Supplemental Material: Initiation of Clockwise Rotation and Eastward Transport of Southeastern Tibet Inferred from Deflected Fault Traces and GPS Observations

Table S1: GPS velocity data in a Eurasian-fixed Reference Frame (velocity in mm/yr); Table S2: GPS velocity data in a South China Block-fixed Reference Frame (velocity in mm/yr); Table S3: GPS stations in the South China Block used to define the Euler Vector for transformation of reference frame (velocity in mm/yr); Table S4: Interpolated velocities of the points on current fault trace and extension line of undeflected fault segment, and the averages of each pair of corresponding points (velocity in mm/yr); Table S5: Position and backward velocity of points on current fault trace (velocity in mm/yr); Table S6: Points inferred from the best estimate of duration time; Table S7: Points on smoothed original fault trace.

Supplemental Material: Initiation of Clockwise Rotation and Eastward Transport of Southeastern Tibet Inferred from Deflected Fault Traces and GPS Observations

Table S1: GPS velocity data in a Eurasian-fixed Reference Frame (velocity in mm/yr); Table S2: GPS velocity data in a South China Block-fixed Reference Frame (velocity in mm/yr); Table S3: GPS stations in the South China Block used to define the Euler Vector for transformation of reference frame (velocity in mm/yr); Table S4: Interpolated velocities of the points on current fault trace and extension line of undeflected fault segment, and the averages of each pair of corresponding points (velocity in mm/yr); Table S5: Position and backward velocity of points on current fault trace (velocity in mm/yr); Table S6: Points inferred from the best estimate of duration time; Table S7: Points on smoothed original fault trace.

Variability of Characteristics of the Coastal Current at the Southern Coast of Crimea in 2017–2019

This paper aims at specifying peculiarities of the coastal water circulation according to the current monitoring data obtained at the stationary oceanographic platform of the Black Sea hydrophysical sub-satellite testing area of the MHI RAS near the Southern coast of Crimea in 2017–2019. The monitoring was performed using the technology of continuous measurements with a vertically distributed (from the surface to bottom layer) complex of Euler vector-averaging meters of the horizontal current component. The new results are matched to those of the coastal current monitoring obtained for the previous period from 2008 to 2016. For the entire observation period (2008–2019), the annual focused current of coastal waters kept the west-south-western direction, with its vertical structure remaining stable. In 2017–2019, a verifiable decrease was registered in the annual longshore current velocity, on average by 10 % throughout the depth up to 7.8 cm/s at a depth of 5 m and up to 6.4 cm/s at a depth of 20 m. Also, the relevant characteristics of bimodal distribution of direction repeatability within original (nonaveraged) data remained unchanged. Further, for 12 years, the oscillation intensity of the coastal current with periods of 10–13 days or less remained reliably unchanged. While analyzing the vertical structure of averaged for 2017–2019 kinetic energy spectra in the inertial-gravitational fluctuation range, two separate regions are reliably detected of regular oscillations with daily (24 h) and local inertia (about 17 h) periods. The obtained new research results can be used while performing validation calculations of local models of the coastal water circulation in the water area of the Southern coast of Crimea. This includes also planning measures to provide crisis monitoring of the coastal ecotone of the sea due to pollution of the coastal and shelf waters

Determination of vector Euler parameters

Improving the accuracy of points coordinates determination from geodetic networks with the use of modern space geodesy techniques (GPS, SLR, VLBI, DORIS) identified factors that were earlier considered as insignificant. Such factors include the movement of tectonic plates. This made possible the transition from the static coordinate system model to the kinematic one. For the effect of the tectonic plates movement on the points coordinates you must know kinematic parameters of the tectonic plates movement – the Euler vector parameters – angular velocity of the tectonic plates rotation and the poles rotation coordinates (latitude and longitude) of tectonic plates. Many modern kinematic models of tectonic plates are used observations, performed by geophysical methods, to estimate kinematic parameters of the tectonic plates movement. The article presents the algorithm that allows to estimate the parameters of the tectonic plates movement from mathematical processing of geodetic measurements carried out at points distributed over the surface of tectonic plates. Based on the presented algorithm the EULER program was developed in the algorithmic FORTRAN language, which was experimentally tested. The analysis results showed that the parameters of the Euler vector obtained by the EULER program are in good agreement with the results obtained by using ITRF 2005 and ITRF 2008 models.

Multi-quadric collocation model of horizontal crustal movement

To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used. However, the kernel function, nodes, and smoothing factor are difficult to determine in the Hardy function interpolation. Furthermore, the covariance function of the stochastic signal must be carefully constructed in the collocation model, which is not trivial. In this paper, a new combined estimation method for establishing the velocity field, based on collocation and multi-quadric equation interpolation, is presented. The crustal movement estimation simultaneously takes into consideration an Euler vector as the crustal movement trend and the local distortions as the stochastic signals, and a kernel function of the multi-quadric fitting model substitutes for the covariance function of collocation. The velocities of a set of 1070 reference stations were obtained from the Crustal Movement Observation Network of China, and the corresponding velocity field was established using the new combined estimation method. A total of 85 reference stations were used as checkpoints, and the precision in the north and east component was 1.25 and 0.80 mm yr−1, respectively. The result obtained by the new method corresponds with the collocation method and multi-quadric interpolation without requiring the covariance equation for the signals.

Multi-quadric collocation model of horizontal crustal movement

To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used, but the kernel function, nodes, and smoothing factor are difficult to determine in the Hardy function interpolation, and in the collocation model the covariance function of the stochastic signal must be carefully constructed. In this paper, a new combined estimation method for establishing the velocity field, based on collocation and multi-quadric equation interpolation, is presented. The crustal movement estimation simultaneously takes into consideration an Euler vector as the crustal movement trend and the local distortions as the stochastic signals, and a kernel function of the multi-quadric fitting model substitutes for the covariance function of collocation. The velocities of a set of 1070 reference stations were obtained from the Crustal Movement Observation Network of China (CMONOC), and the corresponding velocity field established using the new combined estimation method. A total of 85 reference stations were used as check points, and the precision in the north and east directions was 1.25 and 0.80 mm yr−1, respectively. The result obtained by the new method corresponds with the collocation method and multi-quadric interpolation without requiring the covariance equation for the signals.

Does the nontrivially deformed field–antifield formalism exist?

We reformulate the Lagrange deformed field–antifield BV-formalism suggested, in terms of the general Euler vector field N generated by the antisymplectic potential. That N generalizes, in a natural anticanonically-invariant manner, the usual power-counting operator. We provide for the "usual" gauge-fixing mechanism as applied to the deformed BV-formalism.

Plate Convergence and Block Motions in Mindanao Island, Philippine as Derived from Campaign GPS Observations

We conducted yearlyGlobal Positioning System(GPS) campaigns in the eastern part of Mindanao from March 2010 to March 2014. The obtained station velocities with respect to the Sunda plate (SU) show that WNW motions are dominant due to the convergence of the Philippine Sea plate (PHS). However, it was found that elastic deformations caused by a full coupling of the plate interface down to 80 km could explain a maximum of only 29% of the observed station velocities. In order to interpret the displacement pattern, we applied a rigid block rotation model and determined the Euler vector. As a result, we determined that Mindanao Island could be divided into at least three blocks and that the Philippine fault is one of the block boundaries. Although it was not possible to determine the coupling ratio at the Philippine trench, the dislocation pattern of the Philippine fault showed along-strike variation in Mindanao Island.