The sensitivity of Born inversion to the choice of reference velocity: A simple example

Geophysics ◽  
1983 ◽  
Vol 48 (1) ◽  
pp. 36-38 ◽  
Author(s):  
A. B. Weglein ◽  
S. H. Gray

We examine the sensitivity of the Born model to the input background velocity. We use a one‐dimensional analytic example to point out the difference between a corrective procedure and merely a perturbative one. We examine various aspects of the sensitivity issue, including the trade‐off between velocity determination and mapping of reflector location. Although this problem is discussed within the context of the Born model, it is an issue common to all perturbative methods (e.g., migration methods) which transform surface reflection data into a map of subsurface reflectors.

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. Q15-Q26 ◽  
Author(s):  
Giovanni Angelo Meles ◽  
Kees Wapenaar ◽  
Andrew Curtis

State-of-the-art methods to image the earth’s subsurface using active-source seismic reflection data involve reverse time migration. This and other standard seismic processing methods such as velocity analysis provide best results only when all waves in the data set are primaries (waves reflected only once). A variety of methods are therefore deployed as processing to predict and remove multiples (waves reflected several times); however, accurate removal of those predicted multiples from the recorded data using adaptive subtraction techniques proves challenging, even in cases in which they can be predicted with reasonable accuracy. We present a new, alternative strategy to construct a parallel data set consisting only of primaries, which is calculated directly from recorded data. This obviates the need for multiple prediction and removal methods. Primaries are constructed by using convolutional interferometry to combine the first-arriving events of upgoing and direct-wave downgoing Green’s functions to virtual receivers in the subsurface. The required upgoing wavefields to virtual receivers are constructed by Marchenko redatuming. Crucially, this is possible without detailed models of the earth’s subsurface reflectivity structure: Similar to the most migration techniques, the method only requires surface reflection data and estimates of direct (nonreflected) arrivals between the virtual subsurface sources and the acquisition surface. We evaluate the method on a stratified synclinal model. It is shown to be particularly robust against errors in the reference velocity model used and to improve the migrated images substantially.


Geophysics ◽  
1984 ◽  
Vol 49 (1) ◽  
pp. 54-59 ◽  
Author(s):  
Samuel H. Gray

Two distinct approaches to solving the one‐dimensional seismic inverse problem are compared. These are (1) the “direct” method of Goupillaud (1961), applied to discretely varying media, and (2) the “iterative” methods of Gjevik et al (1976), or Gray and Hagin (1982), applied to discretely or continuously varying media. These two approaches are shown to be equivalent in two important respects. First, each method can be recovered from the other [e.g., the discretized version of the iterative methods yields the same set of equations as the direct method]. Second, because of the first equivalence, each method uses the same amount of information in reconstructing a profile to a certain depth z or traveltime τ into the medium. This information is the reflection data received for times less than 2τ. In particular, neither approach uses the “redundant data” received after time 2T in an inversion for a profile which is known to vary only for depths which correspond to traveltime T. In this sense the methods are as economical as possible, using the minimum amount of information required to solve the idealized problem. The key to relating the discrete, direct inversion to the continuous, iterative inversion is the Bremmer (1951) series for the reflected wave field. By using this series, it is possible to show that the equivalent inversion methods invert the same equation for the unknown acoustic impedance variations. The difference in the approaches used to solve this equation is analogous to the difference between solving a system of linear equations “directly” or “iteratively.”


2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.


1976 ◽  
Vol 54 (14) ◽  
pp. 1454-1460 ◽  
Author(s):  
T. Tiedje ◽  
R. R. Haering

The theory of ultrasonic attenuation in metals is extended so that it applies to quasi one and two dimensional electronic systems. It is shown that the attenuation in such systems differs significantly from the well-known results for three dimensional systems. The difference is particularly marked for one dimensional systems, for which the attenuation is shown to be strongly temperature dependent.


2018 ◽  
Vol 29 (10) ◽  
pp. 1850093
Author(s):  
ShengJie Qiang ◽  
Bin Jia ◽  
QingXia Huang

The asymmetric simple exclusion process (ASEP) is a paradigmatic model for nonequilibrium systems and has been used in many applications. Airplane boarding provides another interesting example where this framework can be applied. We propose a simple model for boarding process, in which a particle moves along a one-dimensional aisle after being injected, and finally is removed at a reserved site. Different from the typical ASEP model, particles are removed in a disorderly or a parallel way. Detailed calculations and discussions of some related characteristics, such as mean boarding time and parallelism indicator, are provided based on Monte-Carlo simulations. Results show that three phases exist in the boarding process: free-flow, jamming and maximum current. Transitions between these phases are governed by the difference between the injection and removal rate. Further analysis shows how the scaling behavior depends on the system size and the boarding conditions. Those results emphasize the importance of utilizing the whole length of the aisle to reduce the boarding time when designing an efficient boarding strategy.


Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2428 ◽  
Author(s):  
Fei Shen ◽  
Linsong Cheng ◽  
Qiang Sun ◽  
Shijun Huang

Recently, commingling production has been widely used for the development of offshore heavy oil reservoirs with multilayers. However, the differences between layers in terms of reservoir physical properties, oil properties and pressure have always resulted in interlayer interference, which makes it more difficult to evaluate the producing degree of commingled production. Based on the Buckley–Leverett theory, this paper presents two theoretical models, a one-dimensional linear flow model and a planar radial flow model, for water-flooded multilayer reservoirs. Through the models, this paper establishes a dynamic method to evaluate seepage resistance, sweep efficiency and recovery percent and then conducts an analysis with field data. The result indicates the following: (1) the dynamic difference in seepage resistance is an important form of interlayer interference during the commingled production of an offshore multilayer reservoir; (2) the difference between commingled production and separated production is small within a certain range of permeability ratio or viscosity ratio, but separated production should be adopted when the ratio exceeds a certain value.


2015 ◽  
Vol 31 ◽  
pp. 23 ◽  
Author(s):  
Evelyn Sample ◽  
Marije Michel

Studying task repetition for adult and young foreign language learners of English (EFL) has received growing interest in recent literature within the task-based approach (Bygate, 2009; Hawkes, 2012; Mackey, Kanganas, & Oliver, 2007; Pinter, 2007b). Earlier work suggests that second language (L2) learners benefit from repeating the same or a slightly different task. Task repetition has been shown to enhance fluency and may also add to complexity or accuracy of production. However, few investigations have taken a closer look at the underlying relationships between the three dimensions of task performance: complexity, accuracy, and fluency (CAF). Using Skehan’s (2009) trade-off hypothesis as an explanatory framework, our study aims to fill this gap by investigating interactions among CAF measures. We report on the repeated performances on an oral spot- the-difference task by six 9-year-old EFL learners. Mirroring earlier work, our data reveal significant increases of fluency through task repetition. Correlational analyses show that initial performances that benefit in one dimension come at the expense of another; by the third performance, however, trade-off effects disappear. Further qualitative explanations support our interpretation that with growing task-familiarity students are able to focus their attention on all three CAF dimensions simultaneously.Au sein de la littérature relative à l’approche fondée sur les tâches, on évoque de plus en plus d’études portant sur la répétition des tâches pour l’enseignement de l’anglais langue étrangère aux jeunes et aux adultes (Bygate, 2009; Hawkes, 2012; Mackey, Kanganas, & Oliver, 2007; Pinter, 2007b). Des études antérieures semblent indiquer que les apprenants en L2 profitent de la répétition de la même tâche ou d’une tâche légèrement différente. Il a été démontré que la répétition des tâches améliore la fluidité et qu’elle pourrait augmenter la complexité ou la précision de la production. Toutefois, peu d’études se sont penchées davantage sur les relations sous-jacentes entre les trois dimensions de l’exécution des tâches : la complexité, la précision et la fluidité. S’appuyant sur l’hypothèse du compromis de Skehan (2009) comme cadre explicatif, notre étude vise à combler cette lacune en examinant les interactions entre les mesures de ces trois éléments. Nous faisons rapport du rendement de six jeunes âgés de 9 ans qui apprennent l’anglais comme langue étrangère alors qu’ils répètent une tâche impliquant l’identification de différences. Nos données reproduisent les résultats de travaux antérieurs en ce qu’elles révèlent une amélioration significative de la fluidité par la répétition de tâches. Des analyses corrélationnelles indiquent que l’amélioration d’une dimension lors des exécutions initiales se fait aux dépens d’une autre; cet effet de compromis disparait, toutefois, à la troisième exécution. Des explications quali- tatives supplémentaires viennent appuyer notre interprétation selon laquelle la familiarité croissante que ressentent les élèves avec une tâche leur permet de se concentrer sur les trois dimensions (complexité, précision et fluidité) à la fois.


2016 ◽  
Author(s):  
Miriam C Klein-Flügge ◽  
Steven W Kennerley ◽  
Karl Friston ◽  
Sven Bestmann

AbstractIntegrating costs and benefits is crucial for optimal decision-making. While much is known about decisions that involve outcome-related costs (e.g., delay, risk), many of our choices are attached to actions and require an evaluation of the associated motor costs. Yet how the brain incorporates motor costs into choices remains largely unclear. We used human functional magnetic resonance imaging during choices involving monetary reward and physical effort to identify brain regions that serve as a choice comparator for effort-reward trade-offs. By independently varying both options' effort and reward levels, we were able to identify the neural signature of a comparator mechanism. A network involving supplementary motor area (SMA) and the caudal portion of dorsal anterior cingulate cortex (dACC) encoded the difference in reward (positively) and effort levels (negatively) between chosen and unchosen choice options. We next modelled effort-discounted subjective values using a novel behavioural model. This revealed that the same network of regions involving dACC and SMA encoded the difference between the chosen and unchosen options' subjective values, and that activity was best described using a concave model of effort-discounting. In addition, this signal reflected how precisely value determined participants' choices. By contrast, separate signals in SMA and ventro-medial PFC (vmPFC) correlated with participants' tendency to avoid effort and seek reward, respectively. This suggests that the critical neural signature of decision-making for choices involving motor costs is found in human cingulate cortex and not vmPFC as typically reported for outcome-based choice. Furthermore, distinct frontal circuits ‘drive’ behaviour towards reward-maximization and effort-minimization.Significance StatementThe neural processes that govern the trade-off between expected benefits and motor costs remain largely unknown. This is striking because energetic requirements play an integral role in our day-to-day choices and instrumental behaviour, and a diminished willingness to exert effort is a characteristic feature of a range of neurological disorders. We use a new behavioural characterization of how humans trade-off reward-maximization with effort-minimization to examine the neural signatures that underpin such choices, using BOLD MRI neuroimaging data. We find the critical neural signature of decision-making, a signal that reflects the comparison of value between choice options, in human cingulate cortex, whereas two distinct brain circuits ‘drive’ behaviour towards reward-maximization or effort-minimization.


2009 ◽  
Vol 8 (3) ◽  
pp. 943-950
Author(s):  
Norihiro TANAKA ◽  
Jae-Yong WOO ◽  
Tomohiro SARASHINA ◽  
Kosuke MOCHIZUKI

2016 ◽  
Vol 72 (8) ◽  
pp. 1214-1218 ◽  
Author(s):  
Montserrat Alfonso ◽  
Helen Stoeckli-Evans

The isotypic title one-dimensional coordination polymers, [CdCl2(C18H14N4O4)]n, (I), and [HgCl2(C18H14N4O4)]n, (II), are, respectively, the cadmium(II) and mercury(II) complexes of the dimethyl ester of 5,6-bis(pyridin-2-yl)pyrazine-2,3-dicarboxylic acid. In both compounds, the metal ions are located on a twofold rotation axis and a second such axis bisects the Car—Carbonds of the pyrazine ring. The metal ions are bridged by binding to the N atoms of the two pyridine rings and have anMN2Cl2bisphenoidal coordination geometry. The metal–Npyrazinedistances are much longer than the metal–Npyridinedistances; the difference is 0.389 (2) Å for the Cd—N bonds but only 0.286 (5) Å for the Hg—N bond lengths. In the crystals of both compounds, the polymer chains are linkedviapairs of C—H...Cl hydrogen bonds, forming corrugated slabs parallel to theacplane.


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