Removing free-surface multiples from teleseismic transmission and constructed reflection responses using reciprocity and the inverse scattering series

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI71-SI78 ◽  
Author(s):  
Chengliang Fan ◽  
Gary L. Pavlis ◽  
Arthur B. Weglein ◽  
Bogdan G. Nita
Keyword(s):  
Free Surface ◽  
Inverse Scattering ◽  
Synthetic Data ◽  
P Wave ◽  
Transmission Data ◽  
Before And After ◽  
Small Incidence ◽  
Inverse Scattering Series ◽  
Acoustic Media ◽  
The Difference

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.

Comparison of the inverse scattering series free-surface multiple elimination (ISS FSME) algorithm with the industry-standard surface-related multiple elimination (SRME): Defining the circumstances in which each method is the appropriate toolbox choice

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. S459-S478
Author(s):  
Chao Ma ◽  
Qiang Fu ◽  
Arthur B. Weglein
Keyword(s):  
Free Surface ◽  
Inverse Scattering ◽  
Energy Minimization ◽  
Cost Effective ◽  
Adaptive Process ◽  
Industry Standard ◽  
Inverse Scattering Series ◽  
The Difference ◽  
Multiple Prediction ◽  
Multiple Elimination

The industry-standard surface-related multiple elimination (SRME) method provides an approximate predictor of the amplitude and phase of free-surface multiples. This approximate predictor then calls upon an energy-minimization adaptive subtraction step to bridge the difference between the SRME prediction and the actual free-surface multiple. For free-surface multiples that are proximal to other events, the criteria behind energy-minimization adaptive subtraction can be invalid. When applied under these circumstances, a proximal primary can often be damaged. To reduce the dependence on the adaptive process, a more accurate free-surface multiple prediction is required. The inverse scattering series (ISS) free-surface multiple elimination (FSME) method predicts free-surface multiples with accurate time and accurate amplitude of free-surface multiples for a multidimensional earth, directly and without any subsurface information. To quantify these differences, a comparison with analytic data was carried out, confirming that when a free-surface multiple interferes with a primary, applying SRME with adaptive subtraction can and will damage the primary, whereas ISS free-surface elimination will precisely remove the free-surface multiple without damaging the interfering primary. On the other hand, if the free-surface multiple is isolated, then SRME with adaptive subtraction can be a cost-effective toolbox choice. SRME and ISS FSME each have an important and distinct role to play in the seismic toolbox, and each method is the indicated choice under different circumstances.

scholarly journals Relating source-receiver interferometry to an inverse-scattering series to derive a new method to estimate internal multiples

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. Q27-Q40 ◽  
Author(s):  
Katrin Löer ◽  
Andrew Curtis ◽  
Giovanni Angelo Meles
Keyword(s):  
Inverse Scattering ◽  
Computational Cost ◽  
Synthetic Data ◽  
Data Set ◽  
Inverse Scattering Series ◽  
Internal Multiples ◽  
Multiple Prediction ◽  
New Formula ◽  
3D Applications ◽  
Insight Into

We have evaluated an explicit relationship between the representations of internal multiples by source-receiver interferometry and an inverse-scattering series. This provides a new insight into the interaction of different terms in each of these internal multiple prediction equations and explains why amplitudes of estimated multiples are typically incorrect. A downside of the existing representations is that their computational cost is extremely high, which can be a precluding factor especially in 3D applications. Using our insight from source-receiver interferometry, we have developed an alternative, computationally more efficient way to predict internal multiples. The new formula is based on crosscorrelation and convolution: two operations that are computationally cheap and routinely used in interferometric methods. We have compared the results of the standard and the alternative formulas qualitatively in terms of the constructed wavefields and quantitatively in terms of the computational cost using examples from a synthetic data set.

Using the inverse scattering series to predict the wavefield at depth and the transmitted wavefield without an assumption about the phase of the measured reflection data or back propagation in the overburden

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI125-SI137 ◽  
Author(s):  
A. B. Weglein ◽  
B. G. Nita ◽  
K. A. Innanen ◽  
E. Otnes ◽  
S. A. Shaw ◽  
...  
Keyword(s):  
Inverse Scattering ◽  
Back Propagation ◽  
Single Frequency ◽  
Data Mapping ◽  
Reflection Data ◽  
Construction Techniques ◽  
Starting Point ◽  
Transmission Data ◽  
Inverse Scattering Series ◽  
Reference Medium

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 nonlinear), 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 wavefield), 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 only) 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 unknown). 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 data) is also derivable from the inverse scattering series framework.

Direct nonlinear inversion of 1D acoustic media using inverse scattering subseries

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCD29-WCD39 ◽  
Author(s):  
Haiyan Zhang ◽  
Arthur B. Weglein
Keyword(s):  
Inverse Scattering ◽  
Target Identification ◽  
Numerical Test ◽  
Added Value ◽  
Acoustic Medium ◽  
Nonlinear Inversion ◽  
Model Matching ◽  
Inverse Scattering Series ◽  
Acoustic Media ◽  
Property Changes

A task-specific, multiparameter (more than one mechanical property changes across a reflector), direct nonlinear inversion subseries of the inverse-scattering series is derived and tested for an acoustic medium in which velocity and density vary vertically. Task-specific means that terms in the distinct subseries corresponding to tasks for imaging only and inversion only are identified and separated. Direct means there are formulas that solve explicitly for and output the physical properties, without, e.g., search algorithms, model matching and optimization schemes, and proxies that typically characterize indirect methods. Numerical test results with analytic data indicate that one term beyond linear provides added value beyond standard linear techniques, and the improved estimates are valid over a larger range of angles. The direct acoustic inversion is nonlinear. It serves as an important step for new concepts and methods to guide the much more complicated and minimally realistic elastic inverse for exploration seismology target identification purposes.

Polarization-based wave-equation migration velocity analysis in acoustic media

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. U77-U88 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Wave Equation ◽  
Velocity Ratio ◽  
Empirical Relation ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Seismic Reflection Data ◽  
Prestack Migration ◽  
Time Migration ◽  
Acoustic Media

The source extrapolation step in wave-equation prestack reverse-time migration gives wavefield polarization information, which can be used to generate angle-domain common-image gathers (ADCIGs) from seismic reflection data from acoustic media. Concatenation of P-wave polarization segments gives wavefield propagation paths (“wavepaths”), which are similar to the raypaths in ray-based velocity tomography. The ADCIGs provide residual depth moveout (RMO) information, from which a system of linear equations is constructed for tomography to solve for the velocity ratio used for velocity updating. An empirical relation between the RMO data and the velocity ratio updates reduces the amount of computation, and is stabilized by the feedback provided by the iterative loop through prestack migration, to RMO, to velocity update, to prestack migration. Correcting the RMOs to flatten the ADGIGs is the convergence condition. Synthetic data for a layered model with a fault successfully illustrates the method.

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