CN116819622B - Background noise level vertical spectrum ratio joint inversion method for soil layer three-dimensional speed structure - Google Patents
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Abstract
The invention discloses a background noise level vertical spectrum ratio joint inversion method of a soil layer three-dimensional speed structure, relates to the field of shallow seismic exploration, carries out single-measuring point forward modeling calculation based on a background noise level and vertical spectrum ratio method of a scattering field theory, is more comprehensive and reasonable in theory explanation aspect of background noise than the prior common single body wave explanation and single surface wave explanation, and can simultaneously consider the influence of body waves and surface waves in soil layer background noise. According to the invention, by setting up the combined objective function, the simultaneous inversion of the background noise observation records of a plurality of observation points can be realized, so that the three-dimensional speed structure of the soil layer is obtained by using the inversion of the background noise records obtained by a plurality of observation points on the earth surface in an area range. The invention effectively reduces the cost of exploring the underground shallow speed structure in the area range, can be widely applied to areas where drilling holes or earthquake survey lines are difficult to spread, and greatly saves manpower, material resources and financial resources for engineering site exploration.
Description
Technical Field
The invention relates to the field of shallow seismic exploration, in particular to a background noise level vertical spectrum ratio joint inversion method of a soil layer three-dimensional speed structure.
Background
The soil layer characteristic detection and modeling are key links of seismic dynamic field effect numerical simulation in the construction engineering earthquake fortification earthquake motion parameter determination. The work of exploring low-cost engineering geological exploration technology, building a fine regional site three-dimensional model and the like is an important field of great attention in academia and engineering community. The soil layer speed structure has a strong reconstruction effect on earthquake waves, in particular to a loose covering layer near the earth surface, which has low density and small modulus, and the induced in-layer multiple has a strong amplification effect on the ground vibration, so that a large number of buildings, structures and other facilities can be damaged, the soil layer speed structure is an important cause for serious earthquake disasters, and the determination of the soil layer speed structure is extremely important for earthquake prevention and disaster reduction.
The method for researching the soil layer speed structure mainly comprises well drilling detection, engineering earthquake geophysical prospecting, natural earthquake, background noise and the like. Inversion by using background noise earth surface observation records has been greatly developed in recent decades due to the advantages of simple data acquisition, economical and practical technology and the like. The background noise inversion of the soil layer speed structure can be divided into a background noise matrix method and a background noise single method according to the observation mode of the acquired data. The background noise matrix method is a geophysical imaging method, and the basic idea is to approximate the empirical green's function between station pairs by calculating the noise cross-correlation function between station pairs, and then extract the surface wave dispersion to obtain the subsurface velocity structure. In general, high frequency surface waves are sensitive to shallow structures and low frequency surface waves are sensitive to deep structures. The surface wave frequency band of the background noise imaging research is mainly concentrated on a frequency band with a period of 5-40 s, and the research target is mainly inversion of the structure of the crust and the upper earth slow top. The work specific to near-surface shallow velocity structures is relatively less and the error is larger.
The background noise single method uses the background noise observation record of a single station to invert the speed structure below the station, and the inversion method of the horizontal and vertical spectrum ratio (hereinafter referred to as single NHV) of the background noise is the most representative single method. The single NHV inversion methods are broadly divided into three categories: (1) NHV is thought to be mainly affected by bulk wave components in background noise; (2) NHV is considered to be mainly affected by the wave component in the background noise; (3) NHV is thought to be the result of the co-action of two different types of wavefields, including bulk and surface waves. A large number of observation and theoretical researches show that the background noise wave field is the result of the combined action of the surface wave and the bulk wave, and the scattered field theory comprehensively considers different fluctuation types and is a theoretical explanation conforming to the observation reality. Therefore, NHV inversion based on fringe field theory is a relatively more rational inversion method of subsurface structures.
Although NHV inversion based on the fringe field theory comprehensively considers the combined action result of the surface wave and the bulk wave, at present, only a single-point fringe field NHV inversion method is provided, a method aiming at the measuring point joint inversion is not provided, and the joint inversion of a plurality of observation points cannot be realized.
Disclosure of Invention
Aiming at the defects in the prior art, the background noise level vertical spectrum ratio joint inversion method of the soil layer three-dimensional speed structure solves the problem that the exploration error of the shallow speed structure in the prior art is large.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the background noise level vertical spectrum ratio joint inversion method for the soil layer three-dimensional speed structure comprises the following steps:
s1, carrying out single-measuring-point forward modeling calculation by a background noise level and vertical spectrum ratio method based on a scattered field theory to obtain a single-measuring-point forward modeling calculation result of a three-dimensional soil layer speed structure;
s2, constructing a multi-measuring point global inversion objective function of the three-dimensional soil layer speed structure based on a Shan Cedian forward calculation result;
s3, performing global optimization on a multi-measuring point global inversion objective function of the three-dimensional soil layer speed structure;
and S4, calculating the minimum value of the global inversion objective function of the multiple measuring points after global optimization to obtain a three-dimensional soil layer speed structure corresponding to the minimum value of the global inversion objective function.
Further, the specific method in step S1 is as follows:
acquiring the density, the thickness, the P wave velocity and the S wave velocity of each soil layer, and according to the formula:
carrying out single-measuring-point forward modeling calculation based on background noise level and vertical spectrum ratio method of a scattered field theory; wherein the method comprises the steps ofThe horizontal and vertical spectrum ratio of background noise is represented, namely, the single-measuring-point forward modeling calculation result is obtained; />Is a green's function expressed in +.>Dot->Simple harmonic point force of one unit acting in direction +.>At->Dot->Displacement caused by direction; the superscript 1D indicates that the current green's function is that of a one-dimensional soil layer; />Representing the imaginary part of the green's function; />Expressed in natural constanteAn exponential function of the base; x represents the vector of earth model parameters to be inverted,，/>soil layer model representing the to-be-invertediThe parameters of the layer soil are set up,，/>、/>、/>、/>、/>and->Respectively represent soil layer model NoiThe P wave velocity, the S wave velocity, the soil layer thickness, the soil layer density, the quality factor of the P wave and the quality factor of the S wave of the soil layer; n represents the number of soil layers; />Representing a transpose of the matrix; />Representing the circle frequency; />Representation->Direction Unit impulse force induced +.>A unit impulse force of direction;representing a dirac function, i.e. a unit impulse function; t represents time; />In (a) and (b)iRepresenting imaginary units.
Further, in step S2, the expression of the multi-measuring point global inversion objective function of the three-dimensional soil layer velocity structure is:
wherein the method comprises the steps ofThe method comprises the steps of globally inverting an objective function for multiple measuring points; />And->Are all weight constants; />Representing the difference between the horizontal and vertical spectrum ratios obtained by calculation of the observed background noise data and the horizontal and vertical spectrum ratio curves obtained by forward calculation of the soil layer model in the inversion process; />Representing the difference in slope ratio between the simulated curve and the observed curve;and->Representing a simulated NHV curve and an observed NHV curve, respectively; />The horizontal axis representing the NHV curve, i.e. frequency; />For frequency->Weights of (2); />And->Respectively indicate->Frequency->Derivative of>Frequency->Is a derivative of (2); />Representing the total number of observation points; />Is constant when->When the value is 1-5, the importance of the regularization item to the P wave speed, the S wave speed, the soil layer density, the quality factor of the P wave and the quality factor of the S wave is respectively expressed; />Representing a degree of similarity between a plurality of observation points for inverting the earth model; />，/>Represent the firstkAnd (d)lCoupling degree between one-dimensional soil layer models corresponding to the observation points, if->Then indicate at the firstkAnd (d)lEnforcing the strongest constraint between locations; if->Then no constraint is added; />Represent the firstkThe observation pointsA value; />Represent the firstlThe->A value; when->When the value is 1-5, the +.>Respectively representing the P wave velocity, the S wave velocity, the soil layer density, the quality factor of the P wave and the quality factor of the S wave at different soil layer model depths z; />Representing the depth value of the bottom of the soil layer model; />Representing a depth value of the top of the soil layer model; z represents the depth of the earth model.
Further, the specific method of step S3 comprises the following sub-steps:
s3-1, setting a P wave speed, an S wave speed, soil layer density, a P wave quality factor and a variation range and a variation step length of the S wave quality factor, and generating all possible combinations of parameters through parameter combination;
s3-2, calculating inversion objective function values under all possible combinations of parameters, and selecting a soil layer model with the minimum inversion objective function value as an inversion optimal model to obtain the overall optimized multi-measuring-point overall inversion objective function.
Further, if the variance of the observed NHV curve exceeds 0.2 times the mean of the observed NHV curve, thenAnd->Set to 0.6 and 0.4, respectively; otherwise will->And->Set to 0.9 and 0.1, respectively.
The beneficial effects of the invention are as follows:
1. according to the invention, by setting up the combined objective function, the simultaneous inversion of the background noise observation records of a plurality of observation points can be realized, so that the three-dimensional speed structure of the soil layer is obtained by using the inversion of the background noise records obtained by the plurality of observation points on the earth surface in an area range, the cost of exploring the underground shallow speed structure in the area range is effectively reduced, the method can be widely applied to areas where drilling or seismic survey lines are difficult to be deployed, and the manpower, material resources and financial resources of engineering field exploration are greatly saved.
2. The invention is based on the scattered field theory (single-measuring point forward modeling calculation is performed by a method based on the background noise level and the vertical spectrum ratio of the scattered field theory) which can reasonably explain the background noise wave field, and compared with the prior common single body wave interpretation and single face wave interpretation, the theoretical interpretation aspect of the background noise is more comprehensive and reasonable, and the influence of the body wave and the face wave in the background noise of the soil layer can be simultaneously considered.
Drawings
FIG. 1 is a schematic flow chart of the method;
FIG. 2 is a plot of background noise at 12 points recorded by a temporarily deployed small background noise observation array;
FIG. 3 is a schematic diagram showing a comparison of NHV curves obtained by observing 12 observation points of a temporarily laid small background noise observation array and theoretical NHV curves of an inverted optimal model;
FIG. 4 shows the optimal three-dimensional soil layer model obtained by inversion of the method.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
As shown in fig. 1, the background noise level vertical spectrum ratio joint inversion method of the soil layer three-dimensional speed structure comprises the following steps:
s1, carrying out single-measuring-point forward modeling calculation by a background noise level and vertical spectrum ratio method based on a scattered field theory to obtain a single-measuring-point forward modeling calculation result of a three-dimensional soil layer speed structure;
s2, constructing a multi-measuring point global inversion objective function of the three-dimensional soil layer speed structure based on a Shan Cedian forward calculation result;
s3, performing global optimization on a multi-measuring point global inversion objective function of the three-dimensional soil layer speed structure;
and S4, calculating the minimum value of the global inversion objective function of the multiple measuring points after global optimization to obtain a three-dimensional soil layer speed structure corresponding to the minimum value of the global inversion objective function.
The specific method of the step S1 is as follows: acquiring the density, the thickness, the P wave velocity and the S wave velocity of each soil layer, and according to the formula:
carrying out single-measuring-point forward modeling calculation based on background noise level and vertical spectrum ratio method of a scattered field theory; wherein the method comprises the steps ofThe horizontal and vertical spectrum ratio of background noise is represented, namely, the single-measuring-point forward modeling calculation result is obtained; />Is a green's function expressed in +.>Dot->Simple harmonic point force of one unit acting in direction +.>At->Dot->Displacement caused by direction; the superscript 1D indicates that the current green's function is that of a one-dimensional soil layer; />Representing the imaginary part of the green's function; />Expressed in natural constanteAn exponential function of the base; x represents the vector of earth model parameters to be inverted,，/>soil layer model representing the to-be-invertediThe parameters of the layer soil are set up,，/>、/>、/>、/>、/>and->Respectively represent soil layer model NoiThe P wave velocity, the S wave velocity, the soil layer thickness, the soil layer density, the quality factor of the P wave and the quality factor of the S wave of the soil layer; n represents the number of soil layers; />Representing a transpose of the matrix; />Representing the circle frequency; />Representation->Direction Unit impulse force induced +.>A unit impulse force of direction;representing a dirac function, i.e. a unit impulse function; t represents time; />In (a) and (b)iRepresenting imaginary units.
In the step S2, the expression of the multi-measuring point global inversion objective function of the three-dimensional soil layer speed structure is as follows:
wherein the method comprises the steps ofThe method comprises the steps of globally inverting an objective function for multiple measuring points; />And->Are all weight constants; />Representing the difference between the horizontal and vertical spectrum ratios obtained by calculation of the observed background noise data and the horizontal and vertical spectrum ratio curves obtained by forward calculation of the soil layer model in the inversion process; />Representing the difference in slope ratio between the simulated curve and the observed curve;and->Representing a simulated NHV curve and an observed NHV curve, respectively; />The horizontal axis representing the NHV curve, i.e. frequency; />For frequency->Weights of (2); />And->Respectively indicate->Frequency->Derivative of>Frequency->Is a derivative of (2); />Representing the total number of observation points; />Is constant when->When the value is 1-5, the importance of the regularization item to the P wave speed, the S wave speed, the soil layer density, the quality factor of the P wave and the quality factor of the S wave is respectively expressed; />Representing a degree of similarity between a plurality of observation points for inverting the earth model; />，/>Represent the firstkAnd (d)lCoupling degree between one-dimensional soil layer models corresponding to the observation points, if->Then indicate at the firstkAnd (d)lEnforcing the strongest constraint between locations; if->Then no constraint is added; />Represent the firstkThe observation pointsA value; />Represent the firstlThe->A value; when->When the value is 1-5, the +.>Respectively representing the P wave velocity, the S wave velocity, the soil layer density, the quality factor of the P wave and the quality factor of the S wave at different soil layer model depths z; />Representing the depth value of the bottom of the soil layer model; />Representing a depth value of the top of the soil layer model; z represents the depth of the earth model.
The specific method of the step S3 comprises the following substeps:
s3-1, setting a P wave speed, an S wave speed, soil layer density, a P wave quality factor and a variation range and a variation step length of the S wave quality factor, and generating all possible combinations of parameters through parameter combination;
s3-2, calculating inversion objective function values under all possible combinations of parameters, and selecting a soil layer model with the minimum inversion objective function value as an inversion optimal model to obtain the overall optimized multi-measuring-point overall inversion objective function.
In one embodiment of the invention, if the variance of the observed NHV curve exceeds 0.2 times the mean of the observed NHV curve, thenAnd->Set to 0.6 and 0.4, respectively; otherwise will->And->Set to 0.9 and 0.1, respectively.
In the specific implementation process, the multi-measuring point global inversion objective function is constructed by utilizing the difference between the single-measuring point forward modeling calculation result and the observed value in the step S1. The multi-measuring point global inversion objective function is divided into three items, namely, in the first itemThe square of the difference between the single-measuring-point forward modeling calculation result and the observation value is calculated; ?>Calculating the square of the difference between the derivative of the result relative to frequency and the derivative of the observed value relative to frequency for each single-measuring point forward modeling; ?>Is a parameter similarity degree term among a plurality of observation points of the soil layer model.
In one embodiment of the invention, taking data of Tangshan as an example, temporarily laying a small background noise observation array in Tangshan, wherein background noise of 12 points recorded by the temporarily laid small background noise observation array is shown as figure 2, inverting the background noise shown in figure 2 by adopting the method, and inverting the optimal three-dimensional soil layer model obtained by inversion of the method by using the method and NHV curve pairs of observation results, such as that shown in figure 3, is shown as figure 4. It can be seen that the NHV curve inverted by the method is relatively close to the observed NHV curve. The comparison of the drilling model, the initial model and the inversion method is shown in table 1 by fixing the P wave velocity, the soil layer thickness, the soil layer density, the quality factor of the P wave and the quality factor of the S wave of each soil layer and taking only the S wave velocity as the inversion parameter based on the data of Tangshan.
TABLE 1
Table 1 shows the parameters fixed during inversion []The number in represents the 1-fold variance of the inversion, h is the soil layer thickness,V S for shear wave velocity, table 1 shows a soil layer model of station No. 3 (i.e., observation point No. 12 in background noise observation array), and a drilling model is actual drilling data; the initial model is an initial velocity model estimated by a simplified half-wavelength method and is obtained according to the research result of the simplified half-wavelength method. The inversion model is a model obtained by inversion according to the present invention. As can be seen from table 1, although there is a larger error in soil layer 3 than in the prior art, the present method has a smaller error in both soil layer 1 and soil layer 2 than in the initial model obtained by the prior art method. Thus, the method is advantageous over the prior art in the exploration of subsurface shallow velocity structures.
In summary, the method is based on the scattered field theory (single-measuring point forward modeling calculation is performed based on the background noise level and the vertical spectrum ratio method of the scattered field theory) which can reasonably explain the background noise wave field, and compared with the prior common single body wave interpretation and single surface wave interpretation, the method is more comprehensive and reasonable in the theoretical interpretation aspect of the background noise, and can simultaneously consider the influence of the body wave and the surface wave in the background noise of the soil layer. According to the invention, by setting up the combined objective function, the simultaneous inversion of the background noise observation records of a plurality of observation points can be realized, so that the three-dimensional speed structure of the soil layer is obtained by using the inversion of the background noise records obtained by a plurality of observation points on the earth surface in an area range. The invention effectively reduces the cost of exploring the underground shallow speed structure in the area range, can be widely applied to areas where drilling holes or earthquake survey lines are difficult to spread, and greatly saves manpower, material resources and financial resources for engineering site exploration.
Claims (3)
1. A background noise level vertical spectrum ratio joint inversion method of a soil layer three-dimensional speed structure is characterized by comprising the following steps:
s1, carrying out single-measuring-point forward modeling calculation by a background noise level and vertical spectrum ratio method based on a scattered field theory to obtain a single-measuring-point forward modeling calculation result of a three-dimensional soil layer speed structure;
s2, constructing a multi-measuring point global inversion objective function of the three-dimensional soil layer speed structure based on a Shan Cedian forward calculation result;
s3, performing global optimization on a multi-measuring point global inversion objective function of the three-dimensional soil layer speed structure;
s4, calculating the minimum value of the global inversion objective function of the multiple measuring points after global optimization to obtain a three-dimensional soil layer speed structure corresponding to the minimum value of the global inversion objective function;
the specific method of the step S1 is as follows:
acquiring the density, the thickness, the P wave velocity and the S wave velocity of each soil layer, and according to the formula:
；
carrying out single-measuring-point forward modeling calculation based on background noise level and vertical spectrum ratio method of a scattered field theory; wherein the method comprises the steps ofThe horizontal and vertical spectrum ratio of background noise is represented, namely, the single-measuring-point forward modeling calculation result is obtained; />Is a green's function expressed in +.>Dot->Simple harmonic point force of one unit acting in direction +.>At->Dot->Displacement caused by direction; the superscript 1D indicates that the current green's function is that of a one-dimensional soil layer; />Representing the imaginary part of the green's function; />Expressed in natural constanteAn exponential function of the base; x represents the vector of earth model parameters to be inverted,，/>soil layer model representing the to-be-invertediThe parameters of the layer soil are set up,，/>、/>、/>、/>、/>and->Respectively represent soil layer model NoiThe P wave velocity, the S wave velocity, the soil layer thickness, the soil layer density, the quality factor of the P wave and the quality factor of the S wave of the soil layer; n represents the number of soil layers; />Representing a transpose of the matrix; />Representing the circle frequency; />Representation->Direction Unit impulse force induced +.>A unit impulse force of direction;representing a dirac function, i.e. a unit impulse function; t represents time; />In (a) and (b)iRepresenting imaginary units;
in the step S2, the expression of the multi-measuring point global inversion objective function of the three-dimensional soil layer speed structure is as follows:
；
；
；
wherein the method comprises the steps ofThe method comprises the steps of globally inverting an objective function for multiple measuring points; />And->Are all weight constants; />Representing the difference between the horizontal and vertical spectrum ratios obtained by calculation of the observed background noise data and the horizontal and vertical spectrum ratio curves obtained by forward calculation of the soil layer model in the inversion process; />Representing the difference in slope ratio between the simulated curve and the observed curve;and->Representing a simulated NHV curve and an observed NHV curve, respectively; />The horizontal axis representing the NHV curve, i.e. frequency; />For frequency->Weights of (2); />And->Respectively indicate->Frequency->Derivative of>Frequency->Is a derivative of (2); />Representing the total number of observation points; />Is constant when->When the value is 1-5, the importance of the regularization item to the P wave speed, the S wave speed, the soil layer density, the quality factor of the P wave and the quality factor of the S wave is respectively expressed; />Representing a degree of similarity between a plurality of observation points for inverting the earth model; />，/>Represent the firstkAnd (d)lCoupling degree between one-dimensional soil layer models corresponding to the observation points, if->Then indicate at the firstkAnd (d)lEnforcing the strongest constraint between locations; if->Then no constraint is added; />Represent the firstkThe observation pointsA value; />Represent the firstlThe->A value; when->When the value is 1-5, the +.>Respectively representing the P wave velocity, the S wave velocity, the soil layer density, the quality factor of the P wave and the quality factor of the S wave at different soil layer model depths z; />Representing the depth value of the bottom of the soil layer model; />Representing a depth value of the top of the soil layer model; z represents the depth of the earth model.
2. The method for joint inversion of the background noise level vertical spectral ratio of a soil layer three-dimensional velocity structure according to claim 1, wherein the specific method of step S3 comprises the following sub-steps:
s3-1, setting a P wave speed, an S wave speed, soil layer density, a P wave quality factor and a variation range and a variation step length of the S wave quality factor, and generating all possible combinations of parameters through parameter combination;
s3-2, calculating inversion objective function values under all possible combinations of parameters, and selecting a soil layer model with the minimum inversion objective function value as an inversion optimal model to obtain the overall optimized multi-measuring-point overall inversion objective function.
3. The method for joint inversion of background noise level vertical spectrum ratio of soil layer three-dimensional velocity structure according to claim 1, wherein if variance of observed NHV curve exceeds 0.2 times mean of observed NHV curve, thenAnd->Set to 0.6 and 0.4, respectively; otherwise will->And->Set to 0.9 and 0.1, respectively.
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