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.

A plane-wave formulation and numerical analysis of elastic multicomponent inverse scattering series internal multiple prediction

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. V255-V269 ◽  
Author(s):  
Jian Sun ◽  
Kristopher A. Innanen
Keyword(s):  
Numerical Analysis ◽  
Plane Wave ◽  
Inverse Scattering ◽  
Simulated Data ◽  
Velocity Model ◽  
Prediction Algorithm ◽  
Inverse Scattering Series ◽  
Elastic Data ◽  
Reference Medium ◽  
Multiple Prediction

Internal multiple prediction and removal is a critical component of seismic data processing prior to imaging, inversion, and quantitative interpretation. Inverse scattering series methods predict multiples without identification of generators, and without requiring a velocity model. Land environments present several challenges to the inverse scattering series prediction process. This is particularly true for algorithm versions that explicitly account for elastic conversions and incorporate multicomponent data. The theory for elastic reference medium inverse scattering series internal multiple prediction was introduced several decades ago, but no numerical analysis or practical discussion of how to prepare data for it currently exists. We have focused our efforts on addressing this gap. We extend the theory from 2D to 3D, analyze the properties of the input data required by the existing algorithm, and, motivated by earlier research results, reformulate the algorithm in the plane-wave domain. The success of the prediction process relies on the ordering of events in either pseudodepth or vertical traveltime being the same as the ordering of reflecting interfaces in true depth. In elastic-multicomponent cases, it is difficult to ensure that this holds true because the events to be combined may have undergone multiple conversions as they were created. Several variants of the elastic-multicomponent prediction algorithm are introduced and examined for their tendency to violate ordering requirements (and create artifacts). A plane-wave domain prediction, based on elastic data that have been prepared (1) using variable, “best-fit” velocities as reference velocities, and (2) with an analytically determined vertical traveltime stretching formula, is identified as being optimal in the sense of generating artifact-free predictions with relatively small values of the search parameter [Formula: see text], while remaining fully data driven. These analyses are confirmed with simulated data from a layered model; these are the first numerical examples of elastic-multicomponent inverse scattering series internal multiple prediction.

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.

Multidimensional inverse-scattering series internal multiple prediction in the coupled plane-wave domain

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. V73-V82 ◽  
Author(s):  
Jian Sun ◽  
Kristopher A. Innanen
Keyword(s):  
Plane Wave ◽  
Inverse Scattering ◽  
Radon Transforms ◽  
Seismic Reflection Data ◽  
Arrival Times ◽  
Computational Expense ◽  
Reflection Data ◽  
Inverse Scattering Series ◽  
Text Prediction ◽  
Multiple Prediction

The inverse-scattering series internal multiple prediction and attenuation algorithm predicts multiples using certain combinations of input seismic reflection data events, which are computed in the wavenumber/pseudodepth or plane-wave/vertical traveltime (i.e., [Formula: see text]) domains. Significant differences can arise in the algorithms’ output and computational expense depending on which domain is used. Many of these are traceable to the response of the algorithm to the users’ choice of the search-limiting parameter [Formula: see text]. The question of which domain is optimal can be addressed with benchmark synthetics. The compactness of the input to the plane-wave domain algorithm leads to the expectation that it will have a reduced computational expense. Also, the lack of increase in the dominant period (i.e., the “width”) of input events as the horizontal slowness increases leads to the expectation that it will respond well to a constant [Formula: see text]. Both of these expectations are borne out with a 1.5D benchmark example. A 2D plane-wave prediction requires the data to be transformed to the [Formula: see text], or coupled plane-wave, domain, involving source- and receiver-side horizontal slownesses. An implementation of this transform leads to the first numerical examples of full 2D inverse series [Formula: see text] prediction. The arrival times, relative amplitudes, and moveout patterns of multiples from dipping horizons are seen in a benchmark synthetic example to be faithfully determined in the plane-wave formulation; waveform mismatches are, however, observed, which are traceable to the numerics of the forward and inverse transforms. High-resolution Radon transforms are a good candidate to improve the match.

Direct nonlinear Q-compensation of seismic primaries reflecting from a stratified, two-parameter absorptive medium

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. V13-V23 ◽  
Author(s):  
Kristopher A. Innanen ◽  
Jose E. Lira
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Text Structure ◽  
Nonlinear Inversion ◽  
Reflection Data ◽  
Born Series ◽  
Highly Nonlinear ◽  
Reference Medium ◽  
Absorptive Medium

[Formula: see text]-compensation of seismic primaries that have reflected from a stratified, absorptive-dispersive medium may be posed as a direct, nonlinear inverse scattering problem. If the reference medium is chosen to be nonattenuating and homogeneous, an inverse-scattering [Formula: see text]-compensation procedure may be derived that is highly nonlinear in the data, but which operates in the absence of prior knowledge of the properties of the subsurface, including its [Formula: see text] structure. It is arrived at by (1) performing an order-by-order inversion of a subset of the Born series, (2) isolating and extracting a component of the resulting nonlinear inversion equations argued to enact [Formula: see text]- compensation, and (3) mapping the result back to data space. Once derived, the procedure can be understood in terms of nonlinear interaction of the input primary reflection data: the attenuation of deeper primaries is corrected by an operator built (automatically) using the angle- and frequency variations of all shallower primaries. A simple synthetic example demonstrates the viability of the procedure in the presence of densely sampled, broadband reflection data.

Elastic inverse scattering for fluid variation with time-lapse seismic data

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. WA61-WA67 ◽  
Author(s):  
Zhaoyun Zong ◽  
Xingyao Yin ◽  
Guochen Wu ◽  
Zhiping Wu
Keyword(s):  
Shear Modulus ◽  
Inverse Scattering ◽  
Seismic Data ◽  
Scattering Theory ◽  
Time Lapse ◽  
Monitoring Data ◽  
Prestack Inversion ◽  
Fluid Factor ◽  
Reference Medium ◽  
The Difference

Elastic inverse-scattering theory has been extended for fluid discrimination using the time-lapse seismic data. The fluid factor, shear modulus, and density are used to parameterize the reference medium and the monitoring medium, and the fluid factor works as the hydrocarbon indicator. The baseline medium is, in the conception of elastic scattering theory, the reference medium, and the monitoring medium is corresponding to the perturbed medium. The difference in the earth properties between the monitoring medium and the baseline medium is taken as the variation in the properties between the reference medium and perturbed medium. The baseline and monitoring data correspond to the background wavefields and measured full fields, respectively. And the variation between the baseline data and monitoring data is taken as the scattered wavefields. Under the above hypothesis, we derived a linearized and qualitative approximation of the reflectivity variation in terms of the changes of fluid factor, shear modulus, and density with the perturbation theory. Incorporating the effect of the wavelet into the reflectivity approximation as the forward solver, we determined a practical prestack inversion approach in a Bayesian scheme to estimate the fluid factor, shear modulus, and density changes directly with the time-lapse seismic data. We evaluated the examples revealing that the proposed approach rendered the estimation of the fluid factor, shear modulus, and density changes stably, even with moderate noise.

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.

scholarly journals Support Vector Machine for Regional Ionospheric Delay Modeling

Sensors ◽  
2019 ◽  
Vol 19 (13) ◽  
pp. 2947 ◽  
Author(s):  
Zhengxie Zhang ◽  
Shuguo Pan ◽  
Chengfa Gao ◽  
Tao Zhao ◽  
Wang Gao
Keyword(s):  
Support Vector Machine ◽  
Regression Model ◽  
Dimensional Space ◽  
Back Propagation ◽  
Single Frequency ◽  
Support Vector ◽  
Electron Content ◽  
Total Electron ◽  
Ionosphere Modeling ◽  
Mean Square Errors

The distribution of total electron content (TEC) in the ionosphere is irregular and complex, and it is hard to model accurately. The polynomial (POLY) model is used extensively for regional ionosphere modeling in two-dimensional space. However, in the active period of the ionosphere, the POLY model is difficult to reflect the distribution and variation of TEC. Aiming at the limitation of the regional POLY model, this paper proposes a new ionosphere modeling method with combining the support vector machine (SVM) regression model and the POLY model. Firstly, the POLY model is established using observations of regional continuously operating reference stations (CORS). Then the SVM regression model is trained to compensate the model error of POLY, and the TEC SVM-P model is obtained by the combination of the POLY and the SVM. The fitting accuracies of the models are verified with the root mean square errors (RMSEs) and static single-frequency precise point positioning (PPP) experiments. The results show that the RMSE of the SVM-P is 0.980 TECU (TEC unit), which produces an improvement of 17.3% compared with the POLY model (1.185 TECU). Using SVM-P models, the positioning accuracies of single-frequency PPP are improved over 40% compared with those using POLY models. The SVM-P is also compared with the back-propagation neural network combined with POLY (BPNN-P), and its performance is also better than BPNN-P (1.070 TECU).

The Imperial City Terrace Locality of the Shimao City Site in Shenmu County, Shaanxi Province

2018 ◽  
Vol 18 (1) ◽  
pp. 28-37 ◽  
Keyword(s):  
Inner City ◽  
Large Scale ◽  
Retaining Wall ◽  
Complex Structure ◽  
Retaining Walls ◽  
Shaanxi Province ◽  
The Core ◽  
Construction Techniques ◽  
Starting Point ◽  
High Terrace

Abstract The Imperial City Terrace (Huangchengtai), a high terrace clad with stone retaining walls on all sides, was the core area of the Shimao Archaic City Site enclosed by the inner city and outer city. In 2016, the gate remains and the upper part of the northern section of the eastern retaining wall, which was the best preserved part of the retaining walls of the Imperial City Terrace, were excavated. The gate remains of the Imperial City Terrace consisted of the square, the outer barbican, the bastions, and the inner barbican. The square was in front of the gate, and the gateway was paved with stone slabs. The entire gate has more complex structure, more magnificent scale and more elaborate construction techniques than that of the eastern gate of the Outer City. This excavation sets a new starting point for the exploration of the large-scale stone city settlement pattern of the Longshan Age.

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