveform signal U synchronously acquired by multi-channel vibration sensors. i (t) and the spatial arrangement coordinates of the sensors. This step does not perform rupture source localization; instead, it uses the existing localization results as input to determine the elastic wave propagation path and propagation distance L based on the rupture source location and the coordinates of each sensor.

[0079] S02: Combination Figure 5 As shown, information on crack detection inside rocks is obtained, and the number, size, spatial distribution, and geometric morphology parameters of cracks along the propagation path are extracted. Crack density and equivalent crack size are used to characterize crack distribution features.

[0080] Crack density is determined by the cube of the number of cracks per unit volume and the equivalent crack size, comprehensively characterizing the crack number density and spatial occupancy. For irregular three-dimensional cracks, the scale along the three principal axes is converted to an equivalent crack scale using the geometric mean, making the scattering ability of the irregular crack equivalent to that of a standard disk crack. Specifically:

[0081] The results of rock internal fracture detection are obtained by means of drilling television, sonic scanning, CT imaging or geological sketching, and the number N, scale, spatial distribution and geometric morphology parameters of fractures along the propagation path are extracted.

[0082] Using crack density Characterizes the distribution of cracks per unit volume, where a is the radius of the crack equivalent disk;

[0083] For irregular three-dimensional cracks, the equivalent radius is used. Characterizing its scale, , , These represent the semi-axis lengths in the three principal axis directions. A propagation path model from the fracture source to each sensor is constructed, and the set of fractures traversed by the path is identified.

[0084] S03: Decompose the total energy attenuation of elastic waves along the propagation path into two independent components: rock matrix absorption attenuation and crack scattering additional attenuation. Establish a frequency-related equivalent quality factor to separate the crack scattering additional attenuation from the total attenuation.

[0085] Furthermore, the absorption attenuation of the rock matrix is ​​characterized by a frequency power-law model, and the additional attenuation of fracture scattering is characterized by a frequency high-power model related to fracture density and fracture size. Taking advantage of the additivity of the quality factors, the inverses of the quality factors corresponding to the two types of attenuation are superimposed to obtain the equivalent quality factor that varies with frequency, so that the matrix absorption term and the fracture scattering term have identifiable different frequency dependence characteristics in the frequency domain.

[0086] Among them, the crack attenuation decoupling calculation module is used to decompose the total energy attenuation during the propagation of elastic waves into rock matrix absorption attenuation and crack scattering attenuation, which is the basis for realizing crack influence correction.

[0087] like Figure 6 As shown, to distinguish between rock matrix absorption and fracture-related losses, the following total attenuation decoupling model is established using this module:

[0088]

[0089] In this formula, the three attenuation coefficients from left to right represent the total attenuation coefficient, the rock matrix absorption attenuation coefficient, and the crack scattering attenuation coefficient, respectively, where ω represents the angular frequency.

[0090]

[0091] This formula is used to characterize the attenuation caused by the absorption of rock materials themselves;

[0092]

[0093] The crack scattering attenuation coefficient is used to characterize the additional energy loss caused by crack scattering.

[0094] According to the elastic wave attenuation theory, the relationship between the total attenuation coefficient and the equivalent quality factor is as follows:

[0095]

[0096] The quality factors corresponding to rock matrix absorption and fracture scattering satisfy:

[0097]

[0098] This yields the frequency-dependent equivalent quality factor under the influence of cracks:

[0099]

[0100] In the formula, c represents the propagation velocity of the elastic wave; the equivalent quality factor is a function of the angular frequency; , and These represent the reference attenuation coefficient, reference angular frequency, and frequency index, respectively; the coefficient in the last term represents the crack scattering coefficient determined by the following formula:

[0101]

[0102] The above model allows for the separation and characterization of the additional attenuation caused by cracks from the total attenuation.

[0103] S04: Based on the relative relationship between crack density, equivalent crack size and elastic wave wavelength, select the corresponding scattering model and establish a quantitative mapping relationship between crack structural parameters and crack scattering additional attenuation.

[0104] Furthermore, the selection of the corresponding scattering model should follow these conditions: when the crack size is much smaller than the wavelength, the Rayleigh scattering model should be used, so that the additional attenuation of crack scattering is proportional to the crack density and the fourth power of the frequency; when the crack size is on the same order of magnitude as the wavelength, the Mie scattering model should be switched to and a scale correction factor should be introduced to cover the range of medium-sized cracks that the Rayleigh model is not applicable to.

[0105] For non-uniform diameter cracks, a crack aspect ratio shape correction factor is introduced into the scattering model to correct the scattering attenuation of flat or elliptical cracks, as detailed below:

[0106] The crack scattering attenuation quantitative characterization module is used to establish the correspondence between crack structural parameters and elastic wave energy loss, when the crack satisfies the following Rayleigh scattering condition:

[0107]

[0108] The scattering cross section of a single crack is expressed as:

[0109]

[0110] Based on the relationship between crack number density and single-crack scattering cross-section, the crack scattering attenuation coefficient is expressed as:

[0111]

[0112] Substituting the crack density parameter, we get:

[0113]

[0114] When the crack size and wavelength are on the same order of magnitude, a Mie scattering correction function is introduced:

[0115]

[0116] For non-uniform diameter cracks, equivalent radius and shape correction functions are further introduced:

[0117]

[0118] This allows for the calculation of scattering attenuation under different crack sizes and morphologies.

[0119] S05: Based on the effective medium theory, the effective wave number and propagation velocity under the combined action of the crack group are corrected according to the crack density level, and the influence of multi-crack interaction and multiple scattering on the propagation characteristics of elastic waves is characterized.

[0120] Furthermore, when the crack density is below a preset threshold, the effective wavenumber and equivalent propagation velocity are approximated using a first-order effective medium. When the crack density is above the preset threshold, a multiple scattering model considering inter-crack multiple scattering and coherence effects is used to correct the complex effective wavenumber, and the imaginary part of the complex effective wavenumber is used as the effective attenuation parameter under multiple scattering conditions. This achieves adaptive selection of the correction strategy based on the crack density level. Specifically:

[0121] The multi-crack effective medium correction module is used to characterize the effects of crack-to-crack interactions and multiple scattering on propagation characteristics under high crack density conditions.

[0122] This module establishes the effective wavenumber under fracture swarm conditions based on Foldy's effective medium theory.

[0123]

[0124] In the formula, K represents the effective wavenumber, k0 represents the wavenumber in the crack-free matrix, N represents the crack number density, and f(0) represents the forward scattering amplitude.

[0125] Among them, the forward scattering amplitude:

[0126]

[0127] Therefore, the effective wavenumber can be approximated as:

[0128]

[0129] Based on the relationship between effective wavenumber and phase velocity, the propagation velocity under the action of a crack swarm is expressed as:

[0130]

[0131] For regions with high crack density, the Waterman-Truell multiple scattering model is used to correct the effective wavenumber:

[0132]

[0133] Based on the corrected complex effective wavenumber, the effective attenuation parameter under multiple scattering conditions is obtained:

[0134]

[0135] S06: Construct a frequency-related compensation function that includes an additional attenuation term for crack scattering, apply differentiated energy compensation to the received signals of each channel according to the frequency components, and determine the effective compensation frequency band through compensation stability constraints to suppress high-frequency over-compensation;

[0136] Furthermore, the compensation function includes both matrix absorption compensation and crack scattering compensation terms. The compensation amount of the crack scattering compensation term increases nonlinearly with increasing frequency, allowing high-frequency components to receive greater compensation to match the crack scattering loss. The upper limit frequency for compensation is solved using a preset maximum compensation gain as a constraint, and compensation is performed only within the effective compensation frequency band. Frequency components exceeding this band are truncated or attenuated to prevent excessive amplification of high-frequency noise. Specifically:

[0137] The crack-affected inverse-Q energy compensation module is used to compensate for energy loss caused by crack scattering during elastic wave propagation.

[0138] Unlike compensation methods that use a constant quality factor, a frequency-division inverse Q compensation function that considers the frequency dependence of cracks is used:

[0139]

[0140] Within the Rayleigh scattering frequency band, the compensation function is expressed as:

[0141]

[0142] To suppress high-frequency noise amplification caused by overcompensation, the following compensation stability constraints are set:

[0143]

[0144] in To maximize the allowable compensation gain, the upper limit frequency and effective compensation frequency band are determined based on stability constraints;

[0145] Combination Figure 7 As shown, the horizontal axis represents frequency, and the vertical axis represents signal amplitude; the gray curve represents the signal spectrum before compensation, and the red curve represents the signal spectrum after differential energy compensation by a frequency-related compensation function that includes an additional attenuation term for crack scattering.

[0146] S07: Based on the causal physical relationship between elastic wave attenuation and dispersion, calculate the change in propagation velocity caused by crack scattering, and correct the elastic wave propagation time along the propagation path;

[0147] Furthermore, based on the causal constraint relationship between attenuation and dispersion, the static velocity reduction caused by crack density and the frequency-related dynamic velocity dispersion are calculated separately and then superimposed to obtain the velocity change of each frequency component; along the actual propagation path from the fracture source to the sensor, the propagation time is integrated segment by segment with the corrected frequency-related velocity to ensure that the travel time parameters on which energy compensation is based are consistent with the crack dispersion characteristics.

[0148] Because crack scattering attenuation is accompanied by changes in propagation velocity, the dispersion travel time correction module corrects the propagation velocity and propagation time under crack conditions based on the causal relationship between attenuation and dispersion.

[0149] According to the Kramers-Kronig relationship:

[0150]

[0151] Calculate the velocity change caused by crack scattering:

[0152]

[0153] The corrected elastic wave propagation time is then calculated using the following formula:

[0154]

[0155] This allows us to obtain the propagation time that takes into account the effects of crack dispersion.

[0156] Combination Figure 8 As shown, the horizontal axis represents frequency, and the vertical axis represents the propagation velocity of elastic waves; the black dashed line represents the velocity curve before frequency dispersion correction as a function of frequency, and the blue solid line represents the velocity curve after correction for the change in velocity after scattering through the crack.

[0157] S08: Based on the compensated and corrected wavefield signal, calculate the estimated energy released by the rupture source within the effective compensation frequency band, and optimize the rupture parameters jointly with the objective of minimizing the deviation between the measured values ​​and model values ​​of the rupture attenuation characteristics and propagation velocity characteristics. Output the results after iterative convergence.

[0158] Furthermore, in the above technical solution, the compensation function is applied to the received signal spectrum to obtain the compensated wavefield. The energy spectrum of the compensated wavefield is integrated within the effective compensation frequency band to obtain an estimate of the energy released by the fracture source. Joint optimization aims to minimize the weighted deviation between the measured attenuation characteristics and measured velocity characteristics and the model predictions. The fracture density field and fracture scale parameters are updated iteratively and synchronously. The iteration terminates and the optimization result is output when the change in fracture parameters between two adjacent iterations is less than a preset convergence threshold. Specifically:

[0159] The fracture energy back-calculation and parameter optimization module is used to calculate the estimated energy released from the rock fracture source after correction for fracture effects. The steps are as follows:

[0160] First, calculate the frequency domain energy based on the wavefield after inverse Q compensation:

[0161]

[0162] in, The result of the Fourier transform of the received signal;

[0163] Subsequently, integration is performed within the effective compensation frequency band:

[0164]

[0165] The frequency domain energy estimate corresponding to the energy released by the rupture source is obtained;

[0166] To reduce the impact of crack parameter uncertainties on the back calculation results, the following joint optimization objective is established:

[0167]

[0168] By iteratively updating the crack density field and velocity field The following conditions are used to determine whether the iteration has converged:

[0169]

[0170] When the convergence condition is met, the optimized fracture parameters, propagation parameters, and estimated energy released from the rock fracture source are output.

[0171] Furthermore, a rock fracture energy back-calculation system considering the influence of fracture energy attenuation is provided for performing the above steps and processing data, including:

[0172] The rupture location result input and signal acquisition module is used to acquire existing rupture source location results, multi-channel elastic wave waveform signals and sensor spatial arrangement parameters, and determine the propagation path.

[0173] Crack parameter acquisition and propagation path construction module: used to extract crack structural parameters on the propagation path, characterize crack distribution with crack density and equivalent crack scale, and construct path model;

[0174] Crack attenuation decoupling calculation module: used to decompose the total energy attenuation into rock matrix absorption attenuation and crack scattering additional attenuation and establish frequency-related equivalent quality factor;

[0175] Quantitative characterization module for crack scattering attenuation: used to select a scattering model based on the relationship between crack size and wavelength, and to establish a quantitative mapping between crack structural parameters and additional scattering attenuation;

[0176] Multi-fracture effective medium correction module: used to adaptively correct effective wavenumber, propagation velocity and effective attenuation based on the effective medium theory and fracture density level;

[0177] Crack-related inverse Q energy compensation module: used to construct a frequency-dependent compensation function containing crack scattering terms and perform frequency-division energy compensation under stability constraints;

[0178] Dispersion travel time correction module: used to correct the propagation speed based on the causal relationship between attenuation and dispersion and to correct the propagation time by integrating along the path;

[0179] Rupture energy back-calculation and parameter optimization module: used to calculate the estimated value of the energy released by the rupture source within the effective compensation frequency band and jointly optimize the fracture parameters;

[0180] Each module is connected in sequence to execute the above methods and data processing.

[0181] Compared with existing rock fracture energy back-calculation methods, this invention incorporates the additional energy attenuation caused by fractures along the propagation path into the energy back-calculation model based on the existing fracture source location results, and establishes a correction relationship for the estimated value of energy released from the received energy to the fracture source.

[0182] Based on the above technical means, the present invention can reduce the energy underestimation caused by cracks in the propagation path and improve the accuracy and interpretability of the back calculation results of rock fracture energy under fractured conditions.

[0183] Specifically, the present invention produces the following beneficial effects:

[0184] Firstly, the additional attenuation of the separation crack improves the interpretability of the attenuation parameters:

[0185] Existing methods are typically based on the assumption of a continuous homogeneous medium, mainly considering energy attenuation caused by factors such as propagation distance, rock matrix absorption, and quality factor, and rarely characterize the fracture along the propagation path from the fracture source to the sensor. When elastic waves pass through the fracture region, additional scattering and local energy dissipation reduce the received signal energy;

[0186] This invention decomposes the total energy attenuation into rock matrix absorption attenuation and fracture scattering additional attenuation, and independently characterizes the influence of fractures;

[0187] The above decomposition reduces the possibility of attributing energy loss caused by fractures to matrix absorption attenuation, thus making the attenuation parameters correspond to the propagation mechanism in fractured rocks.

[0188] Secondly, quantitative characterization of crack loss improves the targeting of energy compensation:

[0189] To address the difference in received energy caused by the structural differences of cracks along different propagation paths in the same rupture event, this invention establishes a quantitative relationship between crack structural characteristics and scattered energy loss using crack density, equivalent scale, and morphological parameters.

[0190] By using the Rayleigh scattering model, the Mie scattering correction function, and the non-uniform crack correction function, the crack geometric parameters are converted into additional crack attenuation parameters, which are used to calculate the energy loss of elastic waves passing through the crack region.

[0191] The above quantitative characterization provides attenuation parameters for compensating for propagation energy under the influence of cracks, thereby reducing the back-calculation bias caused by ignoring cracks in the propagation path.

[0192] Third, consider the combined effects of multiple cracks to improve applicability under complex crack conditions:

[0193] In actual rocks, the propagation path between the fracture source and the sensor may contain multiple cracks of different sizes and directions, and the interaction between the cracks will change the propagation characteristics of elastic waves.

[0194] This invention uses the effective medium theory and multiple scattering model to correct the effective wavenumber, propagation velocity and attenuation characteristics under the action of crack swarms;

[0195] This allows for the characterization of multi-crack propagation losses that are difficult to cover by a single-crack model, thereby improving the applicability of the energy inverse calculation method to complex crack distributions.

[0196] Fourth, implement frequency-related compensation to improve the stability of energy recovery:

[0197] Crack scattering exhibits frequency dependence; different frequency components experience varying degrees of energy loss after passing through the crack region. The inverse Q compensation method with a constant quality factor is insufficient to characterize this frequency-selective attenuation.

[0198] The present invention employs a frequency-division inverse Q compensation model that includes a crack scattering attenuation term, and determines the compensation amount based on the crack attenuation corresponding to each frequency component. At the same time, it determines the effective compensation frequency band through compensation stability constraints to suppress high-frequency noise amplification caused by overcompensation and improve the stability of the compensation process.

[0199] Fifth, it coordinates the correction of attenuation and dispersion to improve the consistency of propagation parameters:

[0200] Because cracks not only cause energy loss during propagation, but also change the equivalent stiffness of the medium and the propagation speed of elastic waves, they cause changes in propagation time and phase characteristics.

[0201] Based on the physical relationship between attenuation and dispersion, this invention corrects the changes in propagation velocity and propagation time caused by cracks, so that energy attenuation compensation and propagation characteristic correction work together. This synergistic correction can reduce the impact of propagation velocity anomalies on energy back calculation and improve the matching degree between the propagation model and the cracked rock structure.

[0202] Sixth, optimize crack parameters to improve the stability of the back calculation process:

[0203] The parameters of the crack along the propagation path are uncertain and can affect the calculation results of the crack's additional attenuation. This invention establishes a joint constraint relationship between crack attenuation characteristics, propagation velocity characteristics, and measured elastic wave response, and iteratively optimizes parameters such as crack density and crack size.

[0204] When the iteration meets the convergence condition, the optimized crack influence parameters and the corresponding energy compensation results are obtained. This closed-loop optimization can reduce the impact of crack parameter errors on the energy back-calculation results and improve the stability of the calculation process.

[0205] Seventh, energy evaluation parameters under fracture formation conditions support engineering analysis:

[0206] By comprehensively characterizing the crack structure, elastic wave attenuation, dispersion effect, and energy compensation process along the propagation path, this invention outputs an estimated value of the energy released from the rupture source after crack influence correction, additional attenuation parameters of the crack, and propagation characteristic parameters. Compared with energy back-calculation methods that do not consider the influence of cracks along the propagation path, this invention can reduce the energy underestimation caused by crack propagation loss and enhance the physical interpretability of the back-calculation results.

[0207] The above output parameters can be used for rock mass damage evolution analysis, underground engineering stability evaluation, rockburst disaster prediction, and safety monitoring of complex fractured rock masses.

[0208] Specifically, the principle of this invention is as follows: based on existing rock fracture source location results, the fracture structure along the propagation path between the fracture source and the sensor is incorporated into the fracture energy back-calculation process, establishing an energy correction and back-calculation method that considers the energy attenuation due to fractures. This method corrects and back-calculates the energy released by the fracture source under fractured conditions through fracture attenuation decoupling, quantitative calculation of scattering loss, energy compensation for fracture influence, and joint parameter optimization.

Claims

1. A method for back-calculating rock fracture energy considering the influence of fracture energy attenuation, characterized in that, Includes the following steps: S01: Obtain existing rock fracture source location results, elastic wave waveform signals collected by multi-channel sensors, and sensor spatial arrangement parameters to determine the propagation path from the fracture source to each sensor; S02: Obtain information on crack detection inside the rock, extract the number, size, spatial distribution and geometric morphology parameters of cracks along the propagation path, and use crack density and equivalent crack size to characterize crack distribution features; S03: Decompose the total energy attenuation of elastic waves along the propagation path into two independent components: rock matrix absorption attenuation and crack scattering additional attenuation. Establish a frequency-dependent equivalent quality factor to separate the crack scattering additional attenuation from the total attenuation. S04: Based on the relative relationship between crack density, equivalent crack size and elastic wave wavelength, select the corresponding scattering model and establish a quantitative mapping relationship between crack structural parameters and crack scattering additional attenuation. S05: Based on the effective medium theory, the effective wave number and propagation velocity under the combined action of the crack group are corrected according to the crack density level, and the influence of multi-crack interaction and multiple scattering on the propagation characteristics of elastic waves is characterized. S06: Construct a frequency-related compensation function that includes a crack scattering additional attenuation term, apply differentiated energy compensation to the received signals of each channel according to frequency components, and determine the effective compensation frequency band through compensation stability constraints to suppress high-frequency over-compensation; S07: Based on the causal physical relationship between elastic wave attenuation and dispersion, calculate the change in propagation velocity caused by crack scattering, and correct the elastic wave propagation time along the propagation path; S08: Based on the compensated and corrected wavefield signal, calculate the estimated energy released by the rupture source within the effective compensation frequency band, and optimize the rupture parameters jointly with the objective of minimizing the deviation between the measured values ​​and model values ​​of the rupture attenuation characteristics and propagation velocity characteristics. Output the results after iterative convergence.

2. The method for back-calculating rock fracture energy considering the influence of fracture energy attenuation according to claim 1, characterized in that, Crack density is determined by the number of cracks per unit volume and the cube of the equivalent crack size, to comprehensively characterize the crack number density and spatial occupancy. For irregular three-dimensional cracks, the scales in the three principal axis directions are converted into equivalent crack scales by geometric mean, so that the scattering ability of irregular cracks is equivalent to that of a standard disk crack.

3. The method for back-calculating rock fracture energy considering the influence of fracture energy attenuation according to claim 1, characterized in that, In S03, the absorption attenuation of the rock matrix is ​​characterized by a frequency power-law model, and the additional attenuation of fracture scattering is characterized by a frequency high-power model related to fracture density and fracture size. Taking advantage of the additivity of the quality factors, the inverses of the quality factors corresponding to the two types of attenuation are superimposed to obtain the equivalent quality factor that varies with frequency, so that the matrix absorption term and the fracture scattering term have identifiable different frequency dependence characteristics in the frequency domain.

4. The method for back-calculating rock fracture energy considering the influence of fracture energy attenuation according to claim 1, characterized in that, In S04, the scattering model is selected based on the ratio of the equivalent crack size to the elastic wave wavelength: when the crack size is much smaller than the wavelength, the Rayleigh scattering model is used, so that the additional attenuation of crack scattering is proportional to the crack density and the fourth power of the frequency; when the crack size and the wavelength are on the same order of magnitude, the Mie scattering model is switched to and a scale correction factor is introduced to cover the range of medium-sized cracks that the Rayleigh model is not applicable to.

5. The method for back-calculating rock fracture energy considering the influence of fracture energy attenuation according to claim 4, characterized in that, For non-uniform cracks, a crack aspect ratio shape correction factor is introduced into the scattering model to correct the scattering attenuation of flat or elliptical cracks; for crack groups with continuous scale distribution, the crack scale distribution function is piecewise integrated over the entire scale range to accumulate the scattering contribution of cracks at different scales.

6. The method for back-calculating rock fracture energy considering the influence of fracture energy attenuation according to claim 1, characterized in that, In S05, when the crack density is lower than the preset threshold, the effective wavenumber and equivalent propagation velocity are calculated by approximating the first-order effective medium. When the crack density is higher than the preset threshold, the complex effective wavenumber is corrected by a multiple scattering model that considers multiple scattering and coherence effects between cracks. The imaginary part of the complex effective wavenumber is used as the effective attenuation parameter under multiple scattering conditions, so as to realize the adaptive selection of correction strategy according to crack density level.

7. The method for back-calculating rock fracture energy considering the influence of fracture energy attenuation according to claim 1, characterized in that, In S06, the compensation function includes both matrix absorption compensation and crack scattering compensation terms. The compensation amount of the crack scattering compensation term increases nonlinearly with increasing frequency, so that high-frequency components receive greater compensation to match the crack scattering loss. The upper limit frequency of compensation is solved with the preset maximum compensation gain as a constraint condition. Compensation is only performed within the effective compensation frequency band. Frequency components outside the band are truncated or attenuated to prevent high-frequency noise from being excessively amplified.

8. The method for back-calculating rock fracture energy considering the influence of fracture energy attenuation according to claim 1, characterized in that, In S07, based on the causal constraint relationship between attenuation and dispersion, the static velocity reduction caused by crack density and the frequency-related dynamic velocity dispersion are calculated separately and then superimposed to obtain the velocity change of each frequency component. Along the actual propagation path from the fracture source to the sensor, the propagation time is integrated segment by segment with the corrected frequency-related velocity to ensure that the travel time parameters on which energy compensation is based are consistent with the crack dispersion characteristics.

9. The method for back-calculating rock fracture energy considering the influence of fracture energy attenuation according to claim 1, characterized in that, In S08, the compensation function is applied to the received signal spectrum to obtain the compensated wavefield. The energy spectrum of the compensated wavefield is integrated within the effective compensation frequency band to obtain the estimated value of the energy released by the rupture source. The joint optimization aims to minimize the weighted deviation between the measured attenuation characteristics and measured velocity characteristics and the model prediction values. The crack density field and crack scale parameters are updated synchronously and iteratively. When the change in crack parameters between two adjacent iterations is less than the preset convergence threshold, the iteration is terminated and the optimization result is output.

10. A rock fracture energy back-calculation system considering the effect of fracture energy attenuation, used to perform the steps and data processing of the method according to any one of claims 1 to 9, characterized in that, include: The rupture location result input and signal acquisition module is used to acquire existing rupture source location results, multi-channel elastic wave waveform signals and sensor spatial arrangement parameters, and determine the propagation path. Crack parameter acquisition and propagation path construction module: used to extract crack structural parameters on the propagation path, characterize crack distribution with crack density and equivalent crack scale, and construct path model; Crack attenuation decoupling calculation module: used to decompose the total energy attenuation into rock matrix absorption attenuation and crack scattering additional attenuation and establish frequency-related equivalent quality factor; Quantitative characterization module for crack scattering attenuation: used to select a scattering model based on the relationship between crack size and wavelength, and to establish a quantitative mapping between crack structural parameters and additional scattering attenuation; Multi-fracture effective medium correction module: used to adaptively correct effective wavenumber, propagation velocity and effective attenuation based on the effective medium theory and fracture density level; Crack-related inverse Q energy compensation module: used to construct a frequency-dependent compensation function containing crack scattering terms and perform frequency-division energy compensation under stability constraints; Dispersion travel time correction module: used to correct the propagation speed based on the causal relationship between attenuation and dispersion and to correct the propagation time by integrating along the path; Rupture energy back-calculation and parameter optimization module: used to calculate the estimated value of the energy released by the rupture source within the effective compensation frequency band and jointly optimize the fracture parameters.

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