CN110333508B - Multisource SAR data-based joint inversion method for time-space sliding distribution after same-seismic - Google Patents

Multisource SAR data-based joint inversion method for time-space sliding distribution after same-seismic Download PDF

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CN110333508B
CN110333508B CN201910655738.4A CN201910655738A CN110333508B CN 110333508 B CN110333508 B CN 110333508B CN 201910655738 A CN201910655738 A CN 201910655738A CN 110333508 B CN110333508 B CN 110333508B
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许文斌
刘小鸽
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Abstract

The invention discloses a post-earthquake spatio-temporal sliding distribution joint inversion method based on logarithmic constraint and multi-source SAR data, which comprises the following steps: firstly, acquiring multisource SAR data of a seismic region and acquiring a time-space deformation field of the region during the same earthquake and after the earthquake by utilizing an InSAR technology; then, constructing a nonlinear function model between the InSAR multi-source observation value and the fault after-earthquake space-time sliding based on the nature of the aftershock sliding following the logarithmic function attenuation and the elastic dislocation theory; then, inverting the homodyne slip distribution, the aftershock attenuation constant and the corresponding slip amplitude coefficient on the finite element fault by using a nonlinear solving method; then, solving post-earthquake sliding space-time distribution by utilizing nonlinear model parameters, and simultaneously combining multi-source SAR data to improve time resolution of fault space-time sliding; and finally, calculating important global physical parameters such as seismic release energy, stress state, structural friction property and the like according to the inverted fault space-time sliding distribution.

Description

Multisource SAR data-based joint inversion method for time-space sliding distribution after same-seismic
Technical Field
The invention belongs to the field of geodetic surveying and geophysical based on a radar remote sensing technology, and particularly relates to a multisource Synthetic Aperture Radar (SAR) data additional logarithm constraint based post-earthquake space-time sliding distribution joint inversion method.
Background
The Interferometric Synthetic Aperture Radar (InSAR) has been successfully applied to deformation monitoring of the whole earthquake period during, during and after the earthquake since the last 90 th century. In particular, when surface data (such as GPS, level, and the like) cannot be acquired, the InSAR technology provides a unique deformation data source for seismic research. SAR (synthetic Aperture Radar) data obtained by a radar satellite can obtain earthquake periodic deformation through an InSAR technology, and then a finite fault sliding model is obtained through inversion. This not only helps to improve our understanding of fault geometry, fault slip, and fault friction properties, but also helps to assess regional seismic risk. However, due to the limited revisit period of the SAR satellite and the data acquisition policy, the isoseismal slip obtained by the InSAR technology usually includes several days or several months of post-earthquake deformation contribution, and on the contrary, the obtained post-earthquake afterslip lacks the influence of the part of post-earthquake deformation, which inevitably increases the uncertainty of the fault slip estimation of the seismic period. How to effectively separate the fault co-seismic slip and the aftershock slip obtained by inversion based on the InSAR technology has important scientific guiding significance for promoting the research of seismology.
However, in practical research application, the isoseismal slip distribution obtained based on the InSAR technology inversion due to the limitation of the SAR satellite revisit period is often severely polluted by aftershock slip, which seriously hinders human understanding and understanding about the earthquake pregnancy mechanism and seriously affects earthquake risk assessment. In order to better understand the characteristics of the internal fault structure of the earth, the sliding of the homoseismal fault and the sliding of the aftershock need to be effectively separated. However, according to the above analysis, the current research on the sliding separation after the same earthquake has certain limitations, and the fault sliding inversion technology based on the SAR data is difficult to effectively separate the sliding of the same earthquake fault and the aftershock.
Disclosure of Invention
The invention aims to overcome the defects and limitations of the existing fault sliding inversion technology based on SAR data and provide a multi-source SAR data additional logarithm constraint-based post-seismographic space-time sliding distribution joint inversion method.
A multisource SAR data additional logarithm constraint based post-seismological space-time sliding distribution joint inversion method comprises the following steps:
the method comprises the following steps: processing multi-source SAR data by using an InSAR technology to obtain observation values of the same-earthquake and post-earthquake radar sight lines (namely the slant range direction) of an earthquake area, and converting an InSAR measurement value from a radar coordinate system to a Universal Transverse-axis Mercator (UTM) projection coordinate system by geocoding;
step two: the method comprises the following steps of (1) sampling an InSAR observed value by a quadtree, solving main fault geometrical parameters such as an earthquake-induced fault dip angle, an earthquake-induced fault trend and uniform sliding quantity by utilizing a multi-peak particle swarm algorithm, fixing the fault dip angle and trend and subdividing the fault dip angle and trend into a plurality of finite element faults;
step three: constructing a Green function model between surface deformation and fault space-time sliding distribution based on an elastic dislocation theory:
Figure GDA0002179125090000031
wherein X is a fault space-time sliding vector, D is surface deformation obtained by InSAR technology, G is a Green function matrix obtained by an Okada elastic dislocation model, B is a design coefficient matrix, and epsilon is a model residual error; t represents the total post-seismic SAR data quantity acquired,
Figure GDA0002179125090000032
and
Figure GDA0002179125090000033
respectively a synchronous vibration sliding vector and a space-time residual sliding accumulated vector of a fault finite element i at a post-earthquake time j, wherein P is the number of the fault finite elements,
Figure GDA0002179125090000034
and
Figure GDA0002179125090000035
respectively representing the same-earthquake deformation field and the deformation field after earthquake at different time nodes.
Aftershock afterslide follows the characteristics of logarithmic decay and is characterized by the following equation:
xpost＝A·log(1+(t-t0)/τ)
wherein, A is an amplitude coefficient for describing the magnitude of aftershock slip after earthquake, t is a time node for acquiring SAR data after earthquake, and t is0And tau is a time constant for describing the aftershock sliding attenuation speed when the earthquake occurs.
Step four: and combining the two formulas to obtain a time-space sliding distribution combined model with additional logarithmic constraint after the same shock. And solving the joint inversion model by using a nonlinear least square algorithm with additional constraint to obtain the homoseismal sliding distribution on all fault finite elements and the aftersliding amplitude coefficient and the attenuation time constant on each fault finite element, thereby obtaining the space-time sliding distribution on the whole earthquake-generating fault in the research time period.
Compared with the prior art, the invention has the following beneficial effects:
1. the whole method has clear flow, is simple to realize, is not limited by regions, does not depend on any other geodetic data (such as GPS) and seismic wave data, and provides an effective and feasible method with low cost and high time resolution for effectively separating the homoseismal sliding distribution and the aftershock sliding.
2. The method breaks through the bottleneck that the homodyne slip and the aftershock slip are difficult to be strictly separated when the fault slip is inverted based on the InSAR observation value, expands the mechanism understanding and comprehension of human beings on the earthquake rupture process and the aftershock slip distribution, and has important scientific value and guiding significance on the research of the internal structure of the earth; the invention has compatibility of multisource SAR satellite data, and actively promotes the practical and marketable development of SAR data and InSAR technology.
3. The invention mainly utilizes the essence that the aftershock sliding follows the logarithmic function type attenuation, and effectively inverts and separates the same-shock sliding and the aftershock sliding based on the InSAR technology, thereby greatly reducing the quantity to be solved by the model. Meanwhile, the multi-source SAR data are fully utilized to make up for the limitation of the revisit period of the single-track SAR satellite so as to improve the time resolution of the space-time sliding distribution.
Drawings
FIG. 1 is a flow chart of a post-seismogenic spatiotemporal sliding distribution joint inversion method based on multi-source SAR data additional logarithm constraint.
Fig. 2 is a schematic diagram of simulated SAR data for different satellite orbits.
FIG. 3 is a plot of spatiotemporal sliding after a simulation (first row) and inversion (second row) seismographs and their relative residuals (third row), the first column representing the results of the seismograph sliding; the other columns represent post-shock slip results, and the black contours at 2.5m intervals in the graph represent the iso-shock slip distributions for both the simulation (first row) and the inversion (second row).
Fig. 4 is a graph simulating the deformation fields of the same rail-ascending earthquake (first row), the rail-ascending earthquake (second row) and the rail-descending earthquake (third row). a-c represent the original analog deformation field; d-f represents the deformation field after corresponding down-sampling; g-i represents a deformation field after down sampling and noise adding; j-l represents the deformation field of the optimal forward modeling; m-o represents a residual error between the original simulated deformation field and the optimal model forward deformation field; p-r represents the corresponding residual histogram.
Fig. 5 is a correlation diagram between the simulated slip distribution and the estimated fault slip.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to facilitate understanding of the invention, the theoretical basis of the invention is first provided:
firstly, processing multi-source SAR data by utilizing an InSAR technology to obtain homoseism and post-seism radar sight line (namely, slant range direction) observed values of a seismic area, and converting an InSAR measured value from a radar coordinate system to a Universal Transverse axis Mercator (UTM) projection coordinate system by geocoding;
then, the quadtree is used for reducing and sampling InSAR observed values, main fault geometric parameters such as an earthquake-induced fault dip angle, an earthquake-induced fault trend and uniform sliding quantity are solved by utilizing a multi-peak particle swarm algorithm, and then the fault dip angle and the trend are fixed and subdivided into a plurality of finite element faults;
according to the elastic dislocation theory, the fault slip X causes the surface deformation D, and the relationship between the two satisfies:
D＝G·B·X+ε
Figure GDA0002179125090000051
Figure GDA0002179125090000052
Figure GDA0002179125090000061
wherein G is a Green function matrix obtained through an Okada elastic dislocation model, B is a design coefficient matrix, and epsilon is a model residual error; t represents the total post-seismic SAR data quantity acquired,
Figure GDA0002179125090000062
and
Figure GDA0002179125090000063
respectively a synchronous vibration sliding vector and a space-time residual sliding accumulated vector of a fault finite element i at a post-earthquake time j, wherein P is the number of the fault finite elements,
Figure GDA0002179125090000064
and
Figure GDA0002179125090000065
respectively representing the same-earthquake deformation field and the deformation field after earthquake at different time nodes.
For aftershock skidding, according to the essence that aftershock skidding follows logarithmic function attenuation, aftershock skidding at any time on finite elements of any fault can be written as follows:
xpost＝A·log(1+(t-t0)/τ) (1)
combining equations (1) and (2) yields a matrix-form combined model as follows:
Figure GDA0002179125090000066
wherein, B1＝[1…1]1×PAnd B0＝[0…0]1×P。
As can be seen from the formula (3), the number of the model parameters is only related to the number of finite elements of the fault, so that the quantity of the parameters to be solved is greatly reduced. The parameters of the combined model shown in the formula (3) are only 2P +3, wherein the parameters comprise P homoseismal finite element fault sliding and P post-seismal sliding amplitude coefficients, a uniform fault sliding attenuation time constant tau and two fault sliding angles nested in a Green matrix, and the parameters to be solved of the model are far less than the parameters to be solved of the model in the formula (1). In addition, due to the addition of logarithmic function constraint, the problem of matrix loss does not exist in the combined model, however, since the system is a nonlinear system, a nonlinear equation solving method is required to be used for solving, and the project aims to solve the combined inversion model by adopting a nonlinear least square method with additional constraint to obtain the optimal solution of the model:
||D-G·B·X||＝min
and II, representing an L2 standard criterion, and recovering the reconstruction space-time sliding by combining the optimal logarithmic function parameter to finally obtain a space-time sliding distribution model in the research time period.
The effects of the present invention can be further explained by the following simulation experiments as examples.
Firstly, lifting orbit data of two different SAR satellite orbits are simulated, as shown in fig. 2, lifting orbit comprises data before 1 scene of earthquake and data after 5 scenes of earthquake, and lowering orbit only comprises data after 5 scenes of earthquake. The lifting rails may form 15 and 10 InSAR interferometric pairs, respectively. The fault strike angle is 350 degrees, the dip angle is 15 degrees, the synchronous sliding angle and the post-earthquake sliding angle are 150 degrees and 120 degrees respectively, and the afterslide decay time constant is 10 days. The fault is then segmented into 120 rectangular finite elements with sides of 5 km. The spatio-temporal sliding distribution is then simulated on the fault plane from the simulated SAR data instants (fig. 3 first line). The InSAR observations are further forward transformed according to a sliding profile (FIGS. 4 a-c). Considering that a single deformation field obtained by InSAR has millions of observations, deformation details are reserved to the maximum extent under the condition of reducing data volume, and a quadtree down-sampling method is adopted to simulate the observations for down-sampling (fig. 4 d-f). To make the simulated observations authentic, white gaussian noise with a mean value of zero and a standard deviation of 10% of the maximum value of the simulated deformation was added to the simulated observations (fig. 4 g-i). It should be noted that fig. 4 only shows a representative deformation diagram of the same rail ascending shock, the post-rail ascending shock and the post-rail descending shock.
By the joint inversion method provided by the invention, the noise-containing InSAR observation value can be utilized to carry out inversion separation on the homoseismal slip and the post-earthquake space-time residual slip. The second row of FIG. 3 shows the spatiotemporal fault sliding distribution obtained by the inversion of the present invention. It can be seen that the model inversion results and the simulated fault sliding have good consistency in the space-time distribution. In order to quantitatively verify the effect of the method, the root mean square error (RMS) of the homoseismal slip distribution residual error (third row in FIG. 3) is calculated to be only 8.5% of the homoseismal slip, and the afterslide residual RMS is 7.1cm at most and is only equivalent to 3.5% of the simulated afterslide amount. Therefore, the model can well recover the slip distribution and the time-space slip of the separated seismic fault, thereby demonstrating that the invention is feasible and reliable. To further illustrate the effect of the present invention, fig. 4j-l show the deformation field obtained by the inversion sliding forward, and it can be seen that the magnitude and spatial distribution thereof are very consistent with the original simulated deformation field. The residuals between the forward deformation results and the simulated values shown in fig. 4m-o, it can be seen that the three interference pair residuals are very small in relative deformation values, the main residuals appear in the northeast of the fault, mainly due to the design fault being tilted to the northeast and the noise added to the downsampled deformation field, and the residuals shown in fig. 4p-r are approximately gaussian in distribution and have RMS less than the level of the added noise, so the residuals mainly originate from the added noise. Fig. 5 is a correlation coefficient diagram between the simulated sliding distribution and the inverted sliding distribution, where the correlation coefficient may reach 0.92 under the condition that the noise level is 10% of the maximum deformation value, and the homodyne sliding angle, the coslidation sliding angle, and the decay time constant obtained by the inversion of the combined model are 150.1 ° ± 0.4 °, 119.4 ° ± 0.8 °, and 10.6 ± 0.9 days, respectively, which are slightly different from the model input value, which indicates that the combined model has good performance. In general, the method can well separate the homoseismal slip and the aftershock slip based on the multi-source SAR data and the logarithmic function constraint, so that the method is feasible and reliable.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Claims (4)

1. A time-space fault sliding joint inversion method based on multi-source data additional logarithmic constraint is characterized by comprising the following steps:
the method comprises the following steps: processing multi-source SAR data by using an InSAR technology to obtain the homoseism and post-seism radar sight line direction observation values of a seismic area, and converting an InSAR measurement value from a radar coordinate system to a universal transverse-axis mercator projection coordinate system through geocoding;
step two: the InSAR observation value is down sampled through a quadtree, the multi-peak particle swarm algorithm is utilized to solve the fault geometric parameters including the earthquake-induced fault dip angle, the earthquake-induced fault trend and the uniform sliding quantity, then the fault dip angle and the trend are fixed and are subdivided into a plurality of finite element faults;
step three: based on the elastic dislocation theory, a Green function model between the earth surface deformation and the fault space-time sliding distribution is constructed and expressed as follows
Figure FDA0002808802060000011
Wherein X is a fault space-time sliding vector, D is surface deformation obtained by InSAR technology, G is a Green function matrix obtained by an elastic dislocation model, B is a design coefficient matrix, and epsilon is a model residual error; t represents the total post-seismic SAR data quantity acquired,
Figure FDA0002808802060000012
is the same-shock sliding vector of the fault finite element i at the aftershock moment j,
Figure FDA0002808802060000013
the fault finite element is a space-time residual slip accumulated vector at a post-earthquake time j, wherein i is 1, 2. j is 1,2, and T and P are the finite element numbers of the fault;
Figure FDA0002808802060000014
represents the homoseismal deformation field of different time nodes, wherein j is 0,1, 2.
Figure FDA0002808802060000015
Representing the post-earthquake deformation fields of different time nodes, wherein i is 1, 2. j-0, 1,2,. said, T-1;
and the aftershock sliding follows the characteristics of logarithmic attenuation and is characterized by the following formula:
xpost＝A·log(1+(t-t0)/τ) (2)
wherein A is an amplitude coefficient for describing the magnitude of aftershock slip after earthquake, t is a time node for acquiring SAR data after earthquake, and t is0Is a time node when an earthquake occurs, and tau is a time constant for describing the afterslide attenuation speed after the earthquake;
the joint formulas (1) and (2) convert the post-earthquake space-time residual slip to be solved in the model of the formula (1) into a logarithmic function model, and the post-earthquake space-time slip distribution joint inversion model with the additional logarithmic constraint in the form of a matrix can be obtained:
Figure FDA0002808802060000021
wherein, B1＝[1…1]1×PAnd B0＝[0…0]1×P；
Step four: and solving the joint inversion model to obtain the homoseismal sliding distribution on all fault finite elements and the aftersliding amplitude coefficient and the attenuation time constant on each fault finite element, and further obtain the space-time sliding distribution on the whole earthquake-generating fault in the research time period.
2. The multisource data additional log constraint-based spatio-temporal fault sliding joint inversion method of claim 1, characterized in that the joint inversion model is solved using an additional constrained nonlinear least squares.
3. The multisource data additional logarithm constraint-based spatio-temporal fault sliding joint inversion method of claim 1, characterized in that the joint inversion model parameters shown in formula (3) are only 2P +3, which include the coefficients of the homoseismal sliding and the P aftersliding amplitudes on the P fault finite elements, a uniform fault sliding attenuation time constant τ, and two fault sliding angles nested in the green matrix.
4. The multisource data additional logarithm constraint-based spatio-temporal fault sliding joint inversion method according to any one of claims 1-3, wherein the seismic deformation is deformation caused by any seismic type in any region.
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