Navegando por Assunto "Teoria do raio"

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Acesso aberto (Open Access)
3D raytracing through homogeneous anisotropic media with smooth interfaces
(2002-12) COSTA, Jessé Carvalho; SCHOENBERG, Michael; URBAN, Jaime Antonio
Two-point raytracing problem is solved for events in a piecewise homogeneous and laterally varying 3D anisotropic media by continuation techniques. In conjunction with the shooting method the algorithm can be used for computation of qP, qS1, and qS2 events. The algorithm has the same performance and robustness as previous implementations of the continuation method for tracing rays in isotropic models. Routines based on our algorithm have several useful applications. First, an efficient forward problem solver for traveltime inversion of elastic parameters in the presence of anisotropy. Second, Newton-Raphson iterations during two-point raytracing produce wavefront attributes, slowness and wavefront curvature. These attributes allows the computation of geometrical spreading and second order approximations for traveltimes. Therefore it can be used to investigate the effects of anisotropy on CRS, in simple velocity models.
Acesso aberto (Open Access)
Análise do efeito da discretização do modelo de velocidades nas migrações Kirchhoff e Kirchhoff-Gaussian- Beam 2D pré-empilhamento em profundidade
(Universidade Federal do Pará, 2014-02-28) PAIXÃO, Marcelo Tavares; CRUZ, João Carlos Ribeiro; http://lattes.cnpq.br/8498743497664023
The Gaussian Beam (GB) is an asymptotic solution of the elastodynamic equation in the paraxial vicinity of a central ray, which approaches better the wave field than the standard zero-order ray theory. The GB regularity in the description of the wave field, as well as its high accuracy in some singular regions of the propagation medium, provide a strong alternative to solve seismic modeling and imaging problems. In this dissertation , I present a new procedure for pre-stack depth migration with true-amplitude, combining the flexibility and robustness of Kirchhoff migration type using superposition of Gaussian beams to represent the wave field. The proposed migration algorithm comprises in two stacking process: the first is the beam stack applied to subsets of seismic data multiplied by a weight function defined such that stack operator has the same formulation of the integral of the Gaussian beams superposition; the second is a weighted diffraction stack by means of the Kirchhoff type integral having as input the stacked data. For these reasons it is called Kirchhoff-Gaussian-Beam (KGB) migration. In order to compare the Kirchhoff and KGB methods with respect to the sensibility on relation to the discretization length, we apply them to the well-know 2D Marmousi dataset using four velocity grids, i.e. 60 m, 80 m, 100 m e 150 m. As result we have that both methods present a much better image for smaller discretization interval of the velocity grid. The amplitude spectrum of the migrated sections provide us with the spatial frequency contents of the obtained image sections.
Acesso aberto (Open Access)
Imageamento homeomórfico de refletores sísmicos
(Universidade Federal do Pará, 1994-10-06) CRUZ, João Carlos Ribeiro; HUBRAL, Peter; http://lattes.cnpq.br/7703430139551941
This thesis presents a new technique for seismic stacking called homeomorphic imaging, which is applicable to the imaging of seismic reflectors in a bidimensional, inhomogeneous and isotropic medium. This new technique is based on ray geometrical approximation and topological properties of reflection surfaces. For this purpose the concepts of wavefront, incidence angle, radius and caustic of wavefront and ray trajetory are used. Considering a circle as the geometrical approximation of the wavefront in propagation, it is possible to define diferent homeomorphic imaging methods, depending on processing configuration. In this way, the following methods are possible: 1) Common Source (Receiver) Element (CS(R)E), which relate to a set of seismograms with a single source (receiver) and a real reflected wavefront is considered; 2) Common-Reflecting-Element (CRE), which relate to a set of seismograms with a single reflection point and a wavefront hipotetically generated in the same reflection point is considered; 3) Common Evolute Element (CEE), which relate to a set of seismograms with each pair of source and geophone located in the same point on the seismic line and a wavefront hipothetically generated in the curvature center of the reflector is considered. In the first method is obtained a stacked seismic section using arbitrary central rays. In the last two methods the result is a zero-offset seismic section. These methods give also other two sections called radiusgram and anglegram, the latter being emergence angles and the former radii of wavefront in the moment that it reaches the observational surface. The seismic stacking is made using a local correction-time applied to the travel time of a ray that leaves the source, and after reflection, is registered as a primary reflection at a geophone, in relation to the reference time which is the travel time of the central ray. The formula used for the temporal correction depends on the radius, the emergence angle of the wavefront and the velocity which is considered constant near the seismic line. It is possible to show that in this new technique the registered signal is not submitted to stretch effects as a consequence of the temporal correction, furthermore there is no problem with reflector point dispersal as a consequence of dip reflectors, in contrast with the techniques that are based on NMO/DMO. In addition, considering that no a prori knowledge of a macromodel is necessary but the velocity near the seismic line, the homeomorphic imaging can be applied to inhomogeneous models without losing the strictness of the formulation.
Acesso aberto (Open Access)
Migração (2,5-D) com amplitudes verdadeiras em meios com gradiente constante de velocidade
(2002-04) CASTILLO, Luis Antonio Lopes; CRUZ, João Carlos Ribeiro; CALLAPINO, German Garabito; URBAN, Jaime Antonio
The true-amplitude seismic migration, in time or depth, provides a measurement of the reflection coefficients of primary reflection events. These are constituted by P-P reflection of longitudinal waves at smooth reflectors. One of the mostly used method is the Kirchhoff migration, by which the seismic image is obtained by stacking the seismic wavefield using a diffraction surface, also called Huygens Surface. In order to obtain true amplitude migration, i.e. the removal of geometrical spreading, it is introduced a weight function in the migration operator. The weight function is determined by the asymptotic solution of the migration integral at stationary points. The ray tracing is a fundamental tool for determining the weight function and the traveltime, that increases the computational costs of the migration process in heterogeneous media. In this work it is presented a true-amplitude migration algorithm tailored for two-and-one-half dimensional model, i.e. when the velocity field varies only with two coordinates of the three dimensional Cartesian system. It is emphasized the special case of constant gradient velocity. As a second topic, this work concerns about recovering seismic attributes from pre-stack seismic data by applying the double diffraction stack inversion. The estimated parameter is the incidence angle at the reflector. Combining the estimated reflection coefficient and the incidence angle, it is possible to perform the so-called Amplitude versus Angle Analysis (AVA) on the interested reflector.
Acesso aberto (Open Access)
Migração 3D no tempo usando a teoria dos raios paraxiais
(Universidade Federal do Pará, 1998-09) QUEIROZ, Norcirio Pantoja; SÖLLNER, Walter Franz
This presentation aims at the 3-D time migration of zero offset data, in true amplitude. This method is based on paraxial ray theory and uses a diffraction time function which is directly and correctly determined by the measurement of pre-stack seismic data. It is not necessary to know a macro velocity model in order to apply the time migration. In order to obtain a true amplitude time migration the migration result must be multiplied by a scaling factor and convolved with a known function. Together with a scaling factor, a filter was applied in order to recover the signal phase altered during the migration process. Due to the computational limitation synthetic dada in 2-D was used aims to test the program efficiency. The result was satisfactory, showing the efficiency and robustness of process.
Acesso aberto (Open Access)
Migração com amplitude verdadeira em meios bidimensionais (2-D) e introdução ao caso 2,5-D
(Universidade Federal do Pará, 1999) URBAN, Jaime Antonio; CRUZ, João Carlos Ribeiro; http://lattes.cnpq.br/8498743497664023
In the recent past years we have seen through various published papers an increasing interest in true amplitude migration methods, in order to obtain more informations about the reflectivity properties of the earth subsurface. The most part of these works has treated of this thema either based on Born approximation as given by Beistein (1987) and Bleistein et al. (1987), or on ray theoretical wavefield approximation as given by Hubral et al. (1991), Schleicher et al. (1993) and Martins et al. (1997). By considering arbitrary source-receiver configurations the compressional primary reflections can be imaged into time or depth-migrated reflections so that the migrated wavefield amplitudes are a measure of angle-dependent reflection coeffients. In order to do this various migration algorithms were proposed in the recent past years based on Born or Kirchhoff approach. Both of them treats of a weighted diffraction stack integral operator that is applied to the input seismic data. As result we have a migrated seismic section where at each reflector point there is the source wavelet with the amplitude proportinal to the reflection coefficient at that point. Based on Kirchhoff approach, in this thesis we derive the weight function and the diffraction stack integral operator for the two dimensional (2-D) and for the two and one half (2.5-D) seismic model and apply it to a set of synthetic seismic data in noise environment. The result shows the accuracy and stability of the 2-D and 2.5-D migration methods as a tool for obtaining important information about the reflectivity properties of the earth subsurface, which is of great interest for the amplitude versus offset (angle) analysis. In summary, we present an expressions for the 2-D and 2.5-D weights as a function of parameters along each ray branch of the in-plane trajectory. Moreover, we show examples of application of the true-amplitude depth migration algorithm to synthetic seismic data obtained by ray theory seismic modeling using the Seis88 package (Cervený e Psencík, 1988), in order to make a numerical analysis and to verify the stability and accuracy of the algorithm. The results confirmed the removal of the geometrical spreading from migrated data, even in presence of noise. Additional tests were performed for pulse distortion analysis in depth rnigrated sections (Tygel et al., 1994) and to obtain reflection points attributes by multiple diffraction stack (Tygel et al., 1993).
Acesso aberto (Open Access)
Migração com amplitude verdadeira em meios com gradiente constante de velocidade
(Universidade Federal do Pará, 2000-05-16) CASTILLO LOPEZ, Luis Antonio; CRUZ, João Carlos Ribeiro; http://lattes.cnpq.br/8498743497664023
One of the most important steps in seismic processing data concerns to migration the seismic reflector. In the last years, we have seen several approaches used to build the migrated section and, simultaneously, to recover reflection coefficient values corrected for geometrical spreading loss, the so-called amplitude preserve migration or true-amplitude migration methods. This work aims at applying a true-amplitude depth migration algorithm in acoustic inhomogeneous media, with a constant gradient velocity function and considering a 2.5-D situation. The 2.5-D migration process is based on the Kirchhoff integral operator and the ray theory. It is performed essencially by a weighted diffraction stacking, with the diffraction traveltime curve given by the ray tracing equations tailored to constant gradient velocity. By choosing appropriate weight function used to stack the data, the result of the migration process is a measure of the reflection coefficient at the searched-for reflection point, that is function of the incidence angle. This is very usefull in other important process as amplitude-versus-offset (AVO) and amplitude-versus-angle (AVA) analysis. As any other depth migration process, it is necessary an accurated macro-velocity model, what means to know the velocity gradient. The algorithm was applied to synthetic seismic data generated by the ray software SEIS88 for two kinds of geophysical models. The results pointed out the precision and stability of the presented 2.5-D migration algorithm. It is available for recovering reflection coefficient measures and gives informations about lithological properties of the seismic reflectors. It is also important to note that this algorithm is not able to migrate in singular ray situations, as for example caustics or diffraction zones.