Plane‐layer prestack inversion in the presence of surface reverberation

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1789-1800 ◽  
Author(s):  
Alastair D. McAulay
Keyword(s):  
Velocity Profile ◽  
Reference Data ◽  
Jacobian Matrix ◽  
High Surface ◽  
Synthetic Data ◽  
Surface Effects ◽  
Plane Layer ◽  
Linear Inversion ◽  
Band Limited ◽  
Shallow Strata

Experiments with synthetic data have indicated that generalized linear inversion may be used to estimate compressional velocities as a function of depth with high resolution directly from band‐limited, unstacked data. The ocean surface was not included in these experiments. In the presence of strong surface multiples, inversion is expected to take longer and be less accurate, because events from multiple surface reflections overlie primary events and normally have differing moveout. Existing velocity‐analysis techniques rely on the ability of an observer to make the difficult distinction between multiples and primaries. Equations are provided for adding the surface to the inversion procedure. This involves adding the surface effects to the Jacobian matrix as well as to the forward modeling procedure. To speed computation, the addition of the surface effects to the Jacobian matrix is delayed until after the matrix has been multiplied by a vector in the linear‐equation solution. Absorption is added to the inversion to represent the real world more closely and to improve computation speed by reducing sampling requirements. Realistic synthetic band‐limited data with high surface reverberation content were generated from a well‐log velocity profile. The inversion recovered the velocity profile to within 3 percent when a velocity increasing linearly with depth was used as a starting profile. The error in the model‐generated seismogram converges from 100 percent to within 2 percent of the reference data. The positions of interfaces are located more accurately at greater depths than at shallower depths because more sensors are observing deep strata than shallow strata. Convergence is to within 0.1 percent of that of the reference data at the maximum depth. The computation required 25 iterations and a total time of 66 hours on a DEC VAX 11/780. Reducing this time should be possible. In a preliminary study of the effects of noise, additive Gaussian noise was seen to limit the accuracy of the velocity estimate monotonically as the variance of the added noise was increased.

Colored and linear inversions to relative acoustic impedance

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. N15-N27 ◽  
Author(s):  
Carlos A. M. Assis ◽  
Henrique B. Santos ◽  
Jörg Schleicher
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Computational Cost ◽  
Synthetic Data ◽  
Seismic Source ◽  
Alternative Methods ◽  
Well Log ◽  
Linear Inversion ◽  
Amplitude Inversion ◽  
Band Limited

Acoustic impedance (AI) is a widely used seismic attribute in stratigraphic interpretation. Because of the frequency-band-limited nature of seismic data, seismic amplitude inversion cannot determine AI itself, but it can only provide an estimate of its variations, the relative AI (RAI). We have revisited and compared two alternative methods to transform stacked seismic data into RAI. One is colored inversion (CI), which requires well-log information, and the other is linear inversion (LI), which requires knowledge of the seismic source wavelet. We start by formulating the two approaches in a theoretically comparable manner. This allows us to conclude that both procedures are theoretically equivalent. We proceed to check whether the use of the CI results as the initial solution for LI can improve the RAI estimation. In our experiments, combining CI and LI cannot provide superior RAI results to those produced by each approach applied individually. Then, we analyze the LI performance with two distinct solvers for the associated linear system. Moreover, we investigate the sensitivity of both methods regarding the frequency content present in synthetic data. The numerical tests using the Marmousi2 model demonstrate that the CI and LI techniques can provide an RAI estimate of similar accuracy. A field-data example confirms the analysis using synthetic-data experiments. Our investigations confirm the theoretical and practical similarities of CI and LI regardless of the numerical strategy used in LI. An important result of our tests is that an increase in the low-frequency gap in the data leads to slightly deteriorated CI quality. In this case, LI required more iterations for the conjugate-gradient least-squares solver, but the final results were not much affected. Both methodologies provided interesting RAI profiles compared with well-log data, at low computational cost and with a simple parameterization.

Frequency‐wavenumber elastic inversion of marine seismic data

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1868-1881 ◽  
Author(s):  
Huasheng Zhao ◽  
Bjørn Ursin ◽  
Lasse Amundsen
Keyword(s):  
Wave Velocity ◽  
Reference Data ◽  
Jacobian Matrix ◽  
Synthetic Data ◽  
Velocity Model ◽  
P Wave ◽  
Stratified Medium ◽  
Inversion Method ◽  
S Wave ◽  
Time Space

We present an inversion method for determining the velocities, densities, and layer thicknesses of a horizontally stratified medium with an acoustic layer at the top and a stack of elastic layers below. The multioffset reflection response of the medium generated by a compressional point source is transformed from the time‐space domain into the frequency‐wavenumber domain where the inversion is performed by minimizing the difference between the reference data and the modeled data using a least‐squares technique. The forward modeling is based on the reflectivity method where the solution for each frequency‐wavenumber component is found by computing the generalized reflection and transmission matrices recursively. The gradient of the objective function is computed from analytical expressions of the Jacobian matrix derived directly from the recursive modeling equations. The partial derivatives of the reflection response of the stratified medium are then computed simultaneously with the reflection response by layer‐recursive formulas. The limited‐aperture and discretization effects in time and space of the reference data are included by applying a pair of frequency and wavenumber dependent filters to the predicted data and to the Jacobian matrix at each iteration. Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorily reconstructs the elastic parameters of a stratified medium. The low‐frequency trends of the S‐wave velocity and density are found when the initial P‐wave velocity model gives approximately correct traveltimes. The convergence of the iterative minimization algorithm is fast.

Prestack inversion with plane‐layer point source modeling

Geophysics ◽  
1985 ◽  
Vol 50 (1) ◽  
pp. 77-89 ◽  
Author(s):  
Alastair D. McAulay
Keyword(s):  
Velocity Profile ◽  
Point Source ◽  
Spherical Wave ◽  
Normal Incidence ◽  
Plane Layer ◽  
Source Modeling ◽  
Low Frequencies ◽  
Prestack Inversion ◽  
Band Limited

Prestack inversion with point‐source plane‐layer modeling has many advantages over poststack or normal incidence inversion. For example, it permits the determination of absolute compressional and shear velocities, density variations, and the accurate accounting of interbed and surface multiples. I neglect shear effects in this paper by assuming that they are adequately suppressed by velocity filtering. In the forward modeling step, a spherical wave expansion into plane waves is used to account for the point source. The plane‐wave reflection response for a set of plane layers is extended to the nonnormal incidence case. I use a Hankel transform to account for cylindrical symmetry. Generalized linear inversion is used because the fast recursive approaches available for normal incidence inversion are no longer applicable. I provide the derivation for the required derivative matrix, and I take into account the band‐limited nature of the data in frequency, time, and space. I demonstrate that moveout of events on realistic simulated prestack data enables the determination of absolute compressional velocity in the velocity‐depth profile, even though the data are band‐limited in frequency. I assume that preprocessing has adequately removed the shear and surface effects and that density is constant. Low frequencies in the velocity profile may be obtained more accurately than with velocity analysis used for stacking, because interbed multiples and other modeling phenomena are accounted for in the computation. Autoregressive modeling procedures that predict into the low frequencies of the velocity profile are also less accurate and cannot generate absolute velocity. I suggest future research leading to cost‐effective inversion of real data.

scholarly journals Reference Measurements in Developing UAV Systems for Detecting Pests, Weeds, and Diseases

2021 ◽  
Vol 13 (7) ◽  
pp. 1238
Author(s):  
Jere Kaivosoja ◽  
Juho Hautsalo ◽  
Jaakko Heikkinen ◽  
Lea Hiltunen ◽  
Pentti Ruuttunen ◽  
...  
Keyword(s):  
Reference Data ◽  
Measurement Techniques ◽  
Synthetic Data ◽  
Ground Truth ◽  
Precision Farming ◽  
Aerial Imaging ◽  
Aerial Vehicle ◽  
Uav Images ◽  
Reference Measurements

The development of UAV (unmanned aerial vehicle) imaging technologies for precision farming applications is rapid, and new studies are published frequently. In cases where measurements are based on aerial imaging, there is the need to have ground truth or reference data in order to develop reliable applications. However, in several precision farming use cases such as pests, weeds, and diseases detection, the reference data can be subjective or relatively difficult to capture. Furthermore, the collection of reference data is usually laborious and time consuming. It also appears that it is difficult to develop generalisable solutions for these areas. This review studies previous research related to pests, weeds, and diseases detection and mapping using UAV imaging in the precision farming context, underpinning the applied reference measurement techniques. The majority of the reviewed studies utilised subjective visual observations of UAV images, and only a few applied in situ measurements. The conclusion of the review is that there is a lack of quantitative and repeatable reference data measurement solutions in the areas of mapping pests, weeds, and diseases. In addition, the results that the studies present should be reflected in the applied references. An option in the future approach could be the use of synthetic data as reference.

Automatic estimation of large residual statics corrections

Geophysics ◽  
1986 ◽  
Vol 51 (2) ◽  
pp. 332-346 ◽  
Author(s):  
Daniel H. Rothman
Keyword(s):  
Monte Carlo ◽  
Statistical Mechanics ◽  
Probability Distributions ◽  
Synthetic Data ◽  
Linear Inversion ◽  
Traveltime Inversion ◽  
Automatic Estimation ◽  
Crucial Component ◽  
Practical Algorithm ◽  
Overthrust Belt

Conventional approaches to residual statics estimation obtain solutions by performing linear inversion of observed traveltime deviations. A crucial component of these procedures is picking time delays; gross errors in these picks are known as “cycle skips” or “leg jumps” and are the bane of linear traveltime inversion schemes. This paper augments Rothman (1985), which demonstrated that the estimation of large statics in noise‐contaminated data is posed better as a nonlinear, rather than as a linear, inverse problem. Cycle skips then appear as local (secondary) minima of the resulting nonlinear optimization problem. In the earlier paper, a Monte Carlo technique from statistical mechanics was adapted to perform global optimization, and the technique was applied to synthetic data. Here I present an application of a similar Monte Carlo method to field data from the Wyoming Overthrust belt. Key changes, however, have led to a more efficient and practical algorithm. The new technique performs explicit crosscorrelation of traces. Instead of picking the peaks of these crosscorrelation functions, the method transforms the crosscorrelation functions to probability distributions and then draws random numbers from the distributions. Estimates of statics are now iteratively updated by this procedure until convergence to the optimal stack is achieved. Here I also derive several theoretical properties of the algorithm. The method is expressed as a Markov chain, in which the equilibrium (steady‐state) distribution is the Gibbs distribution of statistical mechanics.

Feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band-limited reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R57-R74 ◽  
Author(s):  
Santi Kumar Ghosh ◽  
Animesh Mandal
Keyword(s):  
First Principles ◽  
Acoustic Impedance ◽  
Linear Equations ◽  
Synthetic Data ◽  
Reflection Coefficients ◽  
Limited Data ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Impedance Profile ◽  
Band Limited

Because seismic reflection data are band limited, acoustic impedance profiles derived from them are nonunique. The conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients. By making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers, we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data. Drawing only on first principles, the Zoeppritz equation in this case, the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band-limited data. The local layer-cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness, provided that the objective is to reconstruct a smooth version of the impedance profile that includes only its crude structures. Tests on synthetic data generated from elementary models and from measured logs of acoustic impedance demonstrated the efficacy of the method, even when a significant amount of noise was added to the data. The emergence of consistent estimates of impedance, approximating the original impedance, from synthetic data generated for several frequency bands has inspired our confidence in the method. The other attractive outputs of the method are as follows: (1) an accurate estimate of the impedance mean, (2) an accurate reconstruction of the direct-current (DC) frequency of the reflectivity, and (3) an acceptable reconstruction of the broad outline of the original impedance profile. These outputs can serve as constraints for either more refined inversions or geologic interpretations. Beginning from the restriction of band-limited data, we have devised a method that neither requires a starting input model nor imposes mathematical constraints on the earth reflectivity and still yielded significant and relevant geologic information.

Depth-domain seismic reflectivity inversion with compressed sensing technique

2017 ◽  
Vol 5 (1) ◽  
pp. T1-T9 ◽  
Author(s):  
Rui Zhang ◽  
Kui Zhang ◽  
Jude E. Alekhue
Keyword(s):  
Compressed Sensing ◽  
Time Domain ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Synthetic Data ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Depth Migration ◽  
Band Limited ◽  
The Time Domain

More and more seismic surveys produce 3D seismic images in the depth domain by using prestack depth migration methods, which can present a direct subsurface structure in the depth domain rather than in the time domain. This leads to the increasing need for applications of seismic inversion on the depth-imaged seismic data for reservoir characterization. To address this issue, we have developed a depth-domain seismic inversion method by using the compressed sensing technique with output of reflectivity and band-limited impedance without conversion to the time domain. The formulations of the seismic inversion in the depth domain are similar to time-domain methods, but they implement all the elements in depth domain, for example, a depth-domain seismic well tie. The developed method was first tested on synthetic data, showing great improvement of the resolution on inverted reflectivity. We later applied the method on a depth-migrated field data with well-log data validated, showing a great fit between them and also improved resolution on the inversion results, which demonstrates the feasibility and reliability of the proposed method on depth-domain seismic data.

Influence of Defects on the Young's Modulus of [110] Silicon Nanowires with Different Cross Sections

2015 ◽  
Vol 645-646 ◽  
pp. 151-156
Author(s):  
Fang Gu ◽  
Jia Hong Zhang ◽  
Min Li ◽  
Lin Yan Liu ◽  
Jing Su
Keyword(s):  
Young’S Modulus ◽  
Cross Sections ◽  
Silicon Nanowires ◽  
Surface Defects ◽  
Young's Modulus ◽  
High Surface ◽  
Surface Effects ◽  
Native Oxide ◽  
Native Oxide Layer ◽  
Induced Defects

The size dependence becomes more significant as the devices scale down from micro-to nanodimensions, which is generally attributed to surface effects due to the very high surface-to-bulk ratios in nanoscale structures. However, significant discrepancies between experimental measurements and computational studies indicate that there could be other influences besides surface effects, such as the influences of native oxide layer, fabrication-induced defects and boundary conditions. In this paper, our purpose is to investigate mainly the influence of fabrication-induced defects on the elasticity of [110] silicon nanowires (SiNWs) with different cross sections. We accomplish this by using the molecular dynamics (MD) simulation. Our MD results show that the H-passivated [110] SiNWs without surface defects is slightly elastically softer than bulk, which is in good agreement with other literature MD values. However, the effective Young’s modulus of SiNWs with surface defects can significantly decreases as the defects increase. This softening behavior of [110] SiNWs is severe, which indicates the importance of surface defects. It is noted that the influence of defects on the Young's Modulus of SiNWs strongly depended on the distribution and morphology of defects as well as the cross-sectional shapes of SiNWs. It is observed that the influence of defects on square SiNWs is significantly different from those of hexagonal and triangle SiNWs. Our work reveals that fabrication-induced surface defects could be one of the important origins of the reduced effective Young’s modulus experimentally observed in ultra-thin SiNWs. Therefore, the effect of defects on the characterization of the mechanical properties of nanowire must be carefully considered.

scholarly journals PEMODELAN INVERSI DATA MAGNETOTELLURIK 1-D MENGGUNAKAN METODA GENETIC ALGORITHM (GA) DENGAN POPULASI MICRO GENETIC ALGORITHM KASUS 3 LAYER DAN 5 LAYER

2019 ◽  
Vol 8 (2) ◽  
pp. 167-180
Author(s):  
Nia Maharani
Keyword(s):  
Genetic Algorithm ◽  
Natural Selection ◽  
Selection Process ◽  
Synthetic Data ◽  
Inversion Method ◽  
Earth Model ◽  
Observation Data ◽  
Linear Inversion ◽  
Synthetic Model ◽  
Micro Genetic Algorithm

This paper discusses non-linear inversion method with Genetic Algorithm (GA) which inspired by natural selection process (survival for the fittest) and genetic using 20 populations (micro genetic algorithm). The method is applied to 1-D magnetotelluric inverted data with model parameter is resistivity as a function of depth. This research only uses synthetic data obtained from synthetic model. The model is homogeneous earth model with 3 and 5 layers. Perturbation of model is performed until minimum misfit between theoritical and observation data achieved. The 3 layers and 5 layers inversion processes are applied to 3 layers and 5 layers earth model respectively, with satisfactory results in other words it can reproduce the synthetic model.

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