Yüzeye Yakın Saçıcıların Saçılmış Yüzey Dalgaları İle Görüntülenmesi

Abstract

Bu çalışmada saçılmış yüzey dalgaları yardımı ile yüzeye yakın saçıcıların görüntülenmesi amaçlanmıştır. Bu amaç için geliştirilmiş bir yöntem ve program kullanılmıştır. Yöntemde yatay tabakalı ortamda 3 boyutlu elasto-dinamik dalga yayılmı dikkate alınmıştır. Saçıcı ortama gömülerek modellenmektedir. Yöntemde Born yaklaşımı dikkate alınmakta ve saçılmış dalga alanı domen tipi integral yardımı ile ifade edilmektedir. Yöntemde saçılmış dalga alanı hesaplanırken sadece yoğunluk kontrastı dikkate alınmaktadır. Dalga yayılımı saçılma matrisi yöntemi ile modellenmektedir. Yatay tabakalı ortam varsayımı nedeniyle ortamın fiziksel özellikleri sadece düşey yönde değiştiğinden radyal simetriden yararlanılmakta ve integral ifadesinde yer alan Green tensörü elemanlarının hesaplama süresi etkin hale getirilmektedir. Yüzeye yakın saçıcıların belirlenmesi amacıyla Born yaklaşımının geçerli olduğu ve olmadığı iki koşulda farklı saçıcı boyutları ve derinlikleri dikkate alınarak kestirilen yoğunluk kontrast değerlerinin değişimi incelenmiştir. Derinliğin artmasi ile kestirilen yoğunluk kontrastı değerlerinin gerçek değerden uzaklaştığı ve hata oranının arttığı belirlenmiştir. Bunun nedeni ise yüzey dalgaları genliğinin derinlikle azalmasından kaynaklanmaktadır. Ancak her koşulda saçıcının konumu doğru bir şekilde belirlenebilmektedir. Sayısal olarak oluşturulan saçılmış dalga alanları, sinyal bandının tanımlı olduğu düşük, orta ve yüksek frekans bandlarında süzgeçlenerek ters çözümü yapılmıştır. Orta (baskın) frekans bandının yoğunluk kontrastı kestiriminde daha başarılı sonuç verdiği belirlenmiştir. Yapılan çalışmada dikkate alınan koşullar altında yüzey dalgaları yardımıyla saçıcının konumunun belirlenebildiğini gösterilmiştir. Gerçek yoğunluk kontrastı değeri ise koşula bağlı olarak belli hata oranları ile elde edilebilmiştir.

Surface waves are widely used for determining properties of the subsurface on different scales. In most applications, the dispersion of surface waves is analysed to yield depth-dependent velocity profiles. However, the heterogeneity of the shallow subsurface complicates such as analysis because of the scattering it causes. The estimation of the shear-wave velocity from the surface waves become a popular tool and different techniques are applied for this purpose. In civil and environmental engineering the detection of cavities is of great interest and surface waves are convenient for this purpose (Leparoux et al, 2000). Imaging shallow layers by body waves requires high resolution data acquired in a dense spatial array. Surface waves do not require the same dense sampling, since their wavelengths are longer when compared to body waves. Therefore, surface waves are more economic for this purpose. Surface waves are widely used in global, exploration and near-surface geophysics. Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. The types of non-uniformities which can cause scattering, sometimes known as scatterers or scattering centers, are too numerous to list, but a small sample includes particles, bubbles, droplets, density fluctuations in fluids, crystallites in polycrystalline solids, defects in monocrystalline solids, surface roughness, cells in organisms, and textile fibers in clothing. The effects of such features on the path of almost any type of propagating wave or moving particle can be described in the framework of scattering theory. The complex structure of the near subsurface causes scattered surface waves. Scattered surface waves are sensitive to near-surface heterogeneities and they can be used for imaging cavities, buried objects or shallow water reservoirs. A general theory of elastodynamic wave scattering is given by Snieder (2002a, b). The scattered waves often have high amplitudes and mask the reflections from deeper parts of the Earth. In some cases the information on the target reflectors is important, like in hydrocarbon exploration; therefore the elimination of the scattered surface waves becomes an important task. There are many circumstances that necessitate nondestructive detection and characterization of underground cavities. For example, it may be required to locate a utility conduit before an excavation or to examine the presence of subsiding sinkholes to prevent pavement collapse. A number of different physical and geophysical techniques are being tested and used for cavity detection, such as ground penetrating radar (GPR), gravity gradiometer, magnetic and electromagnetic induction, seismic methods, and imagery analysis. Each of these methods has shown limited success in certain circumstances, but none of them has been unconditionally successful. By using the scattered surface waves Snieder (1987), Herman et al (2000) detect near surface objects. By considering a scalar approximation, Campman et al (2005) estimate the lateral variations and relative contrast of the heterogeneities from scattered surface waves. Riyanti and Herman (2005) consider 3D elastodynamic problem and include the effect of multiple scattering for near-surface imaging. In this thesis, the propagation and scattering of elastic waves in an isotropic, laterally homogenous embedding is considered in which bounded objects with contrasting density are present. By using the linearity principle, the wavefield is expressed as the sum of an incident wavefield accounting for propagation in the embedding, and the scattered wavefield, accounting for the presence of the scatterer: . Considering a vertical point force, the incident wave field can be expressed as , where is the source waveform and is the Green’s tensor. The Green’s tensor elements are calculated in an efficient way by considering radial symmetryy of the medium. In this thesis, an inverse scattering method is used to determine the size, the location and properties of the heterogeneity. In the physics field of scattering theory, the inverse scattering problem is that of determining characteristics of an object (its shape, internal constitution, etc.) based on data of how it scatters incoming radiation or particles. In this study, it is aimed to observe the change of density contrast values for the different size of scatterers at the several depths with weak and strong density contrast. The purpose of this thesis is to estimate the size, the location and the density contrast of the heterogeneity by using scattered surface waves. In this study an efficient method developed by Kaslilar and Herman (2006) and Kaslilar (2007) is used for imaging the near surface heterogeneities in a half-space at different depths and sizes. For this reason, several models are considered: Imaging scatterers for several depths (〖0.00〗_d, 〖0.25〗_d, 〖0.50〗_d, 〖1.00〗_d), different sizes of scatterers (〖0.25〗_d, 〖0.50〗_d, 〖1.00〗_d), different density contrasts (density contrast that satisfies the Born Approximation and not) and different frequency bands (low, middle and high bands). First of all, forward problem has been solved. For this aim, different models are considered and by using these models’ parameters, scattered wavefield is calculated. By using the calculated scattered wavefields, inverse problem has been solved. In here, inverse problem can be defined as estimating the size, the location and the density contrast value of scatterers. In all of models, the location and the size of the scatterers were observed; also the density contrast values were calculated. For the models with the scatterers on surface, density contrast values were measured with a high accuracy. On the other hand, when the scatterers located at any depths, the density contrast values are estimated with a low accuracy. But, it is possible to observe that in all conditions the locations of scatterers are well-estimated. It is possible to say that, the scatterer with the size of 〖0.50〗_d gives the best result and the calculated density contrast value is the closer the real denstiy contrast value. Another research in this project is to determine the results for specific frequency bands. In aiming of categorizing these bands, there have been applied Butterworth filter to full-band scattered wavefield which came with the result of three frequency bands: low, mid and high. At the end, the best results on the inversed scattered wavefield have been observed at mid (dominant) frequency band. It is seen that, in all cases considered, the density contrast value is estimated with less accuracy as the depth of the scatterer increases. However in all cases the location of the scatterer is reasonably well estimated.