Effect of various factors on coseismic deformation of the 2015 Mw7.8 earthquake in Nepal

Using natural topography and 3D elastic structure, we also use a numerical model to estimate the coseismic surface deformation caused by the 2015 Nepal earthquake. Based on the homogeneity of the study area in the middle of the longitudinal layers, we analyze the vertical displacement of the surface in the study area.

Mechanical solutions for different seismic sources

In Figure 2, the vertical displacements of the sites calculated based on the seismic mechanism solution for each agency (in Table 2) differ from the observed values. The axial mechanisms provided by the various institutions are all rupture earthquakes. For stations within the black dotted circle, results from other agencies, except those from the USGS, do not agree with the observed values ​​in the trend. For example, in KKN4, KIRT, NAST, and DAMA, the USGS results and actual observed values ​​are all in the upward trend, while the results for GFZ, CPT, and GCMT are all in the downward trend. However, the CHLM vertical displacements calculated based on the USGS are more than twice as large as the actual observed values, and the difference in KKN4 is even more significant. The displacements of each site calculated based on the seismic mechanism solution in this paper are close to the same trend as the actual observed values ​​for stations outside the black dotted line, except for GHER and J339. This may be due to the large difference in lateral heterogeneity between the southern and northern edges of the Tibetan Plateau.

Figure 2

Surface vertical forward displacement based on different focusing mechanism solutions. In the figure, the beach ball represents the source mechanism solution, the blue color represents the actual GNSS observations, and the red, purple, green, and yellow colors represent the displacements of GNSS points corrected using the source mechanism solution of different agencies, respectively. The dashed black circles are the regions with the largest surface displacements.

Table 2 Focal mechanism of the 2015 Mw7.8 earthquake in Nepal. Source parameters for the 2015 Mw7.8 earthquake in Nepal.

The solution of the focal mechanism is determined based on the inversion of the error geometric parameters and average slip parameters by surface displacement, and the focal position is determined by the spectral element method with surface displacement as the constraint condition.

In inversion of fault geometric parameters and mean slip parameters, this study inverses the geometric parameters of coseismic faults based on the Okada model and the Bayesian method (GBIS; http://comet.nerc.ac.uk/gbis/) with GNSS data constraints26. During inversion, the origin of the reference coordinates is 84.731°E, 28.231°N. The range of geometric parameters to identify faults is as follows: dip angle is 0°~90°, strike is 180°~360°, the The fault length is 40 ~ 150 km, the fault width is 10 ~ 80 km, the depth is 2 ~ 60 km, and the number of iterations is 107. After many iterations, the posterior probability density distribution of the geometric parameters of the fault is Gaussian. See Table 3 for error geometric parameters. In Table 3, the first column is the parameter name, the second, third, and fourth columns are the best quality, mean, and median values ​​of the parameters, and the fifth and sixth columns are the 2.5% and 97.5% confidence intervals.

Table 3: Geometric parameters of planar defects.

The error parameters agree with most results3,7,33,34. We use the parameters in Table 3 to simulate the horizontal displacement of the surface, as shown in Figure 3. The results agree with the GNSS observation results. In this paper, we consider GNSS observations as valid values ​​and find that the fitting residuals of all stations in Nepal are within 4 cm, of which the maximum offset station KKN4 has a fitting residual of 1.7 cm, and the average fitting residual of stations in China is 3 cm. This indicates that the reversal of incorrect geometric parameters is reliable.

Figure 3

Comparison of cosmological GNSS displacement and future modeling results in Nepal. The red arrow in the figure is the horizontal displacement observed by GNSS, and the blue arrow is the horizontal displacement of the analog value. The length of the solid and hollow needles represents a displacement of 600 mm and 50 mm, respectively.

First, in this paper, the 290 km × 310 km × 50 km extent around the earthquake was considered a study area and was divided into 1,075,200 grid cells (excluding terrain); We set artificial absorption boundaries at the periphery and bottom of the mesh, and set the upper surface as a free boundary. In order to adapt to the fine grid requirements, we added two double grid layers at 6 km and 26 km depth; Finally, a terrain grid containing 78,061 elevation points was added to complete the computational modeling (Figure 4). The data were then processed for approximately 30 minutes using SPECFEM-X software on a server with four parallel processors and 166 GB of running memory.

Figure 4

3d models of nepal. The figure is a 3D model of Nepal. Different colors in the direction of the Z coordinate axis represent different modes – Table 1 for their parameters.

When describing the solutions of the focal mechanism \(r\), \(\theta\), \(\varphi\). To construct a spherical coordinate system, we use the geometric parameters in Table 3 to calculate the seismic moment \({M})_{0}=6.8e+20\) and the moment tensor M(\({M}_{rr}=1.2975e+20\) ),\({M}_{\theta \theta }=-1.2298e+20\), \({M}_{\varphi \varphi }=-0.06766e+20\), \({M}_{ r\theta}=6.4987e+20\), \({M}_) {r\varphi}=-1.5242e+20\), \({M}_{\theta \varphi}=0.2885e+20 \))36. Establishing a 2° × 2° search area with the vertical offset of GNSS stations close to the source (KKN4, KIRT, CHLM, NAST, DAMA) as a constraint, the objective function is to minimize the residual values ​​of the simulated values. The final specific source position is (85.08°E, 27.985°N), as shown in Figure 5.

Figure 5

RMSE to redirect the cosmic displacement of the source location. The points in (a) are the searched source locations, the red five-pointed star is the optimal source location, and (b) the RMSE of the source locations is shown in the dashed black box in (a). The horizontal axis in Figure (b) represents the transverse distances, where the origin is (85.08°E, 27.985°N), the distance to the northeast is positive and the distance to the southwest is negative. The vertical axis represents the RMSE of the residuals of the simulated values.

Inversion of the cosmic slip distribution

In this paper, using the geometry of the faults inverted by the Bayesian algorithm as input parameters and GNSS and InSAR data as constraints, the slip distributions of the 1500 subfaults along the strike and dip directions, respectively, are calculated using the SDM program. At the same time, we constrain the amount of slip between adjacent subfaults by applying Laplace smoothing. We determine that the weight ratio of GPS to InSAR is 1:0.4 by deducting the residual from GPS and InSAR fit38, as shown in Fig. 6. Calculate the moment tensor for each subfault using the following equation.

$$\begin{array}{*{20}c} {M_{0} = \mu DA} \\ \end{array}$$

(11)

$$\begin{array}{*{20}c} {M_{\theta \theta} = – M_{0} \left( {sin\delta cos\lambda sin2\phi + sin2\delta sin\lambda sin^ {2} \phi } \right)} \\ \end{array}$$

(12)

$$\begin{array}{*{20}c} {M_{\theta \varphi} = – M_{0} \left( {sin\delta cos\lambda cos2\phi + 1/2sin2\delta sin\lambda sin2\phi } \right)}\end{array}$$

(13)

$$\begin{array}{*{20}c} {M_{r\theta} = – M_{0} \left( {cos\delta cos\lambda cos\phi + cos2\delta sin\lambda sin\phi } \right)} \end{array}$$

(14)

$$\begin{array}{*{20}c} {M_{\varphi \varphi} = + M_{0} \left( {sin\delta cos\lambda sin2\phi – sin2\delta sin\lambda cos^ {2} \phi } \right)} \\ \end{array}$$

(15)

$$\begin{array}{*{20}c} {M_{r\varphi} = + M_{0} \left( {cos\delta cos\lambda sin\phi – cos2\delta sin\lambda cos\phi } \right)} \\ \end{array}$$

(16)

$$\begin{array}{*{20}c} {M_{rr} = + M_{0} sin2\delta sin\lambda } \\ \end{array}$$

(17)

where \(\mu\) is the shear modulus, D is the fault displacement, and A is the fault area; \(\delta\) denotes the slope of the fault (0° ≥ \(\delta\) ≥ 90°), \(\lambda\) denotes the fault slip angle (-180° ≥ \(\lambda\) ≥ 180° ), and \(\phi\) represents the strike angle.

Figure 6

Fault-slip displacement calculated by SDM. (a) Shows the InSAR/GPS ratio used to determine the minimum error. (b) The red dashed box in the figure represents the location of the fault, and the middle plot shows the displacement of 1500 subfaults calculated by the SDM.

Effect of terrain on cosmic displacement

First, we created three models: Model (A) represents the heterogeneous model with terrain, Model (B) represents the heterogeneous model without terrain, and Model (C) represents the heterogeneous model without terrain.

This paper uses the following formula to measure the effect of terrain effect:

$$\begin{array}{*{20}c} {P = \frac{{\left| {\Delta i} \right|}}{{\left| {j_{max} } \right|}}\cdot100\% } \\ \end{array}$$

(18)

where \(\Delta i\) is the difference between the cosmological displacement of the calculation point taking into account the terrain factor and without taking into account the terrain factor, \(j_{max}\) is the maximum value of the cosmic displacement at all calculation points, and \(P\) It is the percentage of topographic influence.

In this section, the spectral element method calculates the coseismic surface displacements in Nepal, considering topographic factors and without topographic factors, respectively. When using a single limited fault source, the effect of topography is mainly reflected in the fault zone of Nepal. It shows the morphology of high north and low south, which is consistent with the terrain distribution in the area, and produces a maximum terrain effect of nearly 30%, as shown in Figure 7. When multiple sub-terrains exist, the faults are used as a source, and the vertical displacement is analyzed In terms of the presence of two shaded peaks in the direction of fault movement, which corresponds to the backwash type of earthquake. When a heterogeneous topographic model is used, the displacements are closer to the InSAR results processed by Lindesy23, as shown in Fig. 8a–c. Then, in the horizontal direction, the trend of the GNSS offsets is almost the same as that of the GNSS offsets in Nepal. Moreover, by comparing models A and B, it can be seen that there is a northward shift of the peak surface displacement of this earthquake, which also indicates that the presence of terrain changes the position of the peak in the coseismic displacement of this earthquake. Earthquake front surface. In summary, the effect of topography on the coseismic displacement is ~20%, which is larger than the effect of ~9% of topography based on the finite element method by Lin11, ~10% of topography based on the Bayesian method by Yang7, and ~6% of topography based on data InSAR and finite element method by Wang and Fialko39. Effect ~6% greater.

Figure 7

Effect of terrain under a unilateral seismic source. (a) shows the difference between the two models under the influence of topographic factors for a single surface source, and (b) shows the value of the effect of the topographic factor.

Figure 8

Surface cosmological displacements of different models under multiple sub-sources. (a–i) Represents three-component displacements based on three different models under multiple sub-fault sources and is positive in the north, east and up directions. The purple triangles in (a,d,g) are GNSS stations within Nepal.

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