Geodesy
Seyyed Reza Ghaffari-Razin; Navid Hooshangi
Abstract
Extended Abstract
Introduction
In geodesy, three levels are considered: the physical surface of the earth on which mapping measurements are made, the ellipsoidal reference surface (geometric datum) which is the basis of mathematical calculations, the geoid physical surface (physical datum) which is ...
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Extended Abstract
Introduction
In geodesy, three levels are considered: the physical surface of the earth on which mapping measurements are made, the ellipsoidal reference surface (geometric datum) which is the basis of mathematical calculations, the geoid physical surface (physical datum) which is the basis for measuring heights. Satellite positioning systems measure the height of points relative to the ellipsoid surface. The geoid is one of the equipotential surfaces of the earth's gravity field, which approximates the mean sea level (MSL) by least squares. Geoid is very important in geodesy as a representative of the physical space or the space of observations made on the earth and also as the base level of elevations. The separation between the geoid and the geocentric reference ellipse is called geoid height (N). Although there is only one equipotential surface called geoid, various methods are used to determine it. These methods include: geometric method, geoid determination by satellite method, Gravimetric methods and geoid determination using GPS/leveling.
Materials and Methods
In this paper, the aim is to estimate the height of the local geoid using machine learning models. To do this, artificial neural network (ANN), adaptive neuro-fuzzy inference model (ANFIS), support vector regression (SVR) and general regression neural network (GRNN) models are used. The geodetic coordinates of 26 GPS stations in the north-west of Iran along with their orthometric height (H0) and normal height (h) were obtained from the national cartographic center of Iran. In all stations, the difference of orthometric height and normal height is considered as geoid height (N). Therefore, the geodetic longitude and latitude of the GPS stations are considered as the input of the machine learning models, and the corresponding geoid height was considered as the output. In order to test the results of machine learning models, two modes of 4 and 7 test stations are considered. Also, the output of the models is compared with the local geoid model IRG2016 presented by Saadat et al. for the Iranian region and also the global geoid model EGM2008.
Results and Discussion
Due to the availability of a complete set of observations of GPS stations along with orthometric height obtained from leveling in the north-west region of Iran, the study and evaluation of the models proposed in the paper has been carried out in this region. Observations of 26 GPS stations of North-west of Iran were prepared from the national cartographic center (https://www.ncc.gov.ir/). Two modes are considered for training and testing of ANN, ANFIS, SVR and GRNN models. In the first case, the number of training stations is 22 and the number of test stations is 4. But in the second case, by increasing the number of test stations to 7 stations, the error evaluation of the models has been done. It should be noted that the distribution of training and test stations is completely random.
After the training step of machine learning models and choosing the optimal structure, the test step is performed in two different modes (4 and 7 stations). At this step, the value of the geoid height in the test stations is estimated and compared with the value obtained from the difference of orthometric height and normal height as a basis. Two statistical indices of relative error in percentage and RMSE in centimeters were calculated for all models and presented in Table (1) for the first case.
Table 1. Relative error (%) of ANN, ANFIS, SVR, GRNN and IRG2016 models in the test stations considered for the first case
According to the results of Table (1) and comparing the relative error values of all models in the test stations, it shows that the ANFIS model was more accurate than other models. After ANFIS model, IRG2016 model has higher accuracy than ANN, SVR and GRNN models. It should be noted that the IRG2016 local model uses the observations of all Iranian plateau stations to model the local geoid, and therefore it is expected that this model will be more accurate in the study area than other models.
Conclusion
The evaluations show that in the case of 22 training stations and 4 test stations, the RMSE of ANN, ANFIS, SVR, GRNN and IRG2016 models in the test step are 37.32, 19.83, 49.34, 53.82 and 29.65 cm, respectively. However, in the case of 19 training stations and 7 test stations, the error values of the models are 36.63, 58.31, 39.64, 41.29 and 24.68 cm, respectively. Comparison of RMSE shows that ANN model with less number of training stations provides higher accuracy than ANFIS, SVR and GRNN models. The results of this paper show that by using ANN and ANFIS models, geoid height can be estimated and used with high accuracy locally in civil and surveying applications.
Geodesy
Seyyed Reza Ghaffari-Razin; Navid Hooshangi; Behzad Voosoghi
Abstract
Extended AbstractIntroduction The ionosphere extends from an altitude of 80 to more than 1000 km above the earth. Due to its electrical properties, this layer of the atmosphere has very important and fundamental effects on the electromagnetic waves passing through it. A parameter that can be used to ...
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Extended AbstractIntroduction The ionosphere extends from an altitude of 80 to more than 1000 km above the earth. Due to its electrical properties, this layer of the atmosphere has very important and fundamental effects on the electromagnetic waves passing through it. A parameter that can be used to study the ionosphere is the total electron content (TEC). This parameter is the sum of free electrons in a cylinder with a cross section of one square meter between the satellite and the receiver on the ground. The unit of TEC is electron per square meter (ele/m2). The TEC in the vertical direction is called VTEC. Usually, TEC is expressed in terms of TECU, which is equal to 1016 ele/m2.Different methods have been developed to model the TEC. The simplest and most practical method is to use observations of two-frequency receivers. If there is a proper station distribution, it is possible to obtain accurate TEC and model the ionosphere. The main innovation of this paper is in the long-term prediction of TEC in the period of severe solar activity, as well as the modeling of the ionosphere time series with the long-short term memory (LSTM) neural network model in the Iranian region. This model is used for the first time in Iran to model and predict the time series of the ionosphere. To check the capability of the new model in prediction of TEC in the conditions of severe solar activity, observations from 2007 to 2016 are used for training and the TEC in 2017 is predicted. All the observations are related to the Tehran GPS station, which is one of the stations of the IGS network. To evaluate the accuracy of the model presented in this paper, statistical indicators of relative error, correlation coefficient and root mean square error (RMSE) are used. Materials and MethodsLong-short term memory modelLong short-term memory (LSTM) neural network is a special type of recurrent neural network (RNN). RNN is a type of neural network that has internal memory; in other words, this network is a normal neural network that has a loop in its structure through which the output of the previous step, along with the new input, is entered into the network at each step. This loop helps the network to have the previous information along with the new information and can calculate the desired output based on this information’s. One of the problems of RNNs is the vanishing of the gradient when learning from long-term sequences, which reduces the ability to learn in the algorithm. LSTM networks are actually a type of RNNs that have had a change in their block (RNN Unit). This change makes LSTM recurrent neural networks able to manage long-term memory and not have the problem of gradient vanishing. Results and DiscussionAfter the training step, using the trained models, the VTEC value for 2017 has been estimated and compared with the VTEC values obtained from GPS as a reference observation, GIM and NeQuick models. For the test step, the parameters of correlation coefficient, RMSE and relative error were calculated and presented in table (1). It should be noted that the average of all days of 2017 is showed in this table. Also, VTEC values obtained from GPS are considered as reference observations in this table.Table 1. Statistical values of correlation coefficient, RMSE and relative error in the test step of 2017 for GRNN, LSTM, GIM and NeQuick models.The correlation coefficient value of LSTM model is higher than other models. Also, the values of RMSE and relative error of LSTM model are lower than other models. This model has the ability to show the ionosphere time series variations with an accuracy of about 87%. ConclusionAnalysis of the results of the correlation coefficient in 2017 for LSTM, GRNN, NeQuick and GIM models compared to the GPS-TEC was obtained as 0.84, 0.72, 0.77 and 0.71, respectively. The average annual relative error for these four models was calculated as 16.98%, 25.69%, 29.89% and 51.05% respectively. The results of the analysis showed that in the conditions of severe and quiet solar and geomagnetic activities, the accuracy and precision of the LSTM model is higher than the other models evaluated in this paper. The analysis of the coordinate components of Tehran station with PPP method showed that by using the model proposed in this paper, an improvement of about 5.19 to 56.23 mm can be seen in the coordinates of the station compared to other models.
Geodesy
Lida Koshki; Behzad Voosoghi; Seyyed Reza Ghaffari-Razin
Abstract
Extended Abstract IntroductionEarthquake every year in the world, especially in a seismic country like Iran, causes huge human and financial losses. Earthquake prediction has become one of the great challenges of scientists in recent decades. One of the new methods is the evaluation of anomalies ...
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Extended Abstract IntroductionEarthquake every year in the world, especially in a seismic country like Iran, causes huge human and financial losses. Earthquake prediction has become one of the great challenges of scientists in recent decades. One of the new methods is the evaluation of anomalies in the ionospheric parameters before the earthquake. The parameter investigated in this method is the total electron content (TEC). The study areas in this paper are the Ahar-Varzaghan earthquake with a magnitude of 6.5 and 6.3, the Sarpol Zahab earthquake with a magnitude of 6.3. In the Ahar-Varzaghan earthquake, the observations of 6 GPS stations and in the Sarpol Zahab earthquake, the observations of 5 GPS stations of the IGS network were used to calculate the ionosphere TEC. Short time Fourier transform (STFT) along with statistical parameters of mean and standard deviation have been used to detect of ionosphere time series anomalies. Also, geomagnetic and weather indicators KP, Dst, F10.7, Vsw (plasma velocity), Ey (magnetic field) and IMFBz (interplanetary magnetic field) have been investigated and analyzed to know the conditions of the days before the earthquake.Materials & Methods In recent years, the spectral analysis of ionospheric anomalies using the STFT method and its application in earthquake forecasting has become popular. The research results show that spectral methods can be a useful and reliable tool in further analysis, and the STFT method can be evaluated as a successful method for detecting ionosphere anomalies, which is also compatible with classical methods. Also, STFT is a powerful tool for processing a time series without the need for average and median values, so it can be used for other studies such as navigation, geophysics, geology and climatology. STFT is used as a modified version of the classical Fourier transform to obtain the frequency information of a signal in the time domain. This method provides the analysis of a small part of the signal at a certain time through windowing the signal. In STFT, the signal with a constant time-frequency resolution and with the same window length in all frequencies is divided into smaller parts, Fourier transform is applied on it and finally the output will be presented in two time-frequency dimensions. As a result, it is possible to obtain information about when and with what frequency each signal occurred.Results & Discussion In the Sarpol Zahab earthquake and in both classic and STFT methods, anomalies were observed on 309, 314 and 323 DOY, before the earthquake. The amount of these anomalies in the ionosphere time series was in the 0.058 to 5.44 TECU. The parameters related to solar and geomagnetic activities were also investigated in the days before and after the earthquake. Considering that the solar and geomagnetic activities (as an important factor in creating anomalies in the ionosphere time series) were calm in the days before the earthquake, these detected anomalies can be attributed to the earthquake. However, in the Ahar-Varzaghan earthquake and using both methods, in 5 to 15 days before the earthquake, anomalies of about 0.13 to 1.4 TECU were observed. In the days before the Ahar-Varzaghan earthquake, there were almost undisturbed conditions on most days, and therefore it cannot be said with certainty that the observed anomalies are completely related to the earthquake. The results of this paper showed that the STFT method is a powerful tool for spectral analysis without the need for values such as average or median. This feature of STFT is its strength compared to classical methods; because independence from these values minimizes the sources of error related to them (abnormalities, sudden variations in the ionosphere such as annual, semi-annual and seasonal variations). It is important to mention that the STFT method is more accurate in calm solar and geomagnetic conditions and provides high accuracy results.ConclusionThe results show that for the Ahar-Varzaghan earthquake, there are anomalies on the 11, 12, 13 and 5 days before the earthquake. But for the Sarpol Zahab earthquake, anomalies can be seen 6, 7, 13 and 21 days before the earthquake. The analyzes of this paper show that if all the geomagnetic and weather parameters before the earthquake are investigated, the existing anomalies can be directly observed by analyzing the time series of the ionosphere with the STFT method. It is important that on days when geomagnetic conditions and calm weather are not prevailing, the occurrence of earthquake cannot be considered as the cause of anomalies detected in the ionosphere time series.
