Hidden active fault geometric parameter discrimination method based on multi-track InSAR and stress field constraint

Abstract

The invention discloses a hidden active fault geometric parameter discrimination method based on multi-track InSAR and stress field constraint, and belongs to the technical field of remote sensing. The method comprises the following steps of: extracting a spatial connecting line with a maximum deformation gradient value as a fault agent trace by acquiring a rising and falling InSAR co-seismic deformation diagram of a target area; constructing a mutual exclusion tendency hypothesis based on the trace, and screening a reasonable tendency by predicting and comparing multi-track deformation symbol distribution; and meanwhile, in combination with a local main pressure stress axis P orientation of field geological inversion, whether the maximum uplift area is located on a P-axis pointing side is judged so as to constrain the sliding type. According to the method, a fault model does not need to be preset, high-confidence-coefficient judgment of the tendency and the mechanism is achieved through the physical self-consistency of the multi-view InSAR and the actually-measured stress field, the problem of geometric multiplicity of solutions of the fault under the condition of no surface fracture is effectively solved, seismic structure interpretation reliability is remarkably improved, and key parameter support is provided for seismic risk assessment.

Description

Technical Field

[0001] This invention relates to the field of remote sensing technology, and in particular to a method for identifying the geometric parameters of hidden active faults based on multi-track InSAR and stress field constraints. Background Technology

[0002] In seismic tectonic research and disaster risk assessment, accurately identifying the geometric parameters of seismogenic faults, such as dip and slip type, is a crucial prerequisite for understanding earthquake rupture mechanisms and conducting probabilistic seismic hazard analysis (PSHA). In recent years, synthetic aperture radar interferometry (InSAR) technology has become an important means of acquiring coseismic deformation fields due to its high spatial resolution and wide coverage. However, single-track InSAR can only observe one-dimensional deformation along the line-of-sight (LOS), failing to directly reflect the true three-dimensional motion characteristics of the fault. More importantly, in areas without surface rupture or with complex tectonics, fault geometric parameters often exhibit multiple solutions—for example, the same deformation pattern may be generated by eastward-dipping or westward-dipping thrust faults, making it difficult to distinguish based on a single perspective. Existing methods typically rely on regional focal mechanism solutions or simplified fault models as prior inputs. However, when there are deviations between the local stress field and the regional mean field, or when the fault system is highly fragmented, such priors are prone to introducing systematic misjudgments, leading to distorted seismic hazard assessments. Therefore, there is an urgent need for a new method that does not rely on a pre-set fault model and can achieve high-confidence discrimination of fault geometric parameters through multi-source observation self-consistency test.

[0003] To address the aforementioned challenges, Chinese patent CN112233232B discloses a method for three-dimensional crustal deformation transformation based on single-track InSAR observations. This method introduces a simplified rectangular dislocation fault model, obtains the three-dimensional deformation direction vector through forward modeling using elastic dislocation theory, and uses this vector to constrain the single-track LOS deformation into three components: east, north, and vertical. While this method alleviates the problem of insufficient dimensionality in single-track InSAR to some extent, its fundamental premise is that the fault geometry parameters are known or can be reasonably assumed. Once the preset model does not match the actual seismogenic structure, such as in earthquakes dominated by concealed fault zones or secondary faults, the deformation direction vector generated will deviate, leading to distortion in the three-dimensional deformation reconstruction. Furthermore, this method does not consider how to verify or correct the fault geometry itself, nor does it integrate local stress field information, thus failing to fundamentally solve the problem of fault geometry uncertainty. Summary of the Invention

[0004] In view of this, this invention proposes a method for identifying the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints. This invention abandons reliance on prior models and instead utilizes the spatial consistency of deformation signs in ascending and descending InSAR, combined with measured P-axis azimuth for physical mechanism constraints, to construct a closed-loop discrimination logic. This enables reliable identification of the dip and slip type of concealed active faults based on multi-track InSAR and stress field constraints even without surface rupture, significantly improving the objectivity and reliability of seismic tectonic interpretation.

[0005] This invention provides a method for identifying the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints, comprising the following steps: S1. Obtain the ascending and descending InSAR coseismic deformation maps of the target seismic area, and extract the spatial connection of the maximum deformation gradient as the surface projection proxy trace of the concealed fault. S2. Based on the surrogate trace, construct at least two mutually exclusive fault dip hypothesis; S3. For each fault dip assumption, predict the deformation sign distribution on both sides of the fault under the ascending and descending InSAR observation geometry; S4. Compare the predicted deformation symbol distribution with the actual ascending and descending orbit InSAR deformation maps respectively, retain the assumption of consistent deformation symbols, and obtain preliminary screening results; S5. Conduct field geological surveys within the target area, measure the striation direction of multiple fault outcrops, and invert to obtain the concentrated azimuth range of the local principal compressive stress axis P; S6. Based on the concentrated azimuth range of the local principal compressive stress axis P, determine whether the maximum uplift area in the actual InSAR deformation is located on the side pointed to by the P axis: if not, exclude the retrograde sliding mechanism; if yes, retain the retrograde mechanism and add it to the sliding mechanism candidate set. S7. Combining the preliminary screening results with the candidate set of slip mechanisms, output a physically consistent combination of fault dip direction and slip type as a high-confidence geometric parameter discrimination result for hidden active faults based on multi-track InSAR and stress field constraints.

[0006] Furthermore, the consistent deformation sign means that, for any tendency hypothesis, the predicted upper disk deformation sign is the same as the actual InSAR observation sign in both ascending and descending orbits, and the lower disk sign is also the same.

[0007] Furthermore, the at least two mutually exclusive fault dip assumptions include: taking the proxy trace as the orientation, respectively assuming that the fault dip is orthogonal to the orientation normal direction on both sides.

[0008] Furthermore, the side to which the P-axis points is determined as follows: taking the azimuth angle of the local principal compressive stress axis P as a reference, based on the direction of the proxy trace. Define the sector that the P-axis points to as: in, Let P be the azimuth angle of the local principal compressive stress axis, in degrees. The surface azimuth of the center point of the maximum uplift zone, in degrees; if satisfy If so, it is determined to be located on the side pointing to the P-axis.

[0009] Furthermore, the ascending and descending orbit InSAR coseismic deformation maps are obtained by differential interferometry (DInSAR) processing based on TOPS mode images from the Sentinel-1 satellite, and the deformation inversion accuracy is better than ±1.0 mm.

[0010] Furthermore, the local principal compressive stress axis P is obtained by inversion from no less than three outcrops, and the concentrated azimuth interval is obtained by inverting the scratch data using the PBT method or the right two-column method, and the standard deviation of the P-axis azimuth angle of each outcrop inversion result is required to be less than 15 degrees.

[0011] Furthermore, the spatial connection of the maximum deformation gradient is generated through the following steps: S11. Calculate the spatial gradient of the LOS directional deformation d(x,y) in the InSAR deformation map to obtain the gradient magnitude: Where d(x,y) is the surface deformation along the line of sight (LOS), in millimeters; S12. Calculate the maximum value of the gradient magnitude max(∇d) in the entire deformation diagram; S13. Extract the satisfied A continuous chain of pixels serves as the spatial connection for the maximum deformation gradient.

[0012] Furthermore, if the maximum uplift zone is located on the side pointing to the P-axis, and the deformation profile shows that the absolute value of the ratio of the maximum uplift value of the hanging wall to the maximum settlement value of the footwall is not less than 3, then it is determined to be a thrust-type sliding mechanism; if the deformation is nearly symmetrically distributed and the angle between the P-axis and the fault strike is less than 30°, then it is determined to be a strike-slip mechanism.

[0013] Furthermore, the method is applicable to shallow-focus tectonic earthquakes with a magnitude range of Mw5.5–6.8, a focal depth of less than 20 km, and no continuous coseismic rupture on the surface.

[0014] Furthermore, this method also includes inputting the determined fault dip direction and slip type into the probabilistic seismic hazard analysis (PSHA) model to correct the maximum expected magnitude and recurrence period of the potential source area.

[0015] The present invention has the following advantages over the prior art: By constructing a consistency verification mechanism for the deformation symbols of ascending and descending InSAR, mutually exclusive fault dip assumptions are physically falsifiable, effectively eliminating the geometric ambiguity problem caused by single-view observations. Compared with traditional methods that rely on pre-set models, this scheme does not introduce prior bias and makes judgments solely based on the self-consistency of observational data, significantly reducing the risk of misjudgment and substantially improving the reliability and confidence of the geometric parameter discrimination of hidden active faults based on multi-track InSAR and stress field constraints.

[0016] By using the orientation of the local principal compressive stress axis P obtained from field geological surveys as an independent physical constraint, and combining it with the spatial location of the maximum uplift zone to determine the slip type, this approach overcomes the limitations of previous remote sensing inversion methods and achieves, for the first time, quantitative fusion verification of InSAR deformation field and local measured stress field. This fusion strategy shifts the determination of fault slip type from pure geometric fitting to mechanical self-consistency testing, enhancing the rationality of the results.

[0017] By utilizing the InSAR deformation gradient modulus to extract spatially continuous pixel chains with maximum deformation gradient values, and using these chains as surface projection proxy traces of concealed faults, the technical challenge of locating the controlling fault in areas without coseismic surface rupture is solved. This method is objective and quantifiable, avoiding the subjectivity of manual delineation, and accurately locates the seismogenic structure and extracts its strike without the need for surface rupture.

[0018] The output combination of fault dip and slip type has a clear physical self-consistency basis and can be directly used to modify the potential source area model in probabilistic seismic hazard analysis (PSHA), providing high-confidence input parameters for seismic hazard assessment, improving the accuracy of key parameters such as maximum expected magnitude and recurrence cycle, thereby supporting more scientific urban planning and seismic fortification decisions. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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.

[0020] Figure 1 This is a schematic diagram of the overall process of an embodiment of the present invention; Figure 2This is a location map of the study area in an embodiment of the present invention; Figure 3 This is an InSAR interferometric phase diagram of the ascending and descending orbits according to an embodiment of the present invention; Figure 4 The relationship between deformation field characteristics and fault projection in an embodiment of the present invention; Figure 5 The displacements of the ascending and descending rails in this embodiment of the invention; Figure 6 This is a geological evidence and stress field inversion diagram of an active fault according to an embodiment of the present invention; Figure 7 This is a map showing the orientation of the principal compressive stress axis P in the northwestern, central, and southeastern regions of an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] like Figure 1 As shown, this invention provides a method for identifying the geometric parameters of hidden active faults based on multi-track InSAR and stress field constraints. The overall process includes: acquiring coseismic deformation maps of ascending and descending InSAR, extracting the spatial connection of the maximum deformation gradient as a proxy trace, constructing mutually exclusive dip assumptions, predicting the deformation sign distribution, comparing and filtering with measured data, combining P-axis constraints on slip type, and outputting the final parameter combination. The following detailed explanation uses the Alghur earthquake event in northeastern Iran (Mw 6.1, April 5, 2017) as an example. This method includes the following steps: S1. Obtain the ascending and descending InSAR coseismic deformation maps of the target seismic area, and extract the spatial connection of the maximum deformation gradient as the surface projection proxy trace of the concealed fault. The study area of ​​this embodiment is located in Razawi Province, Khorasan, northeastern Iran, near the city of Mashhad. Figure 2 The image shows the location of the study area for this invention. This area is situated in the Kopetdag front thrust belt, a typical compressional tectonic environment. A Mw 6.1 earthquake occurred on April 5, 2017, with a focal depth of approximately 13 km. While it did not produce continuous surface rupture, InSAR observations showed significant coseismic deformation, exhibiting characteristics of obvious deformation but blurred fault traces, making it suitable for verification using this method.

[0023] The primary dataset for this invention comes from the European Space Agency's Sentinel-1 mission, which employs interferometric wide-swath (IW) scanning mode and utilizes Topographic Observation Progressive Scan SAR (TOPS) technology for data acquisition. Sentinel-1 is a C-band SAR sensor operating at 5.405 GHz, with a spatial resolution of approximately 5 m × 20 m, employing VV polarization mode, and an estimated maximum phase error of 5°.

[0024] like Figure 3 As shown, this invention utilizes Sentinel-1 Single Observation Composite (SLC) images and generates differential interferograms using the Sentinel Application Platform (SNAP) toolbox. By analyzing satellite ascent and descent transit data, ground deformation is captured from different observation angles, thereby improving the reliability of displacement measurements. The differential interferometric phase maps generated from these images directly reveal surface displacement information by quantifying the phase differences between pre- and post-earthquake radar data. This measurement method not only accurately reconstructs fault movement trajectories but also provides important evidence for a deeper understanding of earthquake dynamics and its impact on the Earth's surface.

[0025] like Figure 3 As shown, the imagery uses SLC data from the European Space Agency's Sentinel-1A / B satellite in TOPS mode, specifically the data from the ascent orbit. Figure 3 (a): March 24, 2017 (before) and April 5, 2017 (after); down-orbit data, Figure 3 (b): March 30, 2017 (before) and April 11, 2017 (after); The ascending and descending orbit InSAR interferometric phase maps were obtained through a differential interferometry (DInSAR) processing workflow. After atmospheric correction and phase unwrapping, the results were obtained as follows: Figure 4 (C) and Figure 5 The LOS displacement diagram shown has a deformation inversion accuracy better than ±1.0 mm, which meets the requirements for high-precision fault inversion.

[0026] Specifically, such as Figure 4 As shown, Figure 4 (a) represents the InSAR interferogram of the epicenter region; Figure 4 (b) represents the InSAR interferogram on the shaded terrain model of the study area; Figure 4 (c) represents the deformation diagram on the shaded terrain model of the study area; Figure 4(d) indicates that the focal mechanism is related to a thrust fault. Processing was performed using a differential interferometry (DInSAR) workflow, including precise orbit correction, topographic phase removal (using a 30m resolution SRTM DEM), multi-look filtering, phase unwrapping, and LOS-direction deformation inversion, ultimately obtaining coseismic deformation maps with an accuracy better than ±1.0 mm for both the ascending and descending orbits. The ascending orbit deformation map shows a maximum uplift of approximately +9 cm, located on the northwest side of the fault; the descending orbit deformation map exhibits a similar spatial distribution, verifying the reliability of the deformation signal.

[0027] exist Figure 5 As can be seen, both the rising and falling orbits show a deformation field distributed concentrically around the epicenter, with a maximum uplift of +9 cm, mainly concentrated on the northwest side of the fault, while the southeast side shows slight subsidence (around -1 cm), which is consistent with the typical characteristics of the hanging wall uplift of a thrust fault.

[0028] Based on this, the surface projection proxy traces of concealed faults are extracted, which specifically includes the following sub-steps: S11. Calculate the spatial gradient of the LOS directional deformation d(x,y) in the InSAR deformation map to obtain the gradient magnitude: Where d(x,y) represents the surface deformation along the line-of-sight (LOS) direction, in millimeters; partial derivatives and Calculated using the central difference method: S12. Calculate the maximum value of the gradient magnitude max(∇d) in the entire deformation diagram.

[0029] In this embodiment, the calculated maximum (∇d) of the ascending orbit deformation diagram is approximately 18.5 mm / km, and the result of the descending orbit deformation diagram is similar.

[0030] S13. Extract the satisfied The continuous pixel chain, tested against 10 historical earthquakes, found that a threshold of 0.8 achieved the optimal balance between preserving the main gradient band and suppressing noise. The continuous pixel chain is used as the spatial connection of the maximum deformation gradient, as shown below. Figure 4 As shown in (C), a high gradient zone with a length of about 25 km and a trend close to NW–SE is formed. This zone is the surface projection proxy trace of the hidden seismogenic fault, which is used for the subsequent construction of fault geometry assumptions.

[0031] This 80% threshold, verified through multiple experiments, effectively suppresses noise edges while preserving the main deformation gradient band. The resulting continuous high gradient band, trending NW–SE and approximately 25 km in length, was used as a surface projection proxy trace of the concealed seismogenic fault for subsequent fault dip hypothesis construction.

[0032] S2. Based on the surrogate trace, construct at least two mutually exclusive fault dip hypothesis; The at least two mutually exclusive fault dip assumptions include: taking the proxy trace as the orientation, respectively assuming that the fault dip is orthogonal to the orientation normal direction on both sides.

[0033] Using the spatial connection line (i.e., the surrogate trace) of the maximum deformation gradient of the NW–SE strike extracted in step S1 as the basis for fault strike, and considering the complexity and diversity of geological structures, this invention constructs at least two mutually exclusive fault dip assumptions. These assumptions are based on the different dip directions of the fault plane relative to the Earth's surface, considering the orthogonal sides of its strike normal direction respectively. Specifically: Assumption H1: The fault dips NE (i.e., from northwest to southeast); Based on the surrogate trace obtained in step S1, this invention first selects a direction as the fault dip direction. For the Alghur seismic zone in this embodiment, if the surrogate trace points to NW-SE, i.e., northwest-southeast, this invention assumes the fault dips in the NE (northeast) direction. In this case, the fault plane will dip from northwest to southeast, and the expected surface deformation mode under this assumption is mainly caused by thrust or normal fault mechanisms.

[0034] Assume H2: The fault dips SW (i.e., from southeast to northwest).

[0035] For the second mutually exclusive fault dip hypothesis, this invention selects the direction opposite to the first hypothesis as the fault dip direction. Continuing with the above example, if the first hypothesis is that the fault dips in a NE (northeast) direction, then the second hypothesis would be that the fault dips in a SW (southwest) direction. This means that the fault plane dips from southeast to northwest, and the expected ground deformation pattern may be related to a strike-slip fault or a reverse-thrust fault in the opposite direction.

[0036] These two assumptions correspond to two possible dip directions for a fault with the same strike, are orthogonal to each other, and constitute a completely mutually exclusive relationship. In practice, based on... Figure 4 The spatial orientation of the deformation gradient band in (C) is used to determine the direction of the surrogate trace as 315° (NW–SE), and then its normal direction is derived as 045° / 225°. Therefore, H1 corresponds to the dip NE (045°) and H2 corresponds to the dip SW (225°).

[0037] When formulating these hypotheses, it is important to consider the influence of actual topography and known geological conditions on the fault dip. Although this method does not require prior geological information to generate surrogate traces, it is very helpful to consider the local geological context (such as rock type, tectonic stress field, etc.) when evaluating the validity of these hypotheses. Furthermore, by combining them with subsequent steps, the degree of matching between theoretical predictions and observational data under different dip assumptions can be compared, thereby more accurately determining the actual dip of the fault.

[0038] S3. For each fault dip assumption, predict the deformation sign distribution on both sides of the fault under the ascending and descending orbit InSAR observation geometry; After completing step S2, two mutually exclusive fault dip hypotheses have been established: H1: The fault strikes NW–SE and dips NE; H2: The fault strikes NW–SE and dips SW.

[0039] To determine which hypothesis better reflects actual observations, the expected deformation sign distribution for each hypothesis needs to be simulated under the line-of-sight (LOS) direction of InSAR for both ascending and descending orbits. This embodiment uses the classic Okada elastic dislocation model for forward modeling, and the specific process is as follows: (1) Setting fault parameters and slip mechanism

[0040] For each propensity hypothesis, the following parameters are fixed: Direction: Determined as 315° (NW–SE) based on the proxy trace; Dip angle: 45° (typical dip angle of a reverse fault); Slip type: The preliminary assumption is that it is a pure thrust type (slip angle 90°), because the regional tectonic background belongs to the Kopetdag front compression zone; Focal depth: 13 km (provided by the USGS earthquake catalog); Moment magnitude: Mw 6.1 conversion, corresponding to scalar seismic moment N·m.

[0041] (2) Obtaining InSAR observation geometric parameters

[0042] Extracting LOS vectors for ascending and descending orbits using Sentinel-1 metadata: Ascending orbit: incident angle 39°, azimuth angle 101° (clockwise from north); Descending orbit: incident angle 39°, azimuth angle 259°.

[0043] Therefore, the LOS unit vector at any point on the Earth's surface can be calculated. It is used to project the three-dimensional deformation field to the LOS direction.

[0044] (3) Forward modeling of the three-dimensional deformation field and projection onto LOS

[0045] For each hypothesis (H1, H2), the Okada model is invoked to calculate the three-dimensional displacement field of the Earth's surface. Then through the LOS unit vector Projected in the direction of the line of sight: in, This represents the deformation of the line of sight direction; a positive value indicates that the Earth's surface is moving towards the satellite, and a negative value indicates that it is moving away from the satellite. is the LOS direction unit vector, representing the spatial direction vector of the satellite's line of sight. It is a three-dimensional unit vector determined by the satellite's orbital parameters and is usually represented by three directional components: East (E), North (N), and U. d is the three-dimensional surface displacement vector, calculated from a fault dislocation model (such as the Okada model), denoted as . ,in This represents the horizontal displacement of the Earth's surface in the eastward direction; a positive value indicates eastward movement. This represents the horizontal displacement of the Earth's surface in the northward direction; a positive value indicates northward movement. It represents the vertical displacement of the Earth's surface; a positive value indicates uplift. for The projection component in the east direction is usually negative; for The projection component in the north direction depends on the incident angle and the azimuth angle; for The projection component in the vertical direction is usually positive; the negative sign indicates the radar phase convention (positive when it is far from the satellite).

[0046] This formula is used to project the three-dimensional surface displacement d output by the Okada model onto the observation direction of the satellite radar, thereby obtaining the line-of-sight deformation that the radar can detect. This refers to the actual deformation reflected by the InSAR interferometric phase.

[0047] (4) Extract the deformation symbols on both sides of the fault.

[0048] The study area is divided into "upper plate" and "lower plate" using the proxy trace as the boundary: For H1 (leaning towards NE): the upper plate is located on the northwest side of the trace line, and the lower plate is located on the southeast side; For H2 (leaning towards SW): the upper plate is located southeast of the trace line, and the lower plate is located northwest of the trace line.

[0049] Statistical analysis of each disk Average sign: H1 prediction results: Ascending trend: Upper plate (Rising), lower plate (settlement); Descending trend: Similarly, the upper trendline is positive and the lower trendline is negative.

[0050] H2 prediction results: Ascending trend: Upper plate Lower plate ; Descending orbital: Similarly, the sign is opposite to H1.

[0051] Since the LOS vector directions of the ascending and descending orbits are different, for the same thrust event, if the fault dip is correct, the deformation signs on both sides should be consistent under the two orbits, that is, both show uplift of the hanging wall and subsidence of the footwall. This is the physical basis for the sign consistency test.

[0052] (5) Visualization and output

[0053] The predicted deformation symbol distribution is plotted as a binary map (+ indicates uplift, − indicates subsidence), corresponding to ascending and descending orbit scenarios, respectively. These symbol maps will serve as the benchmark for comparison with the measured InSAR deformation map in step S4.

[0054] S4. Compare the predicted deformation symbol distribution with the actual ascending and descending orbit InSAR deformation maps respectively, retain the assumption of consistent deformation symbols, and obtain preliminary screening results; The consistent deformation sign means that, for any trend hypothesis, the predicted upper plate deformation sign is the same as the actual InSAR observation sign in both ascending and descending orbits, and the lower plate sign is also the same.

[0055] After completing step S3, the deformation sign distributions predicted by the two fault dip hypotheses (H1: dip NE; H2: dip SW) under the ascending and descending orbit geometries have been obtained. This step performs a sign consistency test on a track-by-track and disk-by-disk basis with the actual observed InSAR deformation maps to screen out physically consistent dip hypotheses.

[0056] (1) Extraction of InSAR deformation symbols from actual measurements

[0057] according to Figure 5 LOS displacement diagram of ascending and descending orbits in the diagram: The maximum uplift zone is located on the northwest side of the proxy track, with an ascending track deformation of +9cm and a descending track deformation of +8.5cm; The relative settlement zone is located on the southeast side, with a deformation of approximately −1 cm; Therefore, the measured deformation sign distribution is as follows: "+" (uplift) on the northwest side and "−" (settlement) on the southeast side. This pattern is highly consistent in both the rising and falling orbits, indicating that the deformation signal is reliable and has a clear spatial polarity.

[0058] (2) Perform symbol consistency comparison

[0059] For any tendency hypothesis, the predicted upper plate deformation sign is the same as the actual InSAR observation sign in both ascending and descending orbits, and the lower plate sign is also the same.

[0060] Item-by-item inspection: For H1 (preferring NE): Upper plate = Northwest side, prediction symbol = "+"; Lower plate = Southeast side, prediction symbol = "−"; Actual measurement: "+" on the northwest side, "−" on the southeast side; Since the ascending and descending orbits are consistent, H1 is retained.

[0061] For H2 (preferring SW): Upper plate = Southeast side, prediction symbol = "−"; The lower part of the chart corresponds to the northwest side, and the prediction symbol is "+". Although the algebraic symbols seem to match, the physical meanings are contradictory: under the H2 assumption, the main uplift should occur on the southeast side, but the measured maximum uplift (+9cm) is clearly located on the northwest side, and the deformation gradient in this area is the strongest, which is a typical sign of the hanging wall of the fault. More importantly, under the reduced orbit geometry, due to the difference in the azimuth angle of the LOS vector, there is a local mismatch between the edge sign distribution predicted by H2 and the actual measurement. Conclusion: H2 does not meet the physical self-consistency requirement of "consistent signs between the upper and lower plates", therefore it is excluded.

[0062] The judgment criteria emphasize that sign consistency not only refers to the same algebraic signs, but also requires that the spatial distribution of deformation polarity strictly correspond to the definitions of the hanging wall and footwall of the fault. This invention eliminates accidental consistency under single track through dual-track cross-verification.

[0063] (3) Output preliminary screening results

[0064] After comparison, only H1 (dipping NE) met the deformation sign consistency condition under both ascending and descending orbits. Therefore, H1 was retained as the preliminary screening result and proceeded to the subsequent geological constraint step. This result is consistent with... Figure 4 The focal mechanism solution (nodal plane I: strike 315° / dip 45° / slip angle 90°) provided by USGS in (D) is in high agreement, which verifies the effectiveness of this method.

[0065] S5. Conduct field geological surveys within the target area, measure the striation direction of multiple fault outcrops, and invert to obtain the concentrated azimuth range of the local principal compressive stress axis P; The local principal compressive stress axis P is obtained by inversion from no less than three outcrops. The concentrated azimuth interval is obtained by inverting the scratch data using the PBT method or the right two-column method, and the standard deviation of the P-axis azimuth angle of each outcrop inversion result is required to be less than 15 degrees.

[0066] To further constrain the fault slip type, such as thrust, strike-slip, or normal faulting, independent geomechanical evidence is introduced. This embodiment involves conducting field geological surveys in three outcrop areas near the epicenter (northwest, central, and southeast). Field geological surveys are conducted in three outcrop areas near the epicenter (e.g.,... Figure 6 As shown on the left), the direction of fault striations was measured at outcrops of faults such as Haraj and South Mashhad, and the local principal compressive stress axis P was inverted using the PBT method (as shown on the left). Figure 6 As shown in the rose diagram on the right, the azimuth distribution of the P-axis in each region is obtained.

[0067] (1) Results of P-axis measurement

[0068] like Figure 7 As shown, the P-axis inversion results for the northwest, central, and southeast regions are concentrated at 320°±10° (with true north as 0°, clockwise), with a standard deviation of [missing information]. The angle ≈12° indicates that the principal compressive stress direction in the region is stable and exhibits NW–SE compression, which is consistent with the tectonic setting of the Kopetdag front.

[0069] Therefore, take The representative azimuth angle of the local principal compressive stress axis P.

[0070] (2) Define the sector that the P-axis points to.

[0071] According to the technical solution of the present invention, the sector pointed to by the P-axis is defined as: in, Let P be the azimuth angle of the local principal compressive stress axis, in degrees. The surface azimuth of the center point of the maximum uplift zone, in degrees; if satisfy If so, it is determined to be located on the side pointing to the P-axis.

[0072] Substitution ,have to: That is, a 90° wide sector spanning the 0° / 360° boundary, with its center pointing to 320° (NW direction).

[0073] S6. Based on the concentrated azimuth range of the local principal compressive stress axis P, determine whether the maximum uplift area in the actual InSAR deformation is located on the side pointed to by the P axis: if not, exclude the retrograde sliding mechanism; if yes, retain the retrograde mechanism and add it to the sliding mechanism candidate set. If the maximum uplift zone is located on the side pointing towards the P-axis, and the deformation profile shows the uplift of the hanging wall... With the subsidence The ratio satisfies If the deformation is nearly symmetrical and the angle between the P-axis and the fault strike is less than 30°, it is determined to be a strike-slip mechanism.

[0074] Extract the center point of the maximum uplift zone and calculate its surface azimuth relative to the direction of the proxy trace. And determine whether it is located in the sector pointed to by the P-axis. Inside, to constrain the sliding type.

[0075] (1) Determine the center of the maximum uplift zone

[0076] from Figure 5 The region containing the maximum uplift value (+9cm) was identified in the orbital deformation map, and its centroid coordinates were taken as the center point of the maximum uplift zone. This point is located approximately 8km northwest of the proxy track.

[0077] (2) Calculate the azimuth of the Earth's surface

[0078] Taking the midpoint of the proxy trace as the origin, calculate the azimuth angle of that center point relative to true north. .

[0079] (3) Determine whether it is located in the sector pointed to by the P-axis

[0080] Compare and : Therefore, the area of ​​maximum uplift is located on the side pointing towards the P-axis.

[0081] (4) Further verification using asymmetry

[0082] In addition, the ratio of the uplift of the hanging wall (+9cm) to the subsidence of the footwall (−1cm) is 9:1>3, which is significantly asymmetrical and consistent with the characteristics of a thrust fault (strike-slip faults usually have symmetrical deformation on both sides).

[0083] Based on comprehensive judgment, the slip type is reverse slip, rather than run-slip or fracture.

[0084] S7. Combining the preliminary screening results with the candidate set of slip mechanisms, output a physically consistent combination of fault dip direction and slip type as a high-confidence geometric parameter discrimination result for hidden active faults based on multi-track InSAR and stress field constraints.

[0085] Through the InSAR deformation sign consistency test in step S4 (ascending and descending orbits), the only valid fault dip hypothesis H1 (dipping NE) was retained; combined with the azimuth of the local principal compressive stress axis P obtained from the field geological survey in step S5, the test was conducted. And through the azimuth of the center point of the S6 maximum uplift zone. The spatial distribution confirms that it is located in the sector pointed to by the P-axis. Internally, it supports a reverse sliding mechanism.

[0086] Based on the above analysis, the geometric parameters of the concealed active fault output by this invention are as follows: Orientation: 315° (NW–SE)

[0087] Tendency: NE

[0088] Sliding type: Reverse type

[0089] like Figure 5 The location of the maximum uplift zone shown not only matches the actual observation data, but also achieves physical self-consistency verification through multi-source constraints (InSAR deformation field + stress field inversion), significantly improving the confidence of the discrimination results.

[0090] The method is applicable to shallow-focus tectonic earthquakes with a magnitude range of Mw5.5–6.8, a focal depth of less than 20 km, and no continuous coseismic rupture on the surface.

[0091] This method also includes inputting the determined fault dip direction and slip type into the probabilistic seismic hazard analysis (PSHA) model to correct the maximum expected magnitude and recurrence period of potential seismic source areas.

[0092] The determined fault dip direction and slip type are input into the probabilistic seismic hazard analysis (PSHA) model, which can be used to correct key parameters of potential seismic source areas, including but not limited to: (1) Maximum expected magnitude Mmax

[0093] Based on geometric parameters such as fault length L (estimated from proxy traces), dip angle, and slip type, and combined with empirical formulas, estimate Mmax: Where a and b are regression coefficients that vary with the fault type, and Mmax is the moment magnitude (Mw). Taking the thrust fault in this example, the typical parameters are a≈1.05 and b≈0.62. Substituting these into L≈25km, we get Mmax≈6.6.

[0094] (2) Relapse cycle T

[0095] Based on historical earthquake catalogs and fault slip rate V, which is usually obtained through GPS monitoring or paleoseismic studies, it is calculated using the following formula: In the formula, L is the fault length (unit: km), and D is the average displacement (unit: m, which can be calculated based on the magnitude-displacement relationship). If V≈5mm / a, and assuming D≈1.25m corresponds to Mw 6.1, then T≈5000 years.

[0096] (3) Fault segmentation and secondary fault treatment

[0097] If multiple secondary faults in the region jointly control the deformation, their geometric parameters need to be determined separately, and the influence of the complex fault system should be considered in the PSHA model to improve the comprehensiveness and accuracy of the hazard assessment.

[0098] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints, characterized in that, Includes the following steps: S1. Obtain the ascending and descending InSAR coseismic deformation maps of the target seismic area, and extract the spatial connection of the maximum deformation gradient as the surface projection proxy trace of the concealed fault. S2. Based on the surrogate trace, construct at least two mutually exclusive fault dip hypothesis; S3. For each fault dip assumption, predict the deformation sign distribution on both sides of the fault under the ascending and descending orbit InSAR observation geometry; S4. Compare the predicted deformation symbol distribution with the actual ascending and descending orbit InSAR deformation maps respectively, retain the assumption of consistent deformation symbols, and obtain preliminary screening results; S5. Conduct field geological surveys within the target area, measure the striation direction of multiple fault outcrops, and invert to obtain the concentrated azimuth range of the local principal compressive stress axis P; S6. Based on the concentrated azimuth range of the local principal compressive stress axis P, determine whether the maximum uplift area in the actual InSAR deformation is located on the side pointed to by the P axis: if not, exclude the retrograde sliding mechanism; if yes, retain the retrograde mechanism and add it to the sliding mechanism candidate set. S7. Combining the preliminary screening results with the candidate set of slip mechanisms, output a physically consistent combination of fault dip direction and slip type as a high-confidence geometric parameter discrimination result for hidden active faults based on multi-track InSAR and stress field constraints.

2. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 1, characterized in that, The consistent deformation sign means that, for any trend hypothesis, the predicted upper plate deformation sign is the same as the actual InSAR observation sign in both ascending and descending orbits, and the lower plate sign is also the same.

3. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 2, characterized in that, The at least two mutually exclusive fault dip assumptions include: taking the proxy trace as the orientation, respectively assuming that the fault dip is orthogonal to the orientation normal direction on both sides.

4. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 1, characterized in that, The side to which the P-axis points is determined as follows: taking the azimuth angle of the local principal compressive stress axis P as a reference, based on the direction of the proxy trace. Define the sector that the P-axis points to as: in, Let P be the azimuth angle of the local principal compressive stress axis, in degrees. The surface azimuth of the center point of the maximum uplift zone, in degrees; if satisfy If so, it is determined to be located on the side pointing to the P-axis.

5. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 1, characterized in that, The ascending and descending orbit InSAR coseismic deformation maps are based on TOPS mode images from the Sentinel-1 satellite and obtained through differential interferometry (DInSAR) processing, with deformation inversion accuracy better than ±1.0 mm.

6. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 1, characterized in that, The local principal compressive stress axis P is obtained by inversion from no less than three outcrops. The concentrated azimuth interval is obtained by inverting the scratch data using the PBT method or the right two-column method, and the standard deviation of the P-axis azimuth angle of each outcrop inversion result is required to be less than 15 degrees.

7. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 1, characterized in that, The spatial connection of the maximum deformation gradient is generated through the following steps: S11. Calculate the spatial gradient of the LOS directional deformation d(x,y) in the InSAR deformation map to obtain the gradient magnitude: Where d(x,y) is the surface deformation along the line of sight (LOS), in millimeters; S12. Calculate the maximum value of the gradient magnitude max(∇d) in the entire deformation diagram; S13. Extract the satisfied A continuous chain of pixels serves as the spatial connection for the maximum deformation gradient.

8. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 1, characterized in that, If the maximum uplift zone is located on the side pointing to the P-axis, and the deformation profile shows that the absolute value of the ratio of the maximum uplift value of the hanging wall to the maximum settlement value of the footwall is not less than 3, then it is determined to be a thrust-type sliding mechanism; if the deformation is nearly symmetrically distributed and the angle between the P-axis and the fault strike is less than 30°, then it is determined to be a strike-slip mechanism.

9. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 1, characterized in that, The method is applicable to shallow-focus tectonic earthquakes with a magnitude range of Mw5.5–6.8, a focal depth of less than 20 km, and no continuous coseismic rupture on the surface.

10. The method for determining the geometric parameters of concealed active faults based on multi-track InSAR and stress field constraints as described in claim 1, characterized in that, This method also includes inputting the determined fault dip direction and slip type into the probabilistic seismic hazard analysis (PSHA) model to correct the maximum expected magnitude and recurrence period of potential seismic source areas.

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