Funda AKLEMAN, Ercan TOPUZ, Levent SEVGİ

Yer dalgası yayılımının zaman ve frekans domeninde sayısal modellemesi

Dünya üzerinde seçilen herhangi iki nokta arasındaki yer dalgası yayılım problemi, yirminci yüzyılın başından bu yana ilgi odağı olmasına karşın, henüz sayısal olarak hesaplanabilen analitik tam çözüm ya da genel olarak uygulanabilecek üç boyutlu sayısal çözüm bulunamamıştır. Bu çalışmada, problemin çözümü için kullanılmakta olan ışın -mod çözümü gibi yaklaşık analitik ve Fourier dönüşümü yardımı ile parabolik denklem çözümüne dayanan yarı analitik -sayısal teknikler geçerlilik bölgeleri ile birlikte ayrıntılı olarak incelenmiştir. Daha sonra, yer dalgası yayılım probleminin çözümü için zamanda sonlu farklar tekniğine dayanan, saf sayısal yeni bir yöntem önerilmiş ve bahsedilen diğer teknikler ile elde edilen sonuçlarla karşılaştırılmıştır.

Time and frequency domain numerical modelling of ground wave propagation

Ground wave propagation problem has been a subject of interest from the beginning of the 20 th century. The model environment used in this study is a spherical earth, which may have various ground characteristics above which exists a radially inhomogeneous atmosphere. Using this canonical model we pose ourselves the following problem: Determine the ground wave propagation characteristics between two points, which may be selected anywhere on or above the ground. The problem is very complex and neither a full-wave numerically computable analytical solution, nor a three-dimensional (3D), generally applicable numerical solution has yet appeared. Therefore analytical approximate solutions or two-dimensional (2D) numerical approaches have so far been used. Here, first we consider ray - mode solutions and Split Step Parabolic Equation (SSPE) method, and then introduce a novel pure numerical method, which is based on the Finite-Difference Time Domain (FDTD) technique and applicable for a broad range of propagation problems. Since the propagation region is always larger than the available FDTD space, the propagating pulse is traced within a sliding window and this method is named as Time-Domain Wave-Propagator (TDWP). The results obtained via TDWP are compared with the data obtained via ray - mode solutions and/or SSPE technique within their domains of validity and good agreement is observed.

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