Mathematical Parameters Calculation of Double Exponential Function by a New Numerical Method

Background: Lightning electromagnetic pulse (LEMP) and high-altitude electromagnetic pulse (HEMP) are widely described by three physical parameters (rise time tr, full-width at half-maximum pulse width tw, and maximum electric field strength E0). These pulse shapes are often given by a double exponential form concerning four mathematical parameters, namely α, β, k and Ep. Objective: The transformation from physical parameters into mathematical parameters is necessary in waveform simulation and is traditionally accomplished by linear fit functions regarding the two groups of parameters. However, traditional methods commonly rely on data analysis and calculation. In order to obtain more concise and clear mathematical parameters. Methods: In this paper, a numerical method to calculate the mathematical parameters by solving nonlinear equations with three key constraints is proposed. Firstly, we establish the nonlinear system of equations regarding four variables, namely t1, t2, α and β. Then, three constraints are given to converge the solutions of the equations. Lastly, selecting the minimal value of the convergent solution of each equation. Results: Results: Comparing the solutions obtained by our proposed method to the iterated ones, the overall relative error is less than 2×10-8. Conclusion: The results show that our proposed method not only simplifies the transformation from physical parameters to mathematical parameters, but also keeps the solutions highly accurate.

ANALISA KEJADIAN GELOMBANG DENGAN METODE EMPIRIK DAN MODEL MATEMATIK DI KAWASAN PERAIRAN PELABUHAN TANJUNG LAUT

Tanjung Laut is water located in the administrative area of Bontang Regency, East Kalimantan. These waters are widely used for ship traffic to and from the Port. To find out the hydrodynamic conditions, especially waves that occur in the sea and propagate into these waters, it is necessary to analyze wave transformations to describe the conditions and impacts that occur due to wave propagation from the high seas that enter the port waters. The purpose of this study is to look at the shipping security channel. The method used in analyzing wind data from BMKG into wave data and modeling with cgwave mathematical models. Wave analysis is carried out with a cgwave model mathematical to determine the hydrodynamic conditions of the waves and to determine the shipping obstacles and to describe the plan waves that occur as one of the bases in determining the elevation of the pier and port breakwater structures. The results showed the conversion of wind speed and direction to be high, the period and direction of waves in the waters of Tanjung Laut in 2006-2016. The maximum significant wave height in the waters of Tanjung Laut occurred in 2007 was 3.91 meters with a period of 7.89 seconds. The results of statistical analysis using the wave recurrence method show that the wave height can occur or exceed for a 50 year return period is 4.80 meters to 5.54 meters, while the 10 year return period is 3.70 meters to 4.17 meters. The results of the waveform simulation with the cgwave are the wave height in the harbor pool ranging from 0.03 meters to 0.06 meters in the direction of waves from the Northeast, 0.03 meters to 0.07 meters in the direction of waves from the East, and 0.05 meters up to 0.09 meters in the direction of waves from the Southeast. Simulation results show that the conditions in the port pond are quite safe and calm against wave attacksTanjung laut merupakan pelabuhan perairan yang berada di wilayah administrasi Kabupaten Bontang Kalimantan Timur, dimana banyak digunakan untuk lalu lintas kapal yang menuju dan keluar dari Pelabuhan. Untuk mengetahui kondisi hidrodinamika khususnya gelombang yang terjadi di laut dan merambat ke perairan tersebut, perlu adanya analisa transformasi gelombang untuk menggambarkan kondisi dan dampak yang terjadi akibat perambatan gelombang dari laut lepas yang masuk ke kawasan perairan pelabuhan. Tujuan dari penelitian ini adalah untuk melihat keamanan alur pelayaran. Metode yang digunakan yaitu menganalisa data angin dari BMKG menjadi data gelombang dan pemodelan dengan model matematik cgwave. Analisa gelombang dilakukan dengan model matematik model cgwave untuk mengetahui kondisi hidrodinamika gelombang dan untuk mengetahui hambatan pelayaran serta untuk menggambarkan gelombang rencana yang terjadi sebagai salah satu dasar dalam penentuan elevasi dermaga dan bangunan pemecah gelombang pelabuhan. Hasil penelitian menunjukan konversi kecepatan dan arah angin menjadi tinggi, periode dan arah gelombang di perairan Tanjung laut Tahun 2006-2016. Tinggi gelombang signifikan maksimum di perairan Tanjung Laut terjadi pada tahun 2007 adalah 3,91 meter dengan periode 7,89 detik. Hasil analisa statistik menggunakan metode kala ulang kejadian gelombang, menunjukkan tinggi gelombang dapat terjadi atau terlampaui untuk kala ulang 50 tahun adalah 4,80 meter sampai dengan 5,54 meter, sedangkan kala ulang 10 tahun adalah 3,70 meter sampai dengan 4,17 meter. Hasil simulasi trasformasi dgelombang dengan model cgwave adalah tinggi gelombang di kolam pelabuhan berkisar antara 0,03 meter sampai dengan 0,06 meter dengan arah datang gelombang dari Timur Laut, 0,03 meter sampai dengan 0,07 meter dengan arah datang gelombang dari Timur, dan 0,05 meter sampai dengan 0,09 meter dengan arah datang gelombang dari Tenggara. Hasil simulasi menunjukkan kondisi di kolam pelabuhan cukup aman dan tenang terhadap serangan gelombang.

Characteristics of Conrad Discontinuity in the Northern Margin of Tibet Plateau Obtained from Regional Seismic Data

<p>Qaidam Basin, located in the northern margin of the Tibet Plateau, is the junction of several tectonic blocks. The blocks’ extrusion resulted in large faults and strong historical earthquakes. Previous studies have shown that the crustal structures of the eastern and the western Qaidam Basin are obviously different. In this study, the seismic reflection and refraction phases from Conrad and Moho discontinuity in Qaidam Basin are distinguished by waveform simulation and travel time fitting of 3 regional earthquakes on 32 stations. The results of travel time fitting and waveform simulation show that the first arrivals in the epicenter range of 90km ~ 260km are the P* phases from the Conrad discontinuity. The depth of Conrad discontinuity under the eastern basin is about 4 km shallower than that in the western basin, which can be attributed to different crust thickening models between the eastern and western basin. In addition, the focal depths of regional earthquakes occurred within recent 5 years in Qaidam region also shows the difference of the Conrad discontinuity. The Conrad discontinuity is considered to be the lower boundary of the low velocity layer in the upper crust. The upper crust thickening in the western basin led to the sinking of the layer, while the multiple thrusts resulted in the rise of the lower crust in the east. The two different effects could interpret the depth change of the Conrad discontinuity in the basin from the west to the east. </p>