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## Iterative approach of 3D datum transformation with a non-isotropic weight

### Acta Geodaetica et Geophysica (2016-09-01) 51: 557-570 , September 01, 2016

The analytical solution of 3D datum transformation with an isotropic weight has been elegantly presented based on Procrustes algorithm (singular value decomposition). But the existence of analytical solution of 3D datum transformation with a non-isotropic weight needs further investigation. Based on the Lagrangian extremum law, the paper derives the analytical formula for translation parameter and scale factor, but because the rotation matrix is unsolved, the analytical solution does not exist. For this reason, the paper presents two kinds of iterative approach of 3D datum transformation with a non-isotropic weight. One is the iterative approach dependent on the objective function value, which uses the Lagrangian minimum function in the variable of rotation matrix as the objective function, and the other is the iterative approach dependent on the derivative of function, which uses the 3D datum transformation model that eliminates the translation parameter. In order to improve the speed and reliability of iterative computation, the form of rotation matrix represented by Rodrigues matrix instead of rotation angles or unit quaternion is adopted for the two iterative approaches. A numerical experiment is demonstrated, and comparison analysis of the two iterative approaches is carried out. The result shows from the view of computing speed and reliability, the iterative approach based on derivatives is preferred.

## Seismic singularity attribute and its applications in sub-seismic faults detection

### Acta Geodaetica et Geophysica (2014-12-01) 49: 403-414 , December 01, 2014

The sub-seismic faults are below the limit of seismic resolution, and present in 3D seismic data. In general, the sub-seismic faults are providing cross-stratigraphic pathways for fluid expulsion in the tight reservoir. A workflow to analyze sub-seismic faults prediction over different scales is described in this paper. This requires very detailed fault detection in order to bridge the information gap between seismic data and sub-seismic faults. Based on the seismic signal singular value analysis, we made predictions about the sub-seismic faults. We interpreted fault in seismic, and seismic attributes volumes at scales above dozens meters. The seismic signal singular value was performed on a detailed interpreted 3D volume to predict the sub-seismic fault, at a scale below seismic resolution. The modeling results show that considerable seismic signal singular value is observed less than 20 m from the seismic volume. We linked the real data volume from the modeled parameters, and used the singular value as a proxy for sub-seismic faults. With this method we can predict the sub-seismic faults combined with structure in areas. Furthermore, knowing other geological data we can predict the possible leakage and overflow when drilling horizontal well and reduce drilling risk.

## Transformation of solar wind energy into the energy of magnetospheric processes

### Acta Geodaetica et Geophysica (2014-03-01) 49: 1-15 , March 01, 2014

When the solar wind flows round the magnetosphere, its flow structure and interplanetary magnetic field lines are affected. This indicates the appearance of an electric current system in near-Earth space. *t*he magnetized solar wind plasma moving at the solar wind velocity in the coordinate system of near-earth bow shock induces an electric field in this system. When crossing the bow shock front at the nose point, the tangential magnetic field component increases nearly four times, and the magnetic field energy density—15 times.

This paper relies on the results of earlier researches (Ponomarev et al. 2006a, 2006b), where we obtained the expression for electric current generated in the bow shock front and closed through the magnetosphere, as well as finding the magnetopause potential as a function of solar wind parameters—solar wind velocity and *B*_{z}-component of the interplanetary magnetic field. The power *W* consumed by the magnetosphere is equal to the Poynting flux through the magnetopause. According to a special case of Poynting’s theorem, applied to the geomagnetosphere, the energy flux can be expressed through electric potential (integration is over the entire magnetospheric surface). Thus, we obtain the required dependence for *W*. This dependence appears to be a square law relative to IMF *B*_{z}-component.

## Reply to Wu “Comment on Regional level Forecasting of Seismic energy release by Kavitha and Raghukanth”

### Acta Geodaetica et Geophysica (2016-12-01) 51: 777-779 , December 01, 2016

Kavitha and Raghukanth (doi: 10.1007/s40328-015-0131-7 , 2015) have developed an algorithm to forecast earthquake energy for a given seismogenic zone. The forecasting strategy is based on empirical mode decomposition and nonlinear regression analysis. The proposed algorithm has been validated with independent subset of seismicity data. Wu (Acta Geod Geophys 2015) has raised concern about the uncertainties and the input seismicity data used to develop the model. This article discusses the problems associated with the modelling of the seismic energy at regional level.

## Tectonic activity inferred from velocity field of GNSS measurements in Southwest of Turkey

### Acta Geodaetica et Geophysica (2013-06-01) 48: 109-121 , June 01, 2013

Turkey occupies a critical segment in the Alpine-Himalayan orogenic belt that is characterized by many active fault lines. Numerous earthquakes of varying magnitudes have occurred on these fault lines over the years. A significant portion of these earthquakes have been recorded along the Fethiye Burdur Fault Zone (FBFZ). Unfortunately, the latest earthquakes that happened on the FBFZ led to a large loss of human life and extensive economic losses. Southwest Anatolia, including the FBFZ, is monitored by 44 Global Navigation Satellite System (GNSS) stations, comprised of 16 permanent and 28 campaign stations. Measurements have been conducted by combining observations from 2003 to 2006 (Erdogan et al. in J. Earthq. Eng. 12(2):109–118, 2008) with new observations from 2009 and 2010. The combined processes have yielded an updated velocity field of the region. In addition, the effects of the post 2007 earthquakes on the GNSS stations were also investigated. The strain analysis based on the observations made between 2003 and 2010 display high consistency with the earthquakes that occurred in the region. Also, it was observed that the strain analysis is in accordance with the North-South opening created as a result of the African plate being submerged under the Anatolian plate in the southern of the island of Crete.

## Regional level forecasting of seismic energy release

### Acta Geodaetica et Geophysica (2016-09-01) 51: 359-391 , September 01, 2016

This article explores a new strategy for forecasting of earthquake energy release in the seismogenic zones of the world. A total of 41 active seismogenic zones are identified with the help of past seismicity data. The magnitudes of individual events occurred in each zone are converted into seismic energy using an empirical relation. The annual earthquake energy time series is constructed by adding the energy releases of all the events in a particular year. The technique of principal component analysis is employed for the regionalization of these seismogenic zones using seismic energy time series. The annual energy time series of seismogenic zones are decomposed into finite number of intrinsic mode functions (IMFs) using ensemble empirical mode decomposition technique. The periodicities of the IMFs and their contribution to the total variance of the earthquake energy release are examined. The artificial neural network technique is used for modeling and forecasting the energy-time series of seismogenic zones. The model is verified with an independent subset of data and validated using statistical parameters. The forecast of the annual earthquake energy release in each seismogenic zone is provided for the year 2015.

## Investigation into the linear relationship between the AE, Dst and ap indices during different magnetic and solar activity conditions

### Acta Geodaetica et Geophysica (2016-06-01) 51: 315-331 , June 01, 2016

There are numerous geomagnetic indices used in monitoring various magnetospheric and ionospheric phenomena. Some of the most widely used indices are the *ap*, *AE* and *Dst*. In this work, the relationship between these three geomagnetic indices is investigated at different levels of solar and magnetic activity. 3-h average data spanning 8-years were used—high (HSA), moderate (MSA) and low solar activity (LSA) periods cover the years 1999–2001, 2004–2005, and 2006, 2009–2010 respectively. All the investigated correlation pairs recorded the highest/lowest during the LSA/HSA periods. The *ap*/*AE* correlation was found to be highest ranging within 70–78 % at any solar activity. The *ap* versus *AE* and *Dst* multiple correlation reached 94.0, 92.1, and 89.2 % for HSA, MSA, and LSA conditions, respectively, and 72.1, 83.3, and 80.0 % for the main phase, recovery phase and quiet conditions respectively. Moreover, higher percentage correlations were observed for the *ap*/*AE* pair at any geomagnetic conditions than for the *ap*/*Dst* and *AE*/*Dst* pairs. The ring current index *Dst* is observed to have a greater influence on *ap* during geomagnetic storm periods.

## Key results on deep electrical conductivity anomalies in the Pannonian Basin (PB), and their geodynamic aspects

### Acta Geodaetica et Geophysica (2016-12-23): 1-24 , December 23, 2016

In the first part of the paper a brief introduction is given (a) to the magnetotelluric (MT) and magnetovariation (MV) soundings, (b) to electrical resistivity of minerals and rocks, and their dependence on temperature and fluid content. The basic geoelectric model in the Pannonian Basin is a (linear) tectonic zone (“dike”) and a series of dikes. In the second part the main crustal and mantle conductivity anomalies observed in the Pannonian Basin (PB) are summarized: (a) deep conductive crustal fractures and their relation to the occurrence of the earthquakes, boundary of the megablock(s) etc., (b) middle crustal conductors as indicators of decrease in stress and seismic activity depending on thermal regime, (c) the conductive asthenosphere and its lateral change in the PB in connection with the heat flow and tectonics. The general relation between the depth of the conductive asthenosphere and the regional heat flow is also presented, (d) MT anisotropy of the resistivity distribution in the PB and its tectonic explanation based on Haas’s tectonic map (2001, Fig. 1). All these observations and conclusions are considered as results for further investigations.

## Assessment of numerical integration methods in the context of low Earth orbits and inter-satellite observation analysis

### Acta Geodaetica et Geophysica (2016-12-01) 51: 619-641 , December 01, 2016

The integration of differential equations is a fundamental tool in the problem of orbit determination. In the present study, we focus on the accuracy assessment of numerical integrators in what refers to the categories of single-step and multistep methods. The investigation is performed in the frame of current satellite gravity missions i.e. Gravity Recovery and Climate Experiment (GRACE) and Gravity Field and steady-state Ocean Circulation Explorer (GOCE). Precise orbit determination is required at the level of a few cm in order to satisfy the primary missions’ scope which is the rigorous modelling of the Earth’s gravity field. Therefore, the orbit integration errors are critical for these low earth orbiters. As the result of different schemes of numerical integration is strongly affected by the forces acting on the satellites, various validation tests are performed for their accuracy assessment. The performance of the numerical methods is tested in the analysis of Keplerian orbits as well as in real dynamic orbit determination of GRACE and GOCE satellites by taking into account their sophisticated observation techniques and orbit design. Numerical investigation is performed in a wide range of the fundamental integrators’ parameters i.e. the integration step and the order of the multistep methods.

## Determination of geopotential value W 0 L at Polish tide gauges from GNSS data and geoid model

### Acta Geodaetica et Geophysica (2016-10-20): 1-8 , October 20, 2016

Results of three campaigns of Baltic Sea Level Project and further studies reveal the GPS and spirit levelling data possibly contain errors which affect SST and
$$ W_{0}^{L} $$
computations. For that reason, the old data were revised and additionally, in spring 2015, the new GNNS campaign was carried out at tide gauges in Swinoujscie, Ustka and Wladyslawowo. The study concerns computation of the local average geopotential value
$$ W_{0}^{L} $$
using water level data at the three tide gauges, geoid undulations from a global geopotential model EGM2008 and ellipsoidal heights from GNSS observations, which were obtained using revised data from three campaigns of Baltic Sea Level Project and from the new campaign conducted in 2015. Results obtained indicate that the best estimation of
$$ W_{0}^{L} $$
was achieved from the campaign carried out in 2015, where the mean value of
$$ W_{0}^{L} $$
calculated for three investigated tide gauge stations is equal to 62636857.45 m^{2} s^{−2}.