Modeling Tectonic Movements Using the Kalman Filter on GNSS Coordinate Time Series

Using GNSS for many years is the most common technology for the collection, processing, and interpretation of Earth observation data, in particular for the high-precision study of plate tectonics. The results of GNSS observations, such as coordinate time series, allow us to do continuous monitoring of stations, and modern methods of satellite observation processing provide high-precision results for geodynamic interpretation. The aim of our study is to process the results of observations by DD and PPP methods and determine the degree of correlation between GNSS stations based on coordinate time series. For our study, we selected 10 GNSS stations, which merged into two networks - Lviv (SAMB, STOY, STRY, SULP та ZLRS) and Ukrainian (BCRV, CHTK, CNIV, CRNI, GLSV та SULP). The duration of observations on each of them is about 1.5 years (2019-2020). The downloaded observation files were processed in two software packages: Gamit and GipsyX. After applying the «cleaned» procedures based on the iGPS software package, the residual time series were obtained and the coefficients of the interstation correlation matrices were calculated. After the procedure of "cleaning" the time series, we obtained the RMS value decrease for all components of the coordinates by an average of 7-30%, and some stations by 55%. Based on the obtained RMS values, we can conclude that the influence of unextracted or incorrectly modeled errors can significantly affect the results of satellite observations. The obtained interstation correlation coefficients for both networks show different results depending on the used method for processing satellite observations. The larger correlation values of the DD method can be explained by the fact that the effect of errors is distributed evenly to all network stations, whereas in the PPP method errors for each station are individual. The obtained graphs of the common-mode errors values, after their removal from the residual time series, confirm the more uniform nature of the DD method. The results of our study indicate the feasibility of using the PPP method, as the autonomous processing of stations allows you to see the real geodynamic picture of the studied region.

Active faulting at the Eurasian, North American and Pacific plates junction

The evolution of the San Andreas fault system is controlled by thermal‐mechanical processes associated with the development and evolution of a narrow “slabless window” formed beneath the western edge of North America. This fault zone evolution begins after initiation of transform motion along the plate boundary with the northward migration of the Mendocino triple junction. As a consequence of initial lithospheric structure and the shallow emplacement of asthenospheric mantle, the plate boundary separating the North American and Pacific plates follows a complex three‐dimensional geometry which varies through time. Seismic velocity structure, heat flow, seismicity, surface deformation, uplift, and fault development are controlled by the evolving thermal structure in the region after triple junction passage. Thermal‐mechanical models have been used to evaluate the fault system's time‐varying three‐dimensional dynamical behavior, simulating the principal processes involved in the thermal‐mechanical evolution of the San Andreas fault system. Results from this modeling indicate that the fault system has essentially a three‐stage history. (1) In the vicinity of the Mendocino triple junction the San Andreas fault maps the eastern edge of the Pacific plate, with a broad (∼100 km) zone of asthenospheric mantle separating the Pacific and North American plates in the 25‐ to 90‐km depth range. (2) Between 37°N and ∼39°N the plate boundary (within the mantle) separating the Pacific and North American plates has developed approximately 40–60 km east of the surface trace of the San Andreas fault and lies beneath the Hayward‐Calaveras faults and associated faults. The surface trace of the plate boundary appears to be connected to the mantle segment via a lower crust subhorizontal detachment surface. This fault zone orientation produces the surface deformations observed geodetically in the region. (3) South of 37°N the surface fault again overlies the deeper plate boundary, apparently as a result of an eastward jump in the surface fault.

Observations from permanent GNSS stations are actively used for the research and monitoring of geodynamic processes. Today, with the use of modern scientific programs and IGS products, it is possible to determine GNSS station coordinates and velocities at the level of a few millimeters. However, the scientific community constantly faces the question of increasing the accuracy of coordinate definitions to obtain more reliable data in the study of geodynamic phenomena. One of the main sources of errors is systematic measurement errors. To date, the procedure for their removal is still incomplete and imperfect. Also, during the processing of long-term GNSS measurements, it was found that the coordinate time series, after the removal of trend effects, are also characterized by seasonal variations, mainly of annual and semi-annual periods. We estimated the daily coordinate time series of 10 permanent GNSS stations in the central-eastern part of Europe from 2001 to 2019 and calculated the seasonal variation coefficients for these stations. The average value of the coefficients for the annual cycle for the N, E, and H components is −0.7, −0.2, and −0.7 mm, and for the semi-annual cycle the average value is 0.3, 0.4, and −0.5 mm. The obtained coefficients are less than 1 mm, which is why it can be argued that there is no seasonal component in the coordinate time series or that it is so small that it is a problematic task to calculate it. This practical absence of a seasonal component in long-term time series of GNSS coordinates, in our opinion, is partly compensated by the use of modern models of mapping functions (such as VMF3) for zenith tropospheric delays instead of the empirical GMF. To test the obtained results, we calculated the coefficients of seasonal variations for the sub-network of GNSS stations included in the category of the best EPN stations—C0 and C1. The values of the coefficients for the stations of this network are also less than 1 mm, which confirms the previous statement about the absence of a seasonal component in the long-term time series of coordinates. We also checked the presence of seasonal changes in the time series using the well-known decomposition procedure, which showed that the seasonal component is not observed because the content does not exceed 10% for additive decomposition and 20% for multiplicative decomposition.

Ridge subduction, eduction, and the neogene tectonics of southwestern north america

Geologic observations and previous paleomagnetic studies have suggested that the western Transverse Ranges arrived at their anomalous east‐west orientation by clockwise tectonic rotation. A paleomagnetic study of the northern Channel Islands was undertaken, in order to test the extent of rotated areas and to develop constraints on tectonic models concerning the formation of the southern California Borderland. The islands of Anacapa, Santa Cruz, Santa Rosa, and San Miguel form an east‐west trending chain and are considered part of the Transverse Range physiographic province. Oligocene through Miocene volcanic and intrusive rocks occur on these islands, and were sampled for this paleomagnetic study. Eocene sandstones were sampled on San Miguel Island, and Eocene sandstones and Miocene siltstones were sampled on Santa Cruz Island. Paleomagnetic results from igneous units are characterized by declinations deflected clockwise by 69° to 81° from expected directions and inclinations which are too shallow by 10° to 25°. Normal and reversely magnetized units yield antipodal mean directions. The mean result is concordant to the directions obtained from individual units which passed fold and baked contact tests. These results suggest that the northern Channel Islands have been tectonically rotated into place since early(?) Miocene time as the outer borderland area translated northwestward within a large shear zone between the Pacific and North American Plates. The data from the northern Channel Islands when averaged with the data from the Santa Monica Mountains yield a result of I = 36.1° ± 5.1°, D = 72.6° ± 6.3° for the southern part of the western Transverse Ranges (52 units, 405 samples). The shallow paleomagnetic inclinations suggest a northward latitude translation of 14.0°+3.7° or −3.9° for the western Transverse Ranges. However, most plate tectonic reconstructions suggest only 4°±3° of northward translation. The discrepancy may be due to initial dips of the volcanic flows which would cause an artificial shallowing of inclination when the structural dip of the units was corrected to an assumed original horizontal. Other causes for the shallow inclinations could be the effects of an offset dipole field or nondipole field components, or motions of small tectonic plates between the North American and Pacific plates as the Farallan plate broke up and was subducted.

Artificial corner reflectors (CRs), passive (which have no electronic parts), or active ones, so called electronic CR (ECR) or compact transponders (CAT), are devices which reflect the radar signal back to the SAR satellites and provide measurement points at desired locations. Using, such devices we can measure temporal Line of sight (LOS) changes of the CRs using the InSAR technique and for example monitor the ground movements precisely.Since January 2020, Lantmäteriet, the Swedish mapping, cadastral and land registration authority, has installed three ECRs and several types of passive reflectors (different shape and size, planned for C-band Sentinel-1 satellites) in different locations in Sweden. So far, ECRs are still functioning with no electronic failure. However, from the ESA Geodetic SAR project (https://eo4society.esa.int/projects/sar-hsu/) we experienced that the ECRs electronic characteristics are different, so individual calibrations maybe required by the manufacturer. In addition, thermal effects may also cause problems for measurements with ECRs. Therefore, instead of installing more ECRs, we switched to passive ones which have no electronics and have already shown their high-quality performance in different studies. So far, we have installed ten CRs in different locations and the goal is to continue and complement the national geodetic infrastructure of Sweden with at least twenty passive reflectors which are co-located with permanent GNSS stations. Among others, these co-located corner reflectors can potentially contribute to the development of the national and European ground motion services in future updates. Moreover, the co-location helps to map the relative ground motions estimated with InSAR to an absolute geodetic reference frameAmong different tests and performance analysis of such reflectors, we did multipath analysis to investigate if our corner reflectors cause any multipath error on nearby GNSS stations.  We looked at the coordinate time series of the twin GNSS stations at two locations, Visby and Sveg. The installed corner reflector, double back-flipped squared, in Sveg is about 6 m away from the GNSS stations whereas, in Visby, the twin corner reflectors, ascending and descending, are about 20 meters away and have a trihedral squared trimmed shape. The daily GNSS coordinate time series for three components before and after installation of the corner reflectors didn’t show any significant jump in the time series and the coordinate variations are in the range of expected mm-level variations for all stations.

Plate boundary deformation between the Pacific and North America in the Explorer region

The time series of GNSS coordinates contain signals caused by the age-related movement of tectonic plates, the deformation of the Earth’s surface, as well as errors at different time scales from sub-daily tidal deformation to the long-term deformation of the surface load. Depending on the nature of the signal, specific approaches are used for both the visual interpretation and pre-processing of time series and their statistical analysis. However, none of the present software analyzes the nature of the residual errors but assumes their random nature and obedience to the classical normal distribution. One of the methods for analyzing the time series of coordinates with residual, unaccounted-for systematic errors is the non-classical error theory of measurements. The result of this work is a developed software solution for analyzing the time series of GNSS coordinates to test their normality, or in other words, to test whether a particular GNSS station is subject to the influence of small, unaccounted-for errors. Conclusions: After testing our software on four reference stations in Europe, we concluded that none of the chosen stations followed the normal law of distribution; thus, it is vital to perform such tests before conducting any experiments on the time series from reference stations.

Global positioning system (GPS) has been widely used for real-time deformation monitoring. The Kalman filter is one of the optimal methods to process time series of GPS coordinates for a deformation analysis in real-time, but it requires white noise. However, the time series of GPS coordinates obtained from a GPS receiver with a high sampling rate contain coloured noise. A shaping filter can be used to model the long-term movement of coloured noise based on the estimation of the stochastic model of the time series of GPS height coordinates. Thus, a Kalman filter with a shaping filter is proposed to process the different types of deformation time series of GPS height components in real-time. The results show that not only the time series of stepwise deformations but also the time series of continuous deformations can be processed by the Kalman filter with a shaping filter. The coloured noise can be extracted from the GPS time series and the accuracy of the processed coordinate time series has been improved.

Accuracy estimation of site coordinates derived from GNSS-observations by non-classical error theory of measurements

Thermotectonic history of Mt Logan, Yukon Territory, Canada: implications of multiple episodes of middle to late Cenozoic denudation

Active tectonics of the Loreto area, Baja California Sur, Mexico

The Gulf of Alaska is coincident with a converging plate boundary, along which the Pacific plate under thrusts the North American plate. Evidence of this interaction shows up in the deformational pattern of offshoreTertiary strata, as well as the sedimentary record. A broad belt of compressional structures attributable to plate movement can be traced along the continental shelf and slope of the western Gulf of Alaska, parallel to the Aleutian trench. This field cuts diagonally across the continental shelf of the central Gulf of Alaska, splaying into the Fair weather fault system in an area north and west of Yakutat. Structures within this compressional field show evidence of sequential development - from northwest to southeast. Tertiary sediments record a history of southeastern migration of the "Aleutian" trench, and a tectonic incorporation of early Tertiary oceanic", trench and slope sediments in a late forming continental shelf, all in response to episodic, but persistent plate convergence. The implications of plate tectonics for exploration is significant. Knowledge about timing of structural growth, and distribution of reservoir and source rocks is vital to an exploration program. Plate tectonics is not an oil finding tool but a unifying concept to which one may relate the required interpretations about structure and stratigraphy. INTRODUCTION The concept of global plate tectonics is becoming more and more important to petroleum geologists exploring the Gulf of Alaska. There, two segments of the earth's crust, the Pacific plate and the North American plate, interact in an area where one major O.C.S. lease sale has recently been held, and others are scheduled for the future. The most promising areas for petroleum potential in the Gulf of Alaska are in the northern Gulf where O.C.S. Sale 39 was held in April 1976, and in the western Gulf where O.C.S. Sale 46 is tentatively scheduled for November 1977 (Fig. 1). In both areas, petroleum potential lies in Tertiary sediments. Folding and faulting took place in Tertiary time. Both stratigraphy and structure have been affected by the plate-tectonics environment of the region and the time. The regional geology of this area has recently been described by various U.S.G.S. workers.1, 2 Fig. 2 is a vastly simplified geologic map. Mesozoic rocks border the Gulf of Alaska onshore. They are highly deformed and metamorphosed to some extent, and probably have no petroleum potential in the region. Early Tertiary sandstones, shales and volcanics of deep marine (in the west) and shallow marine and non-marine (in the east) environments form the next outcropping belt seaward. They too, are highly deformed. Petroleum potential in these rocks depends on their being found in a location where the degree of deformation is less, and where there is reasonable expectation of reservoir sand development. Late Tertiary rocks outcrop in the next, more seaward out Crop belt.

Using up to 11 years of data from a global network of Global Positioning System (GPS) stations, including 12 stations well distributed across the Pacific Plate, we derive present‐day Euler vectors for the Pacific Plate more precisely than has previously been possible from space geodetic data. After rejecting on statistical grounds the velocity of one station on each of the Pacific and North American plates, we find that the quality of fit of the horizontal velocities of 11 Pacific Plate (PA) stations to the best fitting PA Euler vector is similar to the fit of 11 Australian Plate (AU) velocities to the AU Euler vector and ∼20% better than the fit of nine North American Plate (NA) velocities to the NA Euler vector. The velocities of stations on the Pacific and Australian Plates each fit a rigid plate model with an RMS residual of 0.4 mm/yr, while the North American velocities fit a rigid plate model with an RMS velocity of 0.6 mm/yr. Our best fitting PA/AU relative Euler vector is located ∼170 km southeast of the NUVEL‐1A pole but is not significantly different at the 95% confidence level. It is also close (<70 km in position and <3% in rate) to a pole derived from transform faults identified from satellite altimetry, suggesting that the vector has not changed significantly over the past 3 Myr. Our relative Euler vector is also consistent with all known geological and geodetic evidence concerning the AU/PA plate boundary through New Zealand. The GPS sites offshore of southern California are presently moving 4–5 ± 1 mm/yr relative to predicted Pacific velocity, with their residual velocities in approximately the opposite direction to PA/NA relative motion. Likewise, the easternmost sites in South Island, New Zealand, are moving ∼3 ± 1 mm/yr relative to predicted Pacific velocity, with the residuals in approximately the opposite direction to PA/AU relative motion. These velocity residuals are in the same sense as predicted by elastic strain accumulation on known plate boundary faults but are of a significantly higher magnitude in both southern California and New Zealand, implying that the plate boundary zones in both regions are wider than previously believed.