Fernanda Vieira Araujo

Bio: Fernanda Vieira Araujo is an academic researcher from Federal University of Bahia. The author has contributed to research in topics: Inverse scattering problem & Attenuation. The author has an hindex of 3, co-authored 6 publications receiving 447 citations.

Inverse scattering series and seismic exploration

Abstract: This paper presents an overview and a detailed description of the key logic steps and mathematical-physics framework behind the development of practical algorithms for seismic exploration derived from the inverse scattering series. There are both significant symmetries and critical subtle differences between the forward scattering series construction and the inverse scattering series processing of seismic events. These similarities and differences help explain the efficiency and effectiveness of different inversion objectives. The inverse series performs all of the tasks associated with inversion using the entire wavefield recorded on the measurement surface as input. However, certain terms in the series act as though only one specific task, and no other task, existed. When isolated, these terms constitute a task-specific subseries. We present both the rationale for seeking and methods of identifying uncoupled task-specific subseries that accomplish: (1) free-surface multiple removal; (2) internal multiple attenuation; (3) imaging primaries at depth; and (4) inverting for earth material properties. A combination of forward series analogues and physical intuition is employed to locate those subseries. We show that the sum of the four task-specific subseries does not correspond to the original inverse series since terms with coupled tasks are never considered or computed. Isolated tasks are accomplished sequentially and, after each is achieved, the problem is restarted as though that isolated task had never existed. This strategy avoids choosing portions of the series, at any stage, that correspond to a combination of tasks, i.e., no terms corresponding to coupled tasks are ever computed. This inversion in stages provides a tremendous practical advantage. The achievement of a task is a form of useful information exploited in the redefined and restarted problem; and the latter represents a critically important step in the logic and overall strategy. The individual subseries are analysed and their strengths, limitations and prerequisites exemplified with analytic, numerical and field data examples.

Inverse Scattering Series For Multiple Attenuation: An Example With Surface And Internal Multiples

Abstract: A multiple attenuation method derived from an inverse scattering series is described. The inversion series approach allows a separation of multiple attenuation subseries from the full series. The surface multiple attenuation subseries was described and illustrated in Carvalho et al. (1991, 1992). The internal multiple attenuation method consists of selecting the parts of the odd terms that are associated with removing only multiply reflected energy. The method, for both types of multiples, is multidimensional and does not rely on periodicity or differential moveout, nor does it require a model of the reflectors generating the multiples. An example with internal and surface multiples will be presented.

Multifrequency backscattering tomography for constant and vertically varying backgrounds

Abstract: To improve the resolution and image quality of the SFDT (Sigle-Frequency Diffraction Tomography), a special fast multi-frequency imaging method: Multi-Frequency Backscattering Tomography (MFBT) is introduced in this paper. The method uses only the backscattered waves (after plane wave decomposition) while maintaining the merit of multi-frequency method. The method is formulated for both the constant and vertically varying backgrounds. For the latter case the WKBJ approximation is used for the background Green's function. Formulas are derived both for volume scattering using the Born approximation and for boundary scattering using the physical optics approximation. Two reconstruction methods are presented. The backpropagation method can be used and has the same computation speed for both the constant and vertically varying backgrounds. Meanwhile the direct FT method is only formulated for the constant background, in which the backpropagation in z-direction is implemented by FFT and therefore the computation speed is significantly increased. Compared with the SFDT using backpropagation reconstruction, the MFBT is nearly Nz/log2Nz faster, where Nz is the number of grid points in z-direction, and at the same time has a much better resolution and image quality. When Nz is big, the time saving is remarkable. Compared with other multi-frequency methods such as the multi-frequency holography (prestack migration), the speeding factor becomes NfNz/log2Nz, where Nf, is the number of frequencies used. Numerical simulations for both constant and vertically varying backgrounds are performed to demonstrate the feasibility of the method and the quality of reconstructed images for different situations. Examples are also given to show that when the reconstruction procedure of constant background is applied to the case of vertically varying background, the image quality will be greatly deteriorated.©1994 John Wiley & Sons Inc

Internal multiple attenuation

Abstract: In this paper we present a multidimensional method for attenuating internat multiples that derives from an inverse scattering series. The method doesn't depend on periodicity or differential moveout, nor does it require a model for the multiple generating reflectors.

Multifrequency Backscattering Tomography: Principles And Reconstruction Methods

Abstract: Single-frequency diffraction tomography, though is well known in the literature, has its inherent problems, such as the limited resolution and image distortion due to the existence of “blind areas” of the object spectrum. The introduction of multi-frequency methods can improve the resolution and partly fill out the “blind areas” of the spectrum. The existing multi-frequency methods, such as the multi-frequency holography (prestack migration) or the wide band Born inversion, are time consuming procedures. The Multi-Frequency Backscattering Tomography (MFBT) is a fast method which uses only the backscattered waves (after plane wave decomposition) but meanwhile maintains the merit of multifrequency methods. Two reconstruction methods are presented: the backpropagation method and the direct Fourier transform method. In the latter method, the backpropagation of plane waves in the z-direction is implememted by FFT through a change of variable, this increases significantly the computation speed. Compared with the single-frequency diffraction tomography, the MFBT has a better resolution and image quality, and its reconstruction speed is faster by a factor N,/IogzN,, where N, is the number of grid points in z-direction. When N, is large, the time saving of MFBT is remarkable.

An inverse-scattering series method for attenuating multiples in seismic reflection data

Abstract: We present a multidimensional multiple‐attenuation method that does not require any subsurface information for either surface or internal multiples. To derive these algorithms, we start with a scattering theory description of seismic data. We then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering. These include (1) the idea that the inversion process can be viewed as a series of steps, each with a specific task; (2) the realization that the inverse‐scattering series provides an opportunity for separating out subseries with specific and useful tasks; (3) the recognition that these task‐specific subseries can have different (and more favorable) data requirements, convergence, and stability conditions than does the original complete inverse series; and, most importantly, (4) the development of the first method for physically interpreting the contribution that individual terms (and pieces of terms) in the inv...

Inverse problems in elasticity

Abstract: This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.

Inverse scattering series and seismic exploration

Abstract: This paper presents an overview and a detailed description of the key logic steps and mathematical-physics framework behind the development of practical algorithms for seismic exploration derived from the inverse scattering series. There are both significant symmetries and critical subtle differences between the forward scattering series construction and the inverse scattering series processing of seismic events. These similarities and differences help explain the efficiency and effectiveness of different inversion objectives. The inverse series performs all of the tasks associated with inversion using the entire wavefield recorded on the measurement surface as input. However, certain terms in the series act as though only one specific task, and no other task, existed. When isolated, these terms constitute a task-specific subseries. We present both the rationale for seeking and methods of identifying uncoupled task-specific subseries that accomplish: (1) free-surface multiple removal; (2) internal multiple attenuation; (3) imaging primaries at depth; and (4) inverting for earth material properties. A combination of forward series analogues and physical intuition is employed to locate those subseries. We show that the sum of the four task-specific subseries does not correspond to the original inverse series since terms with coupled tasks are never considered or computed. Isolated tasks are accomplished sequentially and, after each is achieved, the problem is restarted as though that isolated task had never existed. This strategy avoids choosing portions of the series, at any stage, that correspond to a combination of tasks, i.e., no terms corresponding to coupled tasks are ever computed. This inversion in stages provides a tremendous practical advantage. The achievement of a task is a form of useful information exploited in the redefined and restarted problem; and the latter represents a critically important step in the logic and overall strategy. The individual subseries are analysed and their strengths, limitations and prerequisites exemplified with analytic, numerical and field data examples.

Interferometry by deconvolution: Part 1 — Theory for acoustic waves and numerical examples

Abstract: Interferometry allows for synthesis of data recorded at any two receivers into waves that propagate between these receivers as if one of them behaves as a source. This is accomplished typically by crosscorrelations. Based on perturbation theory and representation theorems, we show that interferometry also can be done by deconvolutions for arbitrary media and multidimensional experiments. This is important for interferometry applications in which (1) excitation is a complicated source-time function and/or (2) when wavefield separation methods are used along with interferometry to retrieve specific arrivals. Unlike using crosscorrelations, this method yields only causal scattered waves that propagate between the receivers. We offer a physical interpretation of deconvolution interferometry based on scattering theory. Here we show that deconvolution interferometry in acoustic media imposes an extra boundary condition, which we refer to as the free-point or clamped-point boundary condition, depending on the measured field quantity. This boundary condition generates so-called free-point scattering interactions, which are described in detail. The extra boundary condition and its associated artifacts can be circumvented by separating the reference waves from scattered wavefields prior to interferometry. Three wavefield-separation methods that can be used in interferometry are direct-wave interferometry, dual-field interferometry, and shot-domain separation. Each has different objectives and requirements.

Elimination of free-surface related multiples without need of the source wavelet

Abstract: This paper presents a new, wave‐equation based method for eliminating the effect of the free surface from marine seismic data without destroying primary amplitudes and without any knowledge of the subsurface. Compared with previously published methods which require an estimate of the source wavelet, the present method has the following characteristics: it does not require any information about the marine source array and its signature, it does not rely on removal of the direct wave from the data, and it does not require any explicit deghosting. Moreover, the effect of the source signature is removed from the data in the multiple elimination process by deterministic signature deconvolution, replacing the original source signature radiated from the marine source array with any desired wavelet (within the data frequency‐band) radiated from a monopole point source. The fundamental constraint of the new method is that the vertical derivative of the pressure or the vertical component of the particle velocity is...