3. Propuesta del modelo competitivo del sector bananero
3.3. Conclusiones
Figure 2.11 Comparison of different downsampling methods. (a) Result by the uniform downsampling method, (b) by quadtree downsampling method and (c) by data resolution based downsampling method.
2.2.3 PSOKINV
Several geodetic inversion packages have been developed, e.g. nonlinear Okinv and Slipinv (Wright et al., 1999; Funning et al., 2005b), GEODMOD in Miami University (Amelung et al., 2011) and SDM (Wang et al., 2013a). Nonlinear Okinv has been widely applied in earthquake modelling, particularly in UK NERC COMET team (e.g. 1999; Wright et al., 2001a; 2003; Parsons et al., 2006; Walters et al., 2009; 2012; Elliott et al., 2013). GEODMOD is designed for earthquake and volcano modelling by the InSAR team in Miami University. SDM is fully released by Dr.
Rongjiang Wang in GFZ, which is specifically used for linear slip inversion. Here, a novel self-developed Matlab-based geodetic inversion package, PSOKINV will be introduced, which is employed to solve all linear/nonlinear problems in this thesis.
33 2.2.3.1 Overview of PSOKINV
PSOKINV is an acronym for the Particle Swarm Optimization and OKada Inversion Package. As its name suggests, the package was originally tailored for InSAR inversion using the MPSO nonlinear algorithm based on the elastic Okada dislocation models (Okada, 1985, 1992). The first version of PSOKINV was completed in the summer of 2009. After a few years' development, particularly during the period of my PhD study, the latest version is able to handle multiple geodetic datasets including InSAR, GPS, land and/or space-based gravity changes and field survey measurements. Combining with PSGRN/PSCMP (Wang et al., 2006b), PSOKINV can also treat a geodetic modelling in a layered Earth medium smoothly. As shown in Figure 2.12, four independent sub-packages are included in the current version of PSOKINV such as data preprocessing, nonlinear inversion, linear slip inversion and forward simulation.
Figure 2.12 Flow chart of PSOKINV.
2.2.3.2 PSOKINV features
PSOKINV has following features which make it efficient and easy-to-use:
1) Flexible definitions of a rectangular fault. PSOKINV provides seven different fault definitions that are useful to control the relative locations between adjacent faults.
2) Optional parallel computing. Utilizing the parallel computing environment in Matlab, PSOKINV can automatically assign a computation task to different CPUs. Using Laptop or personal computer with four CPU cores, an inversion job using full computer resources can be accelerated by at least 3 times than that in a single CPU core computer.
3) Fault discretization. PSOKINV provides three strategies to divide a single fault into discrete subfaults for slip distribution inversion (Figure 2.14 (b,c,d)) including regular size sampling, depth-dependent variable size sampling and slip sensitivity analysis based fault discretization.
The regular size method was widely used in previous studies (e.g. Talebian et al., 2004;
Funning et al., 2005a; Biggs et al., 2007), in which each fault patch has equal size. The depth-dependent fault discretization method (DDD) was also applied in several previous studies (e.g. Simons et al., 2002; Fialko, 2004b). A damping factor that controls the sub-patch size increasing with depth is introduced to keep a high model resolution in the shallow part of a fault and also split the fault into a limited number of subfaults. The slip sensitivity analysis
34 based method (SSAM) is a new method first proposed in this thesis. This method is similar with a method proposed in Atzori et al’s study (Atzori and Antonioli, 2011), but the method in this study is fully derived from the data and the smallest patch size is not necessary on the top.
Its basic principle is to allow a smaller patch size where the faults have greater abilities to explain observations, which is similar to the ideas to sample a fault based on aftershock spatial distribution (Ziv, 2012). Triangular dislocation elements are also already allowed in the current version of PSOKINV. However, forward modelling of the angular dislocation derived by Meade et al. (2007) is computationally expensive, thus in practice, rectangular elements are recommended by default.
4) Estimation of parameters uncertainties. Similar to the Monte Carlo method proposed in nonlinear Okinv (e.g. Wright et al., 1999; 2003; Biggs et al., 2006; Parsons et al., 2006), the uncertainties in fault parameters and slip distributions can be estimated in terms of the observation errors.
5) Modular programming. Over 400 m-scripts are developed in PSOKINV, which are also helpful for other independent applications, e.g. Coulomb stress calculation, seismic statistics, regression analysis and geographic applications. For examples, a plane equation in 3D with three control points can be estimated using only one m-script.
6) Being compatible with other public packages. PSOKINV provides independent utilities to implement model format conversion for packages, e.g. Coulomb3.1, PSGRN/PSCMP and OKSAR.
Figure 2.13 An example of a single fault plane with different reference points. Six different definitions for the same fault are given. A, top-left corner on the surface. B, top-middle on the surface. C, top-right corner on the surface. D, E and F are as for A-C, but define the top boundary of real fault plane (red rectangle).
Arrow shows the slip vector, and red thick line shows the fault trace, the line of intersection between the fault plane and the Earth's surface. E is used in the inversion by default.
7) Quick maps using the genetic mapping tools (GMT). An additional package was developed during this thesis, which can plot figures using GMT. In the subpackage, Matlab is used to
35 organize and analyze data, and automatically generate GMT scripts for a high resolution PS.
Some scripts are also available to generate KML files to publish slip models in Google Earth.
2.2.3.3 Validation: a checkerboard test
To validate the efficiency of PSOKINV and compare the effects of different fault discretization methods, a checkerboard test was carried out using 1,005 LOS observations with the same SAR viewing geometric parameters as Figure 2.11 (c). The fault geometric parameters for theoretical simulation were inherited from the 2011 MW 6.8 Burma earthquake by Feng et al. (2013). The three fault discretization methods were all applied to retrieve slip models. Their resultant optimal slip models are shown in Figure 2.14, which can explain the observations equally well with the RMSs of 1.02×10-4, 1.1×10-4 and 1.02×10-4 m, respectively. Due to the roles of slip smoothing and different patch sizes used in the fault discretization, the determined slip models are not completely identical to the input model (Figure 2.14 (a)). However, the two major slip patterns have all been retrieved in the three slip models. Figure 2.15 shows that the stress drop calculated from the SSAM slip model (Figure 2.14 (d)) trends to be uniform, whilst the stress drop resulting from the regular size (Figure 2.14 (b)) and DDD slip models (Figure 2.14 (c)) are highly variable.
Figure 2.14 Slip inversion validation with three discretized fault models by a checkerboard test.
36 Figure 2.15 Shear stress drop corresponding to the three resolved slip models in Figure 2.14.