CN118295025B - Multi-point seismic source inversion method and system - Google Patents
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Abstract
The invention discloses a multipoint source inversion method and system, which randomly samples the space-time position of a point source in a specific interval, and determining an acceptance sample according to a likelihood function of the model corresponding to the sample, and obtaining a model optimal solution according to the acceptance sample. The multi-dimensional parameter optimization method can quickly optimize multi-dimensional parameters of the multi-point seismic source model in a limited time and a limited storage space, and avoid unreasonable prior constraint in the prior art on the premise of ensuring the calculation efficiency.
Description
Technical Field
The invention relates to the technical field of seismic source inversion, in particular to a multi-point seismic source inversion method and system.
Background
At present, the moment tensor-based seismic source inversion method is based on the assumption of a single-point model, but when the moment magnitude exceeds the Mw7.3 level, the complexity is reflected in the aspects of fault number, fault geometry, dislocation mode and the like, and at the moment, an accurate fault model is difficult to give out simply according to the moment tensor (single-point model) inversion result. Meanwhile, the finite fault inversion method forcibly constrains the time-space change characteristic of the seismic source to a plane with a trend and a predetermined inclination angle, so that the change of the geometrical parameters of the seismic source fault is difficult to fully embody.
In contrast, the multi-point moment tensor/source mechanism inversion is carried out, the related free parameters contain relatively more complete information, and the space-time variation of the large seismic source mechanism can be reflected to the greatest extent;
However, at present, the inversion of the multi-point source model mainly faces the following bottlenecks:
1) Uncertainty of a priori assumptions, a certain degree of simplification must be performed to avoid excessive model space, and the basis for simplification is that the priori assumptions of certain parameters of the earthquake (such as: spatial coordinates, sub-event half-durations, sub-event centroid times, etc.), if the prior assumption itself does not match the real model, the result of the inversion must have a significant error from the real result. Similarly, in some linear inversion methods requiring model regularization, the selection of regularization factors also affects the inversion result;
2) The multi-point source model inversion needs to optimize the parameters of the multi-dimensional model, and if a traditional grid search mode is adopted, the model space is too large, and each parameter is difficult to search simultaneously in a limited time period; and if the model parameters are optimized one by one, the finally obtained model is not globally optimal.
Disclosure of Invention
In view of the above, the invention provides a multi-point seismic source inversion method and system, which are used for overcoming the defects of unstable solution, too severe constraint condition, undefined physical meaning and the like caused by too large model space and too many model parameters in the prior method.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
The application discloses a multipoint seismic source inversion method, which comprises the following steps:
determining the number of preset point source models according to earth surface displacement observation data of a plurality of stations;
Carrying out iterative inversion on solutions of a plurality of preset point source models, wherein the iterative inversion comprises the following steps:
determining a likelihood function of a point source model, and determining an acceptance sample according to the likelihood function;
and stopping inversion when the received samples meet the fine stability condition, and taking a solution vector corresponding to the received samples meeting the fine stability condition as an optimal solution for multi-point seismic source inversion.
Preferably, the process of determining the number of the preset point source models according to the earth surface displacement observation data of the plurality of stations comprises the following steps:
Performing centroid moment tensor inversion on earth surface displacement observation data of each station respectively;
obtaining a seismic source time function of each station according to the earth surface displacement observation data and the corresponding inversion result;
Obtaining an average focus time function according to the focus time function of each station;
and taking the number of neutron events in the average source time function as the number of preset point source models.
Preferably, according to the earth surface displacement observation data and the corresponding inversion result, obtaining a seismic source time function of each station through deconvolution according to the following formula;
In the method, in the process of the invention, Represents the nth component of the kth point source earth displacement observation,Representing the green's function between the kth point source and the observation point,Representing the spatial coordinates of the kth point source, s (k) representing the source time function of the kth point source; Representing centroid time; the half-duration time is indicated as such, Represents moment tensors calculated by the kth point source according to a seismic source mechanism, and M 0 represents scalar seismic moment,Representing the fault direction,Represents the fault inclination angle,Indicating the slip angle.
Preferably, the likelihood function of the point source model is determined according to the following formula;
wherein G represents a green function, m (f) is a seismic source model generated according to a solution vector f, G x m (f) represents a synthetic record generated under different models, d obs is a vector formed by observed data, and C M is a covariance matrix formed by the observed data error and uncertainty in a modeling process.
Preferably, the process of determining the accepted samples from the likelihood function comprises:
sampling in model space to obtain solution vector ，j=0,1,2,...,j-1；
If it meetsAccepting the sample, otherwise, generating a random number: judging whether u is smaller than min (1, P), if yes, accepting the sample, if no, discarding the sample;
Wherein, Represents the j-th sampling point in the kth point source, and P represents the sampled decision factor.
Preferably, the sampling decision factor is obtained by:
Where C represents the likelihood function calculated at the initial sampling, The exponential form representing the ratio between the current sample and the initial sample is used to calculate a decision factor, M 0 represents a model preset for the first time when the sampling starts, and H is an operator for controlling the acceptance rate.
Preferably, the plateau conditions satisfied by the accepted samples are:
where L represents the likelihood function, Representing solution vectorsTo the point ofIs used for the transfer matrix of (a),Representing solution vectorsTo the point ofIs used for the transfer matrix of (a).
Preferably, the screening of the surface displacement observation data of the plurality of stations in advance includes:
Space uniformity screening, namely constructing grids according to azimuth angles in relative jolts, and ensuring that station space distribution used for inversion is uniform;
Screening amplitude abnormality, namely eliminating too high or too low stations according to the median of peak-to-peak values recorded among all channels;
And screening the model matching degree, carrying out moment-of-moment tensor inversion in advance, and removing data which do not accord with the deviation between the response of the underground medium and the actual model according to the inversion result.
The application discloses a multi-point seismic source inversion system, which comprises the following steps:
The point source model determining unit is used for determining the number of preset point source models according to the earth surface displacement observation data of the plurality of stations;
the iterative inversion unit is used for performing iterative inversion on solutions of a plurality of preset point source models, and comprises the following steps:
determining a likelihood function of a point source model, and determining an acceptance sample according to the likelihood function;
and stopping inversion when the received samples meet the fine stability condition, and taking a solution vector corresponding to the received samples meeting the fine stability condition as an optimal solution for multi-point seismic source inversion.
Preferably, the method further comprises: the observation data screening unit is used for carrying out space uniformity screening, amplitude abnormality screening and/or model matching degree screening on the earth surface displacement observation data of the plurality of stations in advance.
Compared with the prior art, the invention discloses a multi-point seismic source inversion method and a system, which are characterized in that the point source space-time positions are randomly sampled in a specific interval, and a final accepted sample is determined according to a likelihood function of a sample corresponding model, so that the purpose of quickly optimizing multi-dimensional parameters in a limited time length and a limited storage space without adding unreasonable priori constraints is realized.
Meanwhile, the invention can search parameters such as longitude, latitude, depth, centroid time, half-duration time, trend, dip angle, sliding angle and the like of the sub-event at the same time, so that moment tensor solution of more than 4 point source models can be inverted; the inversion result can be quickly converged to the optimal model, so that the calculation efficiency is greatly improved, and the calculation cost is saved;
furthermore, the invention evaluates the fracture speed and the track according to posterior model distribution, so that the inversion process does not need to add regularization conditions to the coefficient matrix, thereby ensuring that the inversion result is more reasonable.
The inversion method disclosed by the invention has important theoretical significance and practical value in large earthquake researches with fuzzy fault geometry understanding and complicated fracture modes, and can also provide important references for subsequent other seismology researches.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a multi-point source inversion method provided by the invention;
FIG. 2 is a graph of the results of inversion of a model of a filtered seismic mid-multipoint source using the method of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
For the traditional linear inversion method, prior constraint is needed to be carried out on the fracture speed and the fracture track of the earthquake, a method is generally adopted that the fracture track of the earthquake is preset to be a straight line and has uniform fracture speed, the fracture track in the actual earthquake can be extremely complex, a plurality of faults can exist, the fracture speed is not constant in the process, and therefore the prior assumption that the fracture speed is over-ideal needs to be removed.
Meanwhile, in order to avoid the occurrence of over-fitting and singular solutions in the inversion process, conditions such as smoothness constraint and the like are added, and the method can influence the accuracy of the inversion result, so that a 'pseudo solution' is generated.
In addition, for the traditional nonlinear inversion method, the prior art often adopts a grid search method to traverse the whole parameter space when searching sub-event parameters, and for a single-point source model (such as a centroid moment tensor), the method can be applied because of fewer parameters to be solved; however, for the multi-point model, if the number of discrete point sources is K and the length of the space to be solved of each point source is j, the number of lattice points of the cumulative search will jump to j K, which results in too high calculation cost to be realized.
The embodiment of the invention provides a multi-point seismic source inversion method and system aiming at the problems.
In particular, in a first embodiment, the first embodiment,
As shown in fig. 1, the multi-point source inversion method includes the steps of:
determining the number of preset point source models according to earth surface displacement observation data of a plurality of stations;
performing iterative inversion on solutions of a plurality of preset point source models, including:
determining a likelihood function of a point source model, and determining an acceptance sample according to the likelihood function;
and stopping inversion when the received samples meet the fine stability condition, and taking a solution vector corresponding to the received samples meeting the fine stability condition as an optimal solution for multi-point seismic source inversion.
In an exemplary embodiment of the present invention,
S1, firstly, obtaining earth surface displacement caused by earthquakes recorded by a plurality of stations, and taking the earth surface displacement as earth surface displacement observation data of the stations; preprocessing the intercepted seismic waveform data u, including the steps of mean value correction, horizontal correction, instrument response removal, filtering, data resampling and the like; the data are spliced together to form an observation data vector d obs during inversion;
s11, in a preferred embodiment, screening the earth surface displacement observation data of a plurality of stations in any one of the following modes in advance comprises the following steps:
space uniformity screening, namely constructing grids according to azimuth angles in relative jolts, and ensuring that station space distribution used for inversion is uniform;
screening amplitude abnormity, namely removing too high or too low stations according to the median of peak-to-peak values recorded among all channels so as to avoid signal interference inversion results with too large or too small amplitude;
And screening the model matching degree, carrying out moment-of-moment tensor inversion in advance, and removing data which do not accord with the deviation between the response of the underground medium and the actual model according to the inversion result. Meanwhile, a single-point source model is obtained and used as a reference for accumulating response of a subsequent multi-point source model.
S12, determining the number of the preset point source models according to earth surface displacement observation data of a plurality of stations, wherein the process comprises the following steps:
1) Respectively inverting the moment tensors of the centroid of earth surface displacement observation data of each station to obtain moment tensors ；
2) According to the earth surface displacement observation data and the corresponding inversion result, combining the earth surface displacement record u n with the underground medium response model G, solving a visual source time function s n of each station by using a deconvolution method, and obtaining a seismic source time function of each station;
In the invention, the displacement expression theorem under the discrete multi-point source moment tensor model can be simplified expressed as:
Where u n represents the displacement record of the nth component; k=1, 2,3,., K represents K point source models; representing a green's function between a kth point source and an observation point; Spatial coordinates (longitude x, latitude y, depth z) representing the kth point source; s (k) denotes the source time function of the kth point source; Representing centroid time; representing a half-duration; Representing the moment tensor of the kth point source.
Or expressed as:
In the method, in the process of the invention, Represents the nth component of the kth point source earth displacement observation,Representing the green's function between the kth point source and the observation point,Representing the spatial coordinates of the kth point source, s (k) representing the source time function of the kth point source; Representing centroid time; the half-duration time is indicated as such, The moment tensor calculated by the kth point source according to the seismic source mechanism is represented, the number of free parameters is increased to 9 at the moment, and the rest 4 parameters are respectively: m 0 represents a scalar seismic moment,Representing the fault direction,Represents the fault inclination angle,Indicating the slip angle.
3) Obtaining an average focus time function according to the focus time function of each station; Average source time functionNamely, the process of releasing the earthquake energy along with time is represented;
4) With reference to an average source time function And judging the number of possible sub-events according to the number of medium pulse or the number of clusters aggregated in the aftershock space, and taking the number of K sub-events of the preset point source model as the number of the preset point source model according to the number of the sub-events.
S2, carrying out iterative inversion on solutions of a plurality of preset point source models, and if the minimum samples of the models in any one dimension are J from the view point of the solution vector f, the space size of K sub-event models in the multi-point moment tensor inversion at least reaches J 5 ×K, and the number in the multi-point source mechanism inversion at least reaches J 9×K, which is difficult to realize for the traditional grid search algorithm.
In this regard, the invention proposes an iterative inversion method, specifically comprising:
S21, determining a likelihood function of the point source model, and determining an acceptance sample according to the likelihood function;
in this embodiment, several parameters of the K-point source model are randomly sampled simultaneously by Monte Carlo method, and the model generated by each sampling is recorded as The method is also called solution vector, and a theoretical seismogram is calculated according to the following formula by combining a medium response function G to obtain a likelihood function of current sampling;
wherein G represents a green function, m (f) is a seismic source model generated according to a solution vector f, G x m (f) represents a synthetic record generated under different models, d obs is a vector formed by observed data, and C M is a covariance matrix formed by the observed data error and uncertainty in a modeling process.
Further, the acceptance samples are determined from the likelihood functions according to the following criteria:
sampling in model space to obtain solution vector ，j=0,1,2,...,j-1；
If it meetsAccepting the sample, otherwise, generating a random number: judging whether u is smaller than min (1, P), if yes, accepting the sample, if no, discarding the sample;
Wherein, Representing the jth sampling point in the kth point source, P represents the sampled decision factor, and the sampled decision factor is obtained by:
Where C represents the likelihood function calculated at the initial sampling, The exponential form representing the ratio between the current sample and the initial sample is used for calculating a decision factor, M 0 represents a model preset for the first time at the beginning of sampling, H is an operator for controlling the acceptance rate, and monotonically increases along with the sampling, so that the convergence efficiency of the whole sampling can be controlled.
In one embodiment, the specific inversion procedure is as follows:
if
receiving a sample:
else
if u<min(1,P)
receiving a sample:
else
Discarding the sample;
end
end
s22, in the present embodiment, the accepted sample is marked as For samples that were not accepted, it was markedStopping inversion when the received samples meet the fine stability condition, and storing the solution vector corresponding to the received samples meeting the fine stability condition as a multi-point seismic source inversion optimal solution, wherein the data storage further comprises: sub-event space-time parameters, model posterior probability distribution, sub-event source parameters.
In one embodiment, the stationary condition is determined based on a Markov Chain; that is, in the present invention, the stationary conditions satisfied by the accepted samples are:
where L represents the likelihood function, Representing solution vectorsTo the point ofIs used for the transfer matrix of (a),Representing solution vectorsTo the point ofIs used for the transfer matrix of (a).
Preferably, according to allAnd the posterior probability distribution is formed, and model disturbance analysis is carried out on the posterior probability distribution so as to further realize error evaluation and provide error distribution of inversion results.
And when the final sampling is terminated, the optimal value of f (1-K) can be obtained, and the posterior probability density distribution (PPDF) of the K sub-event models is gathered towards the optimal solution and is stabilized at the optimal solution.
Example two
The embodiment discloses a multi-point source inversion system, comprising:
The point source model determining unit is used for determining the number of preset point source models according to the earth surface displacement observation data of the plurality of stations;
the iterative inversion unit is used for performing iterative inversion on solutions of a plurality of preset point source models, and comprises the following steps:
determining a likelihood function of a point source model, and determining an acceptance sample according to the likelihood function;
and stopping inversion when the received samples meet the fine stability condition, and taking a solution vector corresponding to the received samples meeting the fine stability condition as an optimal solution for multi-point seismic source inversion.
Further, the method further comprises the following steps: the observation data screening unit is configured to screen surface displacement observation data of a plurality of stations in advance by adopting any one of the following modes, and includes:
constructing grids according to azimuth angles of relative jolts, and ensuring that station space distribution used for inversion is uniform;
removing too high or too low stations according to the median of peak-to-peak values recorded between the tracks;
And performing moment-center tensor inversion in advance, and removing data which do not accord with the deviation between the response of the underground medium and the actual model according to the inversion result.
Compared with the prior art, the method has the greatest advantage that the multidimensional parameters can be quickly optimized in the limited storage space with limited length without adding prior constraint which may be unreasonable. Specifically, parameters such as sub-event longitude, latitude, depth, centroid time, half-duration, trend, dip angle, sliding angle and the like can be searched simultaneously, so that moment tensor solution of more than 4 point source models can be inverted.
In addition, the posterior probability distribution of each parameter can be evaluated under the Bayesian inversion theory, and the error distribution of the inversion result can be directly given.
The inversion method is widely applied to post-earthquake emergency fast reporting work of the China seismic bureau geophysical research institute, and is particularly suitable for double-earthquake or multi-earthquake events because the influence of background noise errors and modeling errors on inversion results is fully considered, so that the centroid moment tensor solution of the small earthquake submerged in the front earthquake can be accurately solved, which is difficult to realize in the classical centroid moment tensor solution.
If the earthquake is well-determined in 2022, the earthquake focus is scattered into 4 clusters according to the aftershock space clustering clusters at the middle periphery of the well-determined earthquake, and the mechanism solution of the earthquake focus under the 4-point source model is finally obtained through 10 ten-thousand sampling, as shown in fig. 2. The above examples all demonstrate the rationality of the process of the invention.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (7)
1. A multipoint seismic source inversion method is characterized in that,
Determining the number of preset point source models according to earth surface displacement observation data of a plurality of stations;
performing iterative inversion on solutions of a plurality of preset point source models, including:
determining a likelihood function of a point source model, and determining an acceptance sample according to the likelihood function;
Stopping inversion when the received samples meet the fine stability condition, and taking a solution vector corresponding to the received samples meeting the fine stability condition as an optimal solution for multi-point seismic source inversion;
Determining a likelihood function of the point source model according to the following formula;
Wherein G represents a green function, m (f) is a seismic source model generated according to a solution vector f, G x m (f) represents a synthetic record generated under different models, d obs is a vector formed by observed data, and C M is a covariance matrix formed by the observed data error and uncertainty in a modeling process;
the process of determining an accepted sample from the likelihood function includes:
sampling in model space to obtain solution vector
If it meetsThen accept the sample, otherwise, generate a random number: judging whether u is smaller than min (1, P), if yes, accepting the sample, if no, discarding the sample;
Wherein, Representing the jth sampling point in the kth point source, and P represents the sampled judgment factor;
The sampling decision factor is obtained by:
Where C represents the likelihood function calculated at the initial sampling, The exponential form representing the ratio between the current sample and the initial sample is used to calculate a decision factor, M 0 represents a model preset for the first time when the sampling starts, and H is an operator for controlling the acceptance rate.
2. The method of multi-point source inversion according to claim 1, wherein determining the number of the predetermined point source models based on the surface displacement observation data of the plurality of stations comprises:
Performing centroid moment tensor inversion on earth surface displacement observation data of each station respectively;
obtaining a seismic source time function of each station according to the earth surface displacement observation data and the corresponding inversion result;
Obtaining an average focus time function according to the focus time function of each station;
and taking the number of neutron events in the average source time function as the number of preset point source models.
3. The multi-point source inversion method according to claim 2, wherein the source time function of each station is obtained by deconvolution according to the following formula based on the surface displacement observation data and the corresponding inversion result;
In the method, in the process of the invention, Represents the nth component of the kth point source earth displacement observation,Representing a green function between a kth point source and an observation point, ζ represents a spatial coordinate of the kth point source, and s (k) represents a source time function of the kth point source; τ c represents centroid time; τ h represents the half-duration time,Represents moment tensors calculated by the kth point source according to a seismic source mechanism, M 0 represents scalar seismic moment, phi represents fault strike, delta represents fault dip angle, and lambda represents slip angle.
4. The method of multi-point source inversion of claim 1, wherein the stationary conditions satisfied by the received samples are:
where L represents the likelihood function, Representing solution vectorsTo the point ofIs used for the transfer matrix of (a),Representing solution vectorsTo the point ofIs used for the transfer matrix of (a).
5. The multi-point source inversion method of claim 1, wherein the surface displacement observation data of the plurality of stations is subjected to spatial uniformity screening, amplitude anomaly screening, and/or model matching degree screening in advance.
6. A multi-point source inversion system, comprising:
The point source model determining unit is used for determining the number of preset point source models according to the earth surface displacement observation data of the plurality of stations;
the iterative inversion unit is used for performing iterative inversion on solutions of a plurality of preset point source models, and comprises the following steps:
determining a likelihood function of a point source model, and determining an acceptance sample according to the likelihood function;
Stopping inversion when the received samples meet the fine stability condition, and taking a solution vector corresponding to the received samples meeting the fine stability condition as an optimal solution for multi-point seismic source inversion;
Determining a likelihood function of the point source model according to the following formula;
Wherein G represents a green function, m (f) is a seismic source model generated according to a solution vector f, G x m (f) represents a synthetic record generated under different models, d obs is a vector formed by observed data, and C M is a covariance matrix formed by the observed data error and uncertainty in a modeling process;
the process of determining an accepted sample from the likelihood function includes:
sampling in model space to obtain solution vector
If it meetsThen accept the sample, otherwise, generate a random number: judging whether u is smaller than min (1, P), if yes, accepting the sample, if no, discarding the sample;
Wherein, Representing the jth sampling point in the kth point source, and P represents the sampled judgment factor;
The sampling decision factor is obtained by:
Where C represents the likelihood function calculated at the initial sampling, The exponential form representing the ratio between the current sample and the initial sample is used to calculate a decision factor, M 0 represents a model preset for the first time when the sampling starts, and H is an operator for controlling the acceptance rate.
7. The multi-point source inversion system of claim 6, further comprising: the observation data screening unit is used for carrying out space uniformity screening, amplitude abnormality screening and/or model matching degree screening on the earth surface displacement observation data of the plurality of stations in advance.
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