Bogdan Nita | Montclair State University (original) (raw)

Papers by Bogdan Nita

We separate the forward and free surface (FS) back-scattered teleseismic wavefields using the one... more We separate the forward and free surface (FS) back-scattered teleseismic wavefields using the one-way wavefield reciprocity theorem and a FS effect removal algorithm. With the correlation type reciprocity relation among flux-normalized one-way wavefields, the reflection responses can be generated from the flux-normalized transmission responses. We apply the FS multiple removal algorithm to the reconstructed reflection responses, and derived a variation of the algorithm to recover the transmission responses with FS back-scattered waves removed. The FS back-scattered waves can be obtained by taking the difference of the transmission responses before and after the FS effect removal. The method depends on accurate reconstruction of the reflection response from the transmission response. Consistency of the reconstructed reflection response and separated FS back-scattered waves may prove useful in validation of results. Theoretical and numerical tests for 1D crustal structure with a normal incident plane P wave validate the theory. We are working on using this as a method of source signature estimation using a criterion of best performance of the FS effect removal (e.g. minimum-energy criterion). This holds promise as an alternative to conventional receiver function deconvolution as it could simultaneously provide source signature estimation and separation of forward and FS back-scattered wavefields.

We examine the free surface effect on teleseismic waves recorded by passive seismic arrays on the... more We examine the free surface effect on teleseismic waves recorded by passive seismic arrays on the surface, and develop a new way to separate the forward and free surface back scattered waves from the total teleseismic wavefield. Using one-way wavefield reciprocity the reflection responses (of seismic reflection geometry) can be reconstructed from the transmission responses (of teleseismic geometry). The free surface effect (back scattered waves) of the total teleseismic wavefield can be removed by using an inverse scattering series for the teleseismic transmission geometry. The removed free surface back scattered waves can be obtained by taking the difference between the teleseismic wavefield before and after free surface effect removal. This gives the equivalent response to that produced from reconstructed reflection waves using the reciprocity relation. Free surface multiples in the reflection waves are removed by the inverse scattering series of reflection geometry. This produces a direct separation of transmission and reflection waves of the total teleseismic wavefield without knowledge of earth models. Numerical tests of acoustic stratified layer lithospheric earth models demonstrate the effectiveness of the algorithm. Noise test shows that the algorithm can work with signal-to-noise ratio as low as 5. Reconstruction demands higher signal-to-noise ratio than the removal procedure. Test with elastic synthetic data indicates that the acoustic algorithm is still effective for small incidence angle that characterize teleseismic P waves at distance greater than 30 degrees. For shallow angles of incidence, either P and SV wave separation or an elastic algorithm will probably be necessary.

We described how the inverse scattering series method can be used for the nonlinear inversion of ... more We described how the inverse scattering series method can be used for the nonlinear inversion of earth properties using forward scattered teleseismic body waves. This is a general series expansion method based on perturbation theory. We derived the first order terms of the inverse scattering series for plane waves in a constant reference medium. For the first order perturbations of bulk modulus, shear modulus, and density (κ 1, μ 1, and ρ 1, respectively), they are dependent on the type of media. That is, 1) for 1D acoustic constant density media, only the summation of κ 1 can be obtained; 2) in 1D elastic media, for P-P scattering mode, ρ 1 and κ 1 are always combined together and not separable. μ 1 can not be inverted. Similarly, for S-S scattering mode, κ 1 can not be inverted, and μ 1 and ρ 1 can not be separated. However, for either P-S or S-P scattering, μ 1 and ρ 1 can be inverted explicitly and κ 1 can not be determined; 3) with 2D elastic media, for P-P scattering mode, all three type of first order perturbations can be inverted uniquely. For P-S, S-S, and S-P scattering modes, only μ 1 and ρ 1 can be inverted. Thus, if we want to invert the three parameters from the forward scattered teleseismic waves by using inverse scattering theory, the algorithms must be expected to accommodate either 2D or 3D elastic media.

We analyze the nature of steady solutions of a sheared ferrofluid between two parallel boundaries... more We analyze the nature of steady solutions of a sheared ferrofluid between two parallel boundaries and subject to an applied magnetic field H perpendicular to the boundaries. Making no a priori assumption about the magnitude of spin, we find solutions numerically for the velocity and spin fields under the combined pressure gradient and boundary flow forcing. The numerical technique is valid for arbitrary spin viscosity, and by approaching asymptotically small values we explore the impact of the spin boundary conditions on the flow. When the imposed magnetic field is time independent, its effect on the flow is dissipative, but spatially varying fields still permit control of the velocity profile, including the breaking of its midplane symmetry. Time dependent or rotating perpendicular fields can drive the flow and allow more complete flow control, as illustrated in a simple numerical experiment that approximates plug flow. Figs 9, Refs 10.

Seg Technical Program Expanded Abstracts, 2007

... V = L0 − L is the per-turbation operator and ψ = G − G0, is the scattered field, and is ... u... more ... V = L0 − L is the per-turbation operator and ψ = G − G0, is the scattered field, and is ... useful analysis and discussion of the velocity in-dependent inverse scattering internal multiple attenuator, andAmund-sen et ... L. Amundsen and E. Otnes thank Statoil for permission to publish. ...

Geophysics, 2006

The starting point for the derivation of a new set of approaches for predicting both the wavefiel... more The starting point for the derivation of a new set of approaches for predicting both the wavefield at depth in an unknown medium and transmission data from measured reflection data is the inverse scattering series. We present a selection of these maps that differ in order ͑i.e., linear or nonlin-ear͒, capability, and data requirements. They have their roots in the consideration of a data format known as the T-matrix and have direct applicability to the data construction techniques motivating this special issue. Of particular note, one of these, a construction of the wavefield at any depth ͑including the transmitted wavefield͒, order-by-order in the measured reflected wavefield, has an unusual set of capabilities ͑e.g., it does not involve an assumption regarding the minimum-phase nature of the data and is accomplished with processing in the simple reference medium only͒ and requirements ͑e.g., a suite of frequencies from surface data are required to compute a single frequency of the wavefield at depth when the subsurface is unknown͒. An alternative reflection-to-transmission data mapping ͑which does not require a knowledge of the wavelet, and in which the component of the unknown medium that is linear in the reflection data is used as a proxy for the component of the unknown medium that is linear in the transmission data͒ is also derivable from the inverse scattering series framework.

General Relativity and Gravitation, 2003

Algebraically special gravitational fields are described using algebraic and differential invaria... more Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.

Classical and Quantum Gravity, 2000

A differential invariant is found for null fields of arbitrary spin. For null gravitational field... more A differential invariant is found for null fields of arbitrary spin. For null gravitational fields, the invariant is identified as that of Bicác and Pravda; its derivation from the Bel-Robinson tensor is given; and a simple expression is found for its value in null perturbations of flat spacetimes.

Seg Technical Program Expanded Abstracts, 2007

Pseudo-depth monotonicity condition is an important assumption of the inverse scattering internal... more Pseudo-depth monotonicity condition is an important assumption of the inverse scattering internal multiple attenuation algorithm. Analysis reveals that this condition is equivalent to a vertical-time monotonicity condition which is different than the total traveltime monotonicity suggested in recent literature/discussions. For certain complex media, the monotonicity condition can be too restrictive and, as a result, some multiples will not be predicted by the algorithm. Those cases have to be analyzed in the forward scattering series to determine how the multiples are modeled and to establish if an analogy between the forward and the inverse process would be useful to expand the algorithm to address these kind of events.

Solutions of types N and III with twisting rays are derived in the linear approximation by means ... more Solutions of types N and III with twisting rays are derived in the linear approximation by means of complex coordinate transformations. Some solutions are shown to have Riemann tensors which vanish asymptotically and are everywhere regular.

International Journal of Modern Physics A, 2002

A class of solutions to the Bianchi identities in linearized gravitational theory is given which ... more A class of solutions to the Bianchi identities in linearized gravitational theory is given which includes fields which vanish asymptotically and are nowhere singular.

New type III and type N approximate solutions which are regular in the linear approximation are s... more New type III and type N approximate solutions which are regular in the linear approximation are shown to exist. For that, we use complex transformations on self-dual Robinson-Trautman metrics rather then the classical approach. The regularity criterion is the boundedness and vanishing at infinity of a scalar obtained by saturating the Bel-Robinson tensor of the first approximation by a time-like vector which is constant with respect to the zeroth approximation.

Seg Technical Program Expanded Abstracts, 2007

In AVO (Amplitude Variation with Offset) analysis, the amplitudes of reflected waves with differe... more In AVO (Amplitude Variation with Offset) analysis, the amplitudes of reflected waves with different incident angles are studied to deduce lithology information beyond the structure map obtained by seismic imaging algorithms. The quantitative analysis of the amplitude, relies on common-image gathers being flat (or equivalently, at the same depth). But the waves with different incident angles will have different apparent velocities, resulting in different depths for the same image point at different angles, or non-flat common image gathers. In many scenarios, non-flat common-image gather was flattened by trim means at the cost of compromising zero-crossing and polarity-reversal information. This work presents a solution based on the seismic imaging subseries of the inverse scattering series (ISS) that flattens the common image gather without knowing or determining the subsurface velocity, and without any harmful amplitude consequencies. Araujo, F. V., 1994, Linear and non-linear methods derived from scattering theory: Backscattered tomography and internal multiple attenuation: Ph.

In this paper we discuss the inverse scattering algorithm for predicting internal multiple reflec... more In this paper we discuss the inverse scattering algorithm for predicting internal multiple reflections (reverberation artefacts), focusing our attention on the construction mechanisms. Roughly speaking, the algorithm combines amplitude and phase information of three different arrivals (sub-events) in the data set to predict one multiple reflection. The three events are conditioned by a certain relation which requires that their pseudo-depths, defined as the depths of their turning points relative to the constant background velocity, satisfy a lower-higher-lower relationship. This implicitly assumes a pseudo-depth monotonicity condition, i.e., the relation between the actual depths and the pseudo-depths of any two sub-events is the same. We study this relation in pseudo-depth and show that it is directly connected with a similar relation between the vertical or intercept times of the sub-events. The paper also provides the first multidimensional analysis of the algorithm (for a vertically varying acoustic model) with analytical data. We show that the construction of internal multiples is performed in the plane waves domain and, as a consequence, the internal multiples with headwaves sub-events are also predicted by the algorithm. Furthermore we analyze the differences between the time monotonicity condition in vertical or intercept time and total travel time and show a 2D example which satisfies the former but not the latter. Finally we discuss one case in which the monotonicity condition is not satisfied by the sub-events of an internal multiple and discuss ways of lowering these restrictions and of expanding the algorithm to address these types of multiples.

Geophysics, 2006

We develop a new way to remove free-surface multiples from teleseismic P-transmission and constru... more We develop a new way to remove free-surface multiples from teleseismic P-transmission and constructed reflection responses. We consider two types of teleseismic waves with the presence of the free surface: One is the recorded waves under the real transmission geometry; the other is the constructed waves under a virtual reflection geometry. The theory presented is limited to 1D plane wave acoustic media, but this approximation is reasonable for the teleseismic P-wave problem resulting from the steep emergence angle of the wavefield. Using one-way wavefield reciprocity, we show how the teleseismic reflection responses can be reconstructed from the teleseismic transmission responses. We use the inverse scattering series to remove free-surface multiples from the original transmission data and from the reconstructed reflection response. We derive an alternative algorithm for reconstructing the reflection response from the transmission data that is obtained by taking the difference between the teleseismic transmission waves before and after free-surface multiple removal. Numerical tests with 1D acoustic layered earth models demonstrate the validity of the theory we develop. Noise test shows that the algorithm can work with S/N ratio as low as 5 compared to actual data with S/N ratio from 30 to 50. Testing with elastic synthetic data indicates that the acoustic algorithm is still effective for small incidence angles of typical teleseismic wavefields.

Seg Technical Program Expanded Abstracts, 1999

The inverse scattering subseries for removing free surface and internal multiples provided the fi... more The inverse scattering subseries for removing free surface and internal multiples provided the first comprehensive theory for removing multiples from an arbitrary heterogeneous earth without any subsurface information whatsoever. Furthermore, taken as a whole, the inverse series provides a fully inclusive theory for processing both primaries and multiples directly in terms of an inadequate velocity model, without updating or in any other way determining the accurate velocity configuration. Hence, the inverse series and, more specifically, its subseries that perform imaging and inversion of primaries, has the potential to allow processing primaries to catch up to processing multiples in concept and effectiveness.

Seg Technical Program Expanded Abstracts, 2006

Journal of Physics-condensed Matter, 2008

Page 1. Modeling bubbles and droplets in magnetic fluids This article has been downloaded from IO... more Page 1. Modeling bubbles and droplets in magnetic fluids This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2008 J. Phys.: Condens. Matter 20 204143 (http://iopscience.iop.org/0953-8984/20/20/204143) ...

Siam Journal on Applied Mathematics, 2004

Inverse scattering series is the only nonlinear, direct inversion method for the multidimensional... more Inverse scattering series is the only nonlinear, direct inversion method for the multidimensional, acoustic or elastic equation. Recently developed techniques for inverse problems based on the inverse scattering series were shown to require two mappings, one associating nonperturbative description of seismic events with their forward scattering series description and a second relating the construction of events in the forward to their treatment in the inverse scattering series. This paper extends and further analyzes the first of these two mappings, introduced, for 1D normal incidence, in Matson [J. ]. It brings a new and more rigorous understanding of the mathematics and physics underlying the calculation of terms in the forward scattering series and the events in the seismic model. The convergence of the series for 1D acoustic models is examined, and the earlier precritical analysis is extended to critical and postcritical reflections. An explanation is proposed for the divergence of the series for postcritical incident planewaves.

We separate the forward and free surface (FS) back-scattered teleseismic wavefields using the one... more We separate the forward and free surface (FS) back-scattered teleseismic wavefields using the one-way wavefield reciprocity theorem and a FS effect removal algorithm. With the correlation type reciprocity relation among flux-normalized one-way wavefields, the reflection responses can be generated from the flux-normalized transmission responses. We apply the FS multiple removal algorithm to the reconstructed reflection responses, and derived a variation of the algorithm to recover the transmission responses with FS back-scattered waves removed. The FS back-scattered waves can be obtained by taking the difference of the transmission responses before and after the FS effect removal. The method depends on accurate reconstruction of the reflection response from the transmission response. Consistency of the reconstructed reflection response and separated FS back-scattered waves may prove useful in validation of results. Theoretical and numerical tests for 1D crustal structure with a normal incident plane P wave validate the theory. We are working on using this as a method of source signature estimation using a criterion of best performance of the FS effect removal (e.g. minimum-energy criterion). This holds promise as an alternative to conventional receiver function deconvolution as it could simultaneously provide source signature estimation and separation of forward and FS back-scattered wavefields.

We examine the free surface effect on teleseismic waves recorded by passive seismic arrays on the... more We examine the free surface effect on teleseismic waves recorded by passive seismic arrays on the surface, and develop a new way to separate the forward and free surface back scattered waves from the total teleseismic wavefield. Using one-way wavefield reciprocity the reflection responses (of seismic reflection geometry) can be reconstructed from the transmission responses (of teleseismic geometry). The free surface effect (back scattered waves) of the total teleseismic wavefield can be removed by using an inverse scattering series for the teleseismic transmission geometry. The removed free surface back scattered waves can be obtained by taking the difference between the teleseismic wavefield before and after free surface effect removal. This gives the equivalent response to that produced from reconstructed reflection waves using the reciprocity relation. Free surface multiples in the reflection waves are removed by the inverse scattering series of reflection geometry. This produces a direct separation of transmission and reflection waves of the total teleseismic wavefield without knowledge of earth models. Numerical tests of acoustic stratified layer lithospheric earth models demonstrate the effectiveness of the algorithm. Noise test shows that the algorithm can work with signal-to-noise ratio as low as 5. Reconstruction demands higher signal-to-noise ratio than the removal procedure. Test with elastic synthetic data indicates that the acoustic algorithm is still effective for small incidence angle that characterize teleseismic P waves at distance greater than 30 degrees. For shallow angles of incidence, either P and SV wave separation or an elastic algorithm will probably be necessary.

We described how the inverse scattering series method can be used for the nonlinear inversion of ... more We described how the inverse scattering series method can be used for the nonlinear inversion of earth properties using forward scattered teleseismic body waves. This is a general series expansion method based on perturbation theory. We derived the first order terms of the inverse scattering series for plane waves in a constant reference medium. For the first order perturbations of bulk modulus, shear modulus, and density (κ 1, μ 1, and ρ 1, respectively), they are dependent on the type of media. That is, 1) for 1D acoustic constant density media, only the summation of κ 1 can be obtained; 2) in 1D elastic media, for P-P scattering mode, ρ 1 and κ 1 are always combined together and not separable. μ 1 can not be inverted. Similarly, for S-S scattering mode, κ 1 can not be inverted, and μ 1 and ρ 1 can not be separated. However, for either P-S or S-P scattering, μ 1 and ρ 1 can be inverted explicitly and κ 1 can not be determined; 3) with 2D elastic media, for P-P scattering mode, all three type of first order perturbations can be inverted uniquely. For P-S, S-S, and S-P scattering modes, only μ 1 and ρ 1 can be inverted. Thus, if we want to invert the three parameters from the forward scattered teleseismic waves by using inverse scattering theory, the algorithms must be expected to accommodate either 2D or 3D elastic media.

We analyze the nature of steady solutions of a sheared ferrofluid between two parallel boundaries... more We analyze the nature of steady solutions of a sheared ferrofluid between two parallel boundaries and subject to an applied magnetic field H perpendicular to the boundaries. Making no a priori assumption about the magnitude of spin, we find solutions numerically for the velocity and spin fields under the combined pressure gradient and boundary flow forcing. The numerical technique is valid for arbitrary spin viscosity, and by approaching asymptotically small values we explore the impact of the spin boundary conditions on the flow. When the imposed magnetic field is time independent, its effect on the flow is dissipative, but spatially varying fields still permit control of the velocity profile, including the breaking of its midplane symmetry. Time dependent or rotating perpendicular fields can drive the flow and allow more complete flow control, as illustrated in a simple numerical experiment that approximates plug flow. Figs 9, Refs 10.

Seg Technical Program Expanded Abstracts, 2007

... V = L0 − L is the per-turbation operator and ψ = G − G0, is the scattered field, and is ... u... more ... V = L0 − L is the per-turbation operator and ψ = G − G0, is the scattered field, and is ... useful analysis and discussion of the velocity in-dependent inverse scattering internal multiple attenuator, andAmund-sen et ... L. Amundsen and E. Otnes thank Statoil for permission to publish. ...

Geophysics, 2006

The starting point for the derivation of a new set of approaches for predicting both the wavefiel... more The starting point for the derivation of a new set of approaches for predicting both the wavefield at depth in an unknown medium and transmission data from measured reflection data is the inverse scattering series. We present a selection of these maps that differ in order ͑i.e., linear or nonlin-ear͒, capability, and data requirements. They have their roots in the consideration of a data format known as the T-matrix and have direct applicability to the data construction techniques motivating this special issue. Of particular note, one of these, a construction of the wavefield at any depth ͑including the transmitted wavefield͒, order-by-order in the measured reflected wavefield, has an unusual set of capabilities ͑e.g., it does not involve an assumption regarding the minimum-phase nature of the data and is accomplished with processing in the simple reference medium only͒ and requirements ͑e.g., a suite of frequencies from surface data are required to compute a single frequency of the wavefield at depth when the subsurface is unknown͒. An alternative reflection-to-transmission data mapping ͑which does not require a knowledge of the wavelet, and in which the component of the unknown medium that is linear in the reflection data is used as a proxy for the component of the unknown medium that is linear in the transmission data͒ is also derivable from the inverse scattering series framework.

General Relativity and Gravitation, 2003

Algebraically special gravitational fields are described using algebraic and differential invaria... more Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.

Classical and Quantum Gravity, 2000

A differential invariant is found for null fields of arbitrary spin. For null gravitational field... more A differential invariant is found for null fields of arbitrary spin. For null gravitational fields, the invariant is identified as that of Bicác and Pravda; its derivation from the Bel-Robinson tensor is given; and a simple expression is found for its value in null perturbations of flat spacetimes.

Seg Technical Program Expanded Abstracts, 2007

Pseudo-depth monotonicity condition is an important assumption of the inverse scattering internal... more Pseudo-depth monotonicity condition is an important assumption of the inverse scattering internal multiple attenuation algorithm. Analysis reveals that this condition is equivalent to a vertical-time monotonicity condition which is different than the total traveltime monotonicity suggested in recent literature/discussions. For certain complex media, the monotonicity condition can be too restrictive and, as a result, some multiples will not be predicted by the algorithm. Those cases have to be analyzed in the forward scattering series to determine how the multiples are modeled and to establish if an analogy between the forward and the inverse process would be useful to expand the algorithm to address these kind of events.

Solutions of types N and III with twisting rays are derived in the linear approximation by means ... more Solutions of types N and III with twisting rays are derived in the linear approximation by means of complex coordinate transformations. Some solutions are shown to have Riemann tensors which vanish asymptotically and are everywhere regular.

International Journal of Modern Physics A, 2002

A class of solutions to the Bianchi identities in linearized gravitational theory is given which ... more A class of solutions to the Bianchi identities in linearized gravitational theory is given which includes fields which vanish asymptotically and are nowhere singular.

New type III and type N approximate solutions which are regular in the linear approximation are s... more New type III and type N approximate solutions which are regular in the linear approximation are shown to exist. For that, we use complex transformations on self-dual Robinson-Trautman metrics rather then the classical approach. The regularity criterion is the boundedness and vanishing at infinity of a scalar obtained by saturating the Bel-Robinson tensor of the first approximation by a time-like vector which is constant with respect to the zeroth approximation.

Seg Technical Program Expanded Abstracts, 2007

In AVO (Amplitude Variation with Offset) analysis, the amplitudes of reflected waves with differe... more In AVO (Amplitude Variation with Offset) analysis, the amplitudes of reflected waves with different incident angles are studied to deduce lithology information beyond the structure map obtained by seismic imaging algorithms. The quantitative analysis of the amplitude, relies on common-image gathers being flat (or equivalently, at the same depth). But the waves with different incident angles will have different apparent velocities, resulting in different depths for the same image point at different angles, or non-flat common image gathers. In many scenarios, non-flat common-image gather was flattened by trim means at the cost of compromising zero-crossing and polarity-reversal information. This work presents a solution based on the seismic imaging subseries of the inverse scattering series (ISS) that flattens the common image gather without knowing or determining the subsurface velocity, and without any harmful amplitude consequencies. Araujo, F. V., 1994, Linear and non-linear methods derived from scattering theory: Backscattered tomography and internal multiple attenuation: Ph.

In this paper we discuss the inverse scattering algorithm for predicting internal multiple reflec... more In this paper we discuss the inverse scattering algorithm for predicting internal multiple reflections (reverberation artefacts), focusing our attention on the construction mechanisms. Roughly speaking, the algorithm combines amplitude and phase information of three different arrivals (sub-events) in the data set to predict one multiple reflection. The three events are conditioned by a certain relation which requires that their pseudo-depths, defined as the depths of their turning points relative to the constant background velocity, satisfy a lower-higher-lower relationship. This implicitly assumes a pseudo-depth monotonicity condition, i.e., the relation between the actual depths and the pseudo-depths of any two sub-events is the same. We study this relation in pseudo-depth and show that it is directly connected with a similar relation between the vertical or intercept times of the sub-events. The paper also provides the first multidimensional analysis of the algorithm (for a vertically varying acoustic model) with analytical data. We show that the construction of internal multiples is performed in the plane waves domain and, as a consequence, the internal multiples with headwaves sub-events are also predicted by the algorithm. Furthermore we analyze the differences between the time monotonicity condition in vertical or intercept time and total travel time and show a 2D example which satisfies the former but not the latter. Finally we discuss one case in which the monotonicity condition is not satisfied by the sub-events of an internal multiple and discuss ways of lowering these restrictions and of expanding the algorithm to address these types of multiples.

Geophysics, 2006

We develop a new way to remove free-surface multiples from teleseismic P-transmission and constru... more We develop a new way to remove free-surface multiples from teleseismic P-transmission and constructed reflection responses. We consider two types of teleseismic waves with the presence of the free surface: One is the recorded waves under the real transmission geometry; the other is the constructed waves under a virtual reflection geometry. The theory presented is limited to 1D plane wave acoustic media, but this approximation is reasonable for the teleseismic P-wave problem resulting from the steep emergence angle of the wavefield. Using one-way wavefield reciprocity, we show how the teleseismic reflection responses can be reconstructed from the teleseismic transmission responses. We use the inverse scattering series to remove free-surface multiples from the original transmission data and from the reconstructed reflection response. We derive an alternative algorithm for reconstructing the reflection response from the transmission data that is obtained by taking the difference between the teleseismic transmission waves before and after free-surface multiple removal. Numerical tests with 1D acoustic layered earth models demonstrate the validity of the theory we develop. Noise test shows that the algorithm can work with S/N ratio as low as 5 compared to actual data with S/N ratio from 30 to 50. Testing with elastic synthetic data indicates that the acoustic algorithm is still effective for small incidence angles of typical teleseismic wavefields.

Seg Technical Program Expanded Abstracts, 1999

The inverse scattering subseries for removing free surface and internal multiples provided the fi... more The inverse scattering subseries for removing free surface and internal multiples provided the first comprehensive theory for removing multiples from an arbitrary heterogeneous earth without any subsurface information whatsoever. Furthermore, taken as a whole, the inverse series provides a fully inclusive theory for processing both primaries and multiples directly in terms of an inadequate velocity model, without updating or in any other way determining the accurate velocity configuration. Hence, the inverse series and, more specifically, its subseries that perform imaging and inversion of primaries, has the potential to allow processing primaries to catch up to processing multiples in concept and effectiveness.

Seg Technical Program Expanded Abstracts, 2006

Journal of Physics-condensed Matter, 2008

Page 1. Modeling bubbles and droplets in magnetic fluids This article has been downloaded from IO... more Page 1. Modeling bubbles and droplets in magnetic fluids This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2008 J. Phys.: Condens. Matter 20 204143 (http://iopscience.iop.org/0953-8984/20/20/204143) ...

Siam Journal on Applied Mathematics, 2004

Inverse scattering series is the only nonlinear, direct inversion method for the multidimensional... more Inverse scattering series is the only nonlinear, direct inversion method for the multidimensional, acoustic or elastic equation. Recently developed techniques for inverse problems based on the inverse scattering series were shown to require two mappings, one associating nonperturbative description of seismic events with their forward scattering series description and a second relating the construction of events in the forward to their treatment in the inverse scattering series. This paper extends and further analyzes the first of these two mappings, introduced, for 1D normal incidence, in Matson [J. ]. It brings a new and more rigorous understanding of the mathematics and physics underlying the calculation of terms in the forward scattering series and the events in the seismic model. The convergence of the series for 1D acoustic models is examined, and the earlier precritical analysis is extended to critical and postcritical reflections. An explanation is proposed for the divergence of the series for postcritical incident planewaves.