Diffraction tomography for inhomogeneities in layered background medium

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 570-583 ◽  
Author(s):  
Jerry M. Harris ◽  
Guan Y. Wang
Keyword(s):  
Field Data ◽  
Large Scale ◽  
Selection Rule ◽  
Back Propagation ◽  
Reconstruction Algorithm ◽  
Point Sources ◽  
Diffraction Tomography ◽  
Transmission Tomography ◽  
Background Medium ◽  
Uniform Background

Diffraction tomography was originally formulated for a constant velocity background medium. A variable background medium, e.g., layered, with embedded finer scale heterogeneities is a more practical model for subsurface reservoirs than the uniform background. The variable background of large scale variations may be determined from well logs or transmission tomography. To image the finer scale heterogeneities, we have developed a Fourier diffraction back‐propagation method for point sources in a layered background. The method is based on the normal mode solution to the acoustic wave equation in cylindrical coordinates. The Fourier spectrum of the scattered fields is first decomposed into contributions from different layers. Then, a selection rule is applied to sort out the heterogeneity spectrum of the individual layers. The selection rule relates the scattered field in diffraction space to the spectrum of the heterogeneities, i.e., a Fourier diffraction theorem for layered media. The theorem differs from its counterpart for a uniform background medium by a matrix filter that reduces to unity as the stratification degenerates to a uniform background. A reconstruction algorithm based on this theorem is implemented and tested for an arbitrary layered background. The theory deals directly with point sources; therefore, the resulting algorithm does not require application of the “2.5-D correction” to field data as required in previously published diffraction tomography algorithms. Results obtained for both synthetic and field data demonstrate that an inversion with spatial resolution on the order of a wavelength can be achieved for crosswell data. The computations involved are much more efficient than those of traveltime tomography or crosswell migration. Unlike migration or CDP mapping, the diffraction tomography algorithm provides quantitative estimates for fine scale velocity.

A Filtered Backpropagation Algorithm for Diffraction Tomography

1982 ◽  
Vol 4 (4) ◽  
pp. 336-350 ◽  
Author(s):  
A. J. Devaney
Keyword(s):  
Back Propagation ◽  
Three Dimensional ◽  
Reconstruction Algorithm ◽  
Diffraction Tomography ◽  
Filtered Backprojection ◽  
Parallel Beam ◽  
Transmission Tomography ◽  
Complex Phase ◽  
Transmission Computed Tomography ◽  
Beam Transmission

A reconstruction algorithm is derived for parallel beam transmission computed tomography through two-dimensional structures in which diffraction of the insonifying beam must be taken into account. The algorithm is found to be completely analogous to the filtered backprojection algorithm of conventional transmission tomography with the exception that the backprojection operation has to be replaced by a back propagation process whereby the complex phase of a field measured over a line outside the object is made to propagate back through the object space. The algorithm is applicable to diffraction tomography within either the first Born or Rytov approximations. Application of the algorithm to three-dimensional structures is also discussed.

Crosswell seismic reflection/diffraction tomography: A reservoir characterization application

Geophysics ◽  
1994 ◽  
Vol 59 (3) ◽  
pp. 351-361 ◽  
Author(s):  
M. Ali C. Tura ◽  
Robert J. Greaves ◽  
Wafik B. Beydoun
Keyword(s):  
Data Acquisition ◽  
Field Data ◽  
Large Scale ◽  
Reservoir Characterization ◽  
Synthetic Data ◽  
Velocity Model ◽  
Oil Field ◽  
Diffraction Tomography ◽  
Median Filters ◽  
Zero Offset

A crosswell seismic experiment at the San Emidio oil field in Bakersfield, California, is carried out to evaluate crosswell reflection/diffraction tomography and image the interwell region to locate a possible pinchout zone. In this experiment, the two wells used are 2500 ft (762 m) apart, and the zone to be imaged is 11 000 ft (3350 m) to 13 000 ft (3960 m) deep. With the considered distances, this experiment forms the first large scale reservoir characterization application of crosswell reflection/diffraction tomography. A subset of the intended data, formed of two common receiver gathers and one common shot gather, was collected at the San Emidio oil field. The crosswell data display a wide variety of wave modes including tube waves, singly and multiply reflected/diffracted waves, and refracted waves. The data are processed using frequency filters, median filters, and spatial muting filters to enhance the reflected/diffracted energy. A 2-D layered velocity model with gradients is built using zero‐offset VSPs and full‐waveform acoustic logs from the two wells. This model is used to generate synthetic finite‐difference data for the field data acquisition geometry. The synthetic data are processed and imaged using the elastic ray‐Born 𝓁2-migration/inversion (ERBMI) method. A smooth 2-D velocity model incorporating only gradients and a few layers is used as a background model for the imaging. Considering the limited data acquisition geometry, synthetic data images compare favorably with the initial velocity model. With the encouraging results obtained from synthetic data, the ERBMI method, with the smooth background velocity model is used next to image the processed field data. Images obtained from the crosswell data show a good match with the reflected field in the zero‐offset VSPs and with migrated surface seismic data. From the interpretation of these images, the potential of this crosswell seismic method for answering questions regarding reservoir continuity and existence of pinchout zones can be seen.

Investigation of limitations of optical diffraction tomography

2007 ◽  
Vol 15 (2) ◽  
Author(s):  
T. Kozacki ◽  
M. Kujawińska ◽  
P. Kniażewski
Keyword(s):  
Refractive Index ◽  
Dynamic Range ◽  
Tomographic Reconstruction ◽  
Back Propagation ◽  
Reconstruction Algorithm ◽  
Optical Diffraction ◽  
Diffraction Tomography ◽  
Refractive Index Distribution ◽  
Optical Diffraction Tomography ◽  
Index Distribution

AbstractOptical diffraction tomography (ODT) applied to measurement of optical microelements is limited by low dynamic range, i.e., only objects with small deviations of refractive-index distribution can be measured. Therefore in this paper the limitations and errors of ODT are investigated throughout extensive numerical experiments. It is shown that these errors can be reduced by introduction of additional numerical focusing in the tomographic reconstruction algorithm. Additionally, new tomographic reconstruction algorithm using back propagation in reference medium for optical microelements measurement with known design is proposed. This hybrid reconstruction algorithm allows significant extension of ODT applicability in measurement of elements having large deviations of refractive-index distribution.

Application of diffraction tomography to fracture detection

Geophysics ◽  
1992 ◽  
Vol 57 (2) ◽  
pp. 245-257 ◽  
Author(s):  
M. Ali C. Tura ◽  
Lane R. Johnson ◽  
Ernest L. Majer ◽  
John E. Peterson
Keyword(s):  
Quadratic Programming ◽  
Born Approximation ◽  
Field Data ◽  
Granitic Rock ◽  
Back Propagation ◽  
Synthetic Data ◽  
Programming Method ◽  
Diffraction Tomography ◽  
Inversion Methods ◽  
Quadratic Programming Method

Two diffraction tomography techniques are applied to crosshole field data to detect fractures in granitic rock. The techniques used are the conventional back‐propagation method and a new quadratic programming method incorporating constraints. In this formulation, the Born approximation is used for linearization of the inverse problem. Two dimensional (2-D) pseudo spectral finite‐difference synthetic data are generated to demonstrate the inversion methods and justify use of the Born approximation. Also, using 2-D Born synthetic data, the velocity sensitivity of the inversion algorithm and reduction of fracture generated tube waves and S‐waves are investigated. The inversion methods are applied to field data from the Grimsel test site in Switzerland. The data are collected from a [Formula: see text] rectangular area where fractures are known to exist. Data acquisition with 0.5 m spacing of three component receivers and a piezoelectric source is carried out so as to obtain a nearly complete coverage of the region. Crosshole inversions are performed on data from the receiver components in the plane of the rectangular region and normal to its boundary. As the result of a separate experiment conducted in a homogeneous region of the granitic rock, a cosine function was found to best fit the source radiation pattern. A background attenuation value is estimated for the region, using a simple statistical approach, and estimates of the wavelet are found by common source gathers, common receiver gathers, and averages of all traces. The preprocessing steps are: (1) source radiation correction, (2) attenuation correction, (3) removal of the incident wavefield, (4) muting beginning of the traces and windowing the ends, (5) wavelet deconvolution, and (6) two‐and‐a‐half dimensional (2.5-D) corrections. This preprocessing is designed to enhance scattered P‐waves that are used in the inversions. Images obtained from the application of back‐propagation and quadratic programming methods to the preprocessed data show possible fracture zones that agree well at the boundaries of the region with the fracture sets observed from core samples taken from the boreholes. Although the quadratic programming method is an order of magnitude slower than the back‐propagation method, as demonstrated by the synthetic examples, it proves useful by yielding high resolution images when constraints can be imposed. Transmission ray tomography is also applied to the crosshole data, and although the resolution is not as high, general agreement with the wave equation based methods is obtained.

Economic benefit of shale gas exploitation based on back propagation neural network

2020 ◽  
Vol 39 (6) ◽  
pp. 8823-8830
Author(s):  
Jiafeng Li ◽  
Hui Hu ◽  
Xiang Li ◽  
Qian Jin ◽  
Tianhao Huang
Keyword(s):  
Neural Network ◽  
Shale Gas ◽  
Bp Neural Network ◽  
Large Scale ◽  
Linear Prediction ◽  
Back Propagation ◽  
Back Propagation Neural Network ◽  
Economic Benefits ◽  
Gas Well ◽  
Well Production

Under the influence of COVID-19, the economic benefits of shale gas development are greatly affected. With the large-scale development and utilization of shale gas in China, it is increasingly important to assess the economic impact of shale gas development. Therefore, this paper proposes a method for predicting the production of shale gas reservoirs, and uses back propagation (BP) neural network to nonlinearly fit reservoir reconstruction data to obtain shale gas well production forecasting models. Experiments show that compared with the traditional BP neural network, the proposed method can effectively improve the accuracy and stability of the prediction. There is a nonlinear correlation between reservoir reconstruction data and gas well production, which does not apply to traditional linear prediction methods

scholarly journals Estimating CO2 Emissions from Large Scale Coal-Fired Power Plants Using OCO-2 Observations and Emission Inventories

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 811
Author(s):  
Yaqin Hu ◽  
Yusheng Shi
Keyword(s):  
Power Plant ◽  
Co2 Emissions ◽  
Atmospheric Carbon Dioxide ◽  
Power Plants ◽  
Large Scale ◽  
Global Climate ◽  
Gaussian Model ◽  
Point Sources ◽  
Emission Inventories ◽  
Bottom Up

The concentration of atmospheric carbon dioxide (CO2) has increased rapidly worldwide, aggravating the global greenhouse effect, and coal-fired power plants are one of the biggest contributors of greenhouse gas emissions in China. However, efficient methods that can quantify CO2 emissions from individual coal-fired power plants with high accuracy are needed. In this study, we estimated the CO2 emissions of large-scale coal-fired power plants using Orbiting Carbon Observatory-2 (OCO-2) satellite data based on remote sensing inversions and bottom-up methods. First, we mapped the distribution of coal-fired power plants, displaying the total installed capacity, and identified two appropriate targets, the Waigaoqiao and Qinbei power plants in Shanghai and Henan, respectively. Then, an improved Gaussian plume model method was applied for CO2 emission estimations, with input parameters including the geographic coordinates of point sources, wind vectors from the atmospheric reanalysis of the global climate, and OCO-2 observations. The application of the Gaussian model was improved by using wind data with higher temporal and spatial resolutions, employing the physically based unit conversion method, and interpolating OCO-2 observations into different resolutions. Consequently, CO2 emissions were estimated to be 23.06 ± 2.82 (95% CI) Mt/yr using the Gaussian model and 16.28 Mt/yr using the bottom-up method for the Waigaoqiao Power Plant, and 14.58 ± 3.37 (95% CI) and 14.08 Mt/yr for the Qinbei Power Plant, respectively. These estimates were compared with three standard databases for validation: the Carbon Monitoring for Action database, the China coal-fired Power Plant Emissions Database, and the Carbon Brief database. The comparison found that previous emission inventories spanning different time frames might have overestimated the CO2 emissions of one of two Chinese power plants on the two days that the measurements were made. Our study contributes to quantifying CO2 emissions from point sources and helps in advancing satellite-based monitoring techniques of emission sources in the future; this helps in reducing errors due to human intervention in bottom-up statistical methods.

scholarly journals Modeling Gamma-Ray SEDs and Angular Extensions of Extreme TeV Blazars from Intergalactic Proton-Initiated Cascades in Contemporary Astrophysical EGMF Models

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 220
Author(s):  
Emil Khalikov
Keyword(s):  
Gamma Rays ◽  
Large Scale ◽  
Gamma Ray ◽  
High Energy ◽  
Cascade Model ◽  
Point Sources ◽  
Spectral Energy ◽  
Observation Data ◽  
Cherenkov Telescopes ◽  
The Universe

The intrinsic spectra of some distant blazars known as “extreme TeV blazars” have shown a hint at an anomalous hardening in the TeV energy region. Several extragalactic propagation models have been proposed to explain this possible excess transparency of the Universe to gamma-rays starting from a model which assumes the existence of so-called axion-like particles (ALPs) and the new process of gamma-ALP oscillations. Alternative models suppose that some of the observable gamma-rays are produced in the intergalactic cascades. This work focuses on investigating the spectral and angular features of one of the cascade models, the Intergalactic Hadronic Cascade Model (IHCM) in the contemporary astrophysical models of Extragalactic Magnetic Field (EGMF). For IHCM, EGMF largely determines the deflection of primary cosmic rays and electrons of intergalactic cascades and, thus, is of vital importance. Contemporary Hackstein models are considered in this paper and compared to the model of Dolag. The models assumed are based on simulations of the local part of large-scale structure of the Universe and differ in the assumptions for the seed field. This work provides spectral energy distributions (SEDs) and angular extensions of two extreme TeV blazars, 1ES 0229+200 and 1ES 0414+009. It is demonstrated that observable SEDs inside a typical point spread function of imaging atmospheric Cherenkov telescopes (IACTs) for IHCM would exhibit a characteristic high-energy attenuation compared to the ones obtained in hadronic models that do not consider EGMF, which makes it possible to distinguish among these models. At the same time, the spectra for IHCM models would have longer high energy tails than some available spectra for the ALP models and the universal spectra for the Electromagnetic Cascade Model (ECM). The analysis of the IHCM observable angular extensions shows that the sources would likely be identified by most IACTs not as point sources but rather as extended ones. These spectra could later be compared with future observation data of such instruments as Cherenkov Telescope Array (CTA) and LHAASO.

Predicting Seepage of Earth Dams Using Neural Network and Genetic Algorithm

2011 ◽  
Vol 403-408 ◽  
pp. 3081-3085 ◽  
Author(s):  
Xin Ying Miao ◽  
Jin Kui Chu ◽  
Jing Qiao ◽  
Ling Han Zhang
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Field Data ◽  
Back Propagation ◽  
Earth Dam ◽  
Earth Dams ◽  
Gradient Descent Algorithm ◽  
Levenberg Marquardt ◽  
Lm Algorithm ◽  
Good Agreement

Measurements of seepage are fundamental for earth dam surveillance. However, it is difficult to establish an effective and practical dam seepage prediction model due to the nonlinearity between seepage and its influencing factors. Genetic Algorithm for Levenberg-Marquardt(GA-LM), a new neural network(NN) model has been developed for predicting the seepage of an earth dam in China using 381 databases of field data (of which 366 in 2008 were used for training and 15 in 2009 for testing). Genetic algorithm(GA) is an ecological system algorithm, which was adopted to optimize the NN structure. Levenberg-Marquardt (LM) algorithm was originally designed to serve as an intermediate optimization algorithm between the Gauss-Newton(GN) method and the gradient descent algorithm, which was used to train NN. The predicted seepage values using GA-LM model are in good agreement with the field data. It is demonstrated here that the model is capable of predicting the seepage of earth dams accurately. The performance of GA-LM has been compared with that of conventional Back-Propagation(BP) algorithm and LM algorithm with trial-and-error approach. The comparison indicates that the GA-LM model can offer stronger and better performance than conventional NNs when used as a quick interpolation and extrapolation tool.

Reducing Nutrient Loads in Northern Irish Catchments: A Modelling Approach Based on Load Apportionment and Flow Pathway Identification

2021 ◽  
Author(s):  
Russell Adams ◽  
Donnacha Doody
Keyword(s):  
Water Quality ◽  
Large Scale ◽  
Agricultural Land ◽  
Assessment Tool ◽  
Ecological Status ◽  
Point Sources ◽  
Load Reduction ◽  
Nutrient Loads ◽  
Flow Pathways ◽  
Flow Pathway

<p>Northern Ireland has been somewhat overlooked in terms of water quality modelling in the past. Many of its catchments have consistently failed to meet Water Framework Directive targets especially due to high levels of dissolved nutrients and poor ecological status. A catchment based modelling study to address this issue has not been undertaken here previously and the approach described here uses two water quality models to achieve this aim. The objectives of the modelling were firstly to identify the total load reductions (in terms of Phosphorus (P)) required to reduce in-stream loadings sufficiently for concentrations of soluble reactive P (SRP) to be reduced to achieve the WFD “Good” status levels, and secondly to split these loadings into diffuse and point components. The third objective was to identify the most likely flow pathways for the transport of the diffuse component of P to the watercourses particularly for the agricultural (mostly intensive grassland farming) land use which dominates in almost all NI catchments.</p><p>The first model applied is the Source Load Apportionment Model (SLAM) developed by the Irish EPA. This model provides a large-scale assessment of the point and diffuse load components across catchments where multiple pressures are occurring. The second model us the Catchment Runoff Flux Assessment Tool (CRAFT) which is able to back-calculate nutrient loads associated with three major flow pathways. SLAM is a static model which uses averaged loadings from diffuse agriculture and non-agricultural land uses, and point sources (where information can be obtained from various sources) to calculate N and P exports. For P, the agricultural diffuse load component uses an enhanced version of the export coefficient approach based on combining the sources of P from applied nutrients (slurry and fertiliser) and soil P. A modelling tool allows the user to evaluate load reduction scenarios where one or several components of P (both point and diffuse) are adjusted downwards to achieve the catchment’s required load reduction. The CRAFT model works on a dynamic (daily) modelling scale and has simulated sub-catchments where the SLAM model has identified the need for significant load reductions. It identifies the different reductions (P export) that are required for each flow pathway, which will then inform on the type of additional measures (e.g. sediment traps, riparian buffer strips and wetlands) that may also be required.</p><p>The initial aim of this study is to complete a pilot application to the trans-border (UK and ROI) Blackwater catchment (1360 km<sup>2</sup>). Through a review of alternative modelling options for the whole area of NI, an assessment of whether this approach is suitable for application to the entire territory can be made.</p>

S *

1984 ◽  
Vol 74 (1) ◽  
pp. 61-78
Author(s):  
P. R. Gutowski ◽  
F. Hron ◽  
D. E. Wagner ◽  
S. Treitel
Keyword(s):  
Field Data ◽  
Shear Waves ◽  
Grazing Incidence ◽  
Point Sources ◽  
Seismic Exploration ◽  
Source Depth ◽  
Positive Maximum ◽  
Elastic Boundary ◽  
Vertical Changes ◽  
Common Situation

Abstract The interesting and common situation of shallow point sources close to the free surface can be modeled using an explicit elastic finite difference procedure. If the source depth is less than the predominant wavelength from the surface or other well-defined elastic boundary, then shear waves S*, are generated with an amplitude which depends strongly on the source depth. As the source depth is decreased, the amplitude of the resulting shear wave increases exponentially and the particle motion is confined to a plane perpendicular to the direction of propagation. These shear waves radiate from a point on the boundary directly above the source with a radiation pattern that is zero at grazing incidence, rises to a positive maximum at about 55° from the vertical, changes polarity, and increases negatively until merging with the PS wave. Since the use of shallow explosive sources for seismic exploration is favorable for the generation of S*, we present a field data case as an illustration.

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