A method for direct estimation of interval velocities

Geophysics ◽  
1982 ◽  
Vol 47 (12) ◽  
pp. 1657-1671 ◽  
Author(s):  
Philip S. Schultz
Keyword(s):  
Estimation Procedure ◽  
Estimation Accuracy ◽  
Substantial Contribution ◽  
Interval Velocity ◽  
Direct Estimation ◽  
Enhanced Resolution ◽  
Prior Estimate ◽  
Sensitive Function ◽  
Interval Velocities ◽  
Ray Parameter

The most commonly used method for obtaining interval velocities from seismic data requires a prior estimate of the root‐mean‐square (rms) velocity function. A reduction to interval velocity uses the Dix equation, where the interval velocity in a layer emerges as a sensitive function of the rms velocity picks above and below the layer. Approximations implicit in this method are quite appropriate for deep data, and they do not contribute significantly to errors in the interval velocity estimate. However, when the data are from a shallow depth (vertical two‐way traveltime being less than direct arrival to the farthest geophone), the assumption within the rms approximation that propagation angles are small requires that much of the reflection energy be muted, along with, of course, all the refraction energy. By means of a simple data transformation to the ray parameter domain via the slanted plane‐wave stack, three types of arrivals from any given interface (subcritical and supercritical reflections and critical refractions) become organized into a single elliptical trajectory. Such a trajectory replaces the composite hyperbolic and linear moveouts in the offset domain (for reflections and critical refractions, respectively). In a layered medium, the trajectory of all but the first event becomes distorted from a true ellipse into a pseudo‐ellipse. However, by a computationally simple layer stripping operation involving p‐dependent time shifts, the interval velocity in each layer can be estimated in turn and its distorting effect removed from underlying layers, permitting a direct estimation of interval velocities for all layers. Enhanced resolution and estimation accuracy are achieved because previously neglected wide‐angle arrivals, which do not conform to the rms approximation, make a substantial contribution in the estimation procedure.

Derivation of seismic cone interval velocities utilizing forward modeling and the downhill simplex method

2002 ◽  
Vol 39 (5) ◽  
pp. 1181-1192 ◽  
Author(s):  
Erick J Baziw
Keyword(s):  
Elastic Constants ◽  
Simplex Method ◽  
Forward Modeling ◽  
S Wave ◽  
Cone Penetration ◽  
Interval Velocity ◽  
Wave Velocities ◽  
Downhill Simplex Method ◽  
Downhill Simplex ◽  
Interval Velocities

The seismic cone penetration test (SCPT) has proven to be a very valuable geotechnical tool in facilitating the determination of low strain (<10–4%) in situ compression (P) and shear (S) wave velocities. The P- and S-wave velocities are directly related to the soil elastic constants of Poisson's ratio, shear modulus, bulk modulus, and Young's modulus. The accurate determination of P- and S-wave velocities from the recorded seismic cone time series is of paramount importance to the evaluation of reliable elastic constants. Furthermore, since the shear and compression wave velocities are squared in deriving the elastic constants, small variations in the estimated velocities can cause appreciable errors. The standard techniques implemented in deriving SCPT interval velocities rely upon obtaining reference P- and S-wave arrival times as the probe is advanced into the soil profile. By assuming a straight ray travel path from the source to the SCPT seismic receiver and calculating the relative reference arrival time differences, interval SCPT velocities are obtained. The forward modeling – downhill simplex method (FMDSM) outlined in this paper offers distinct advantages over conventional SCPT velocity profile estimation methods. Some of these advantages consist of the allowance of ray path refraction, greater sophistication in interval velocity determination, incorporation of measurement weights, and meaningful interval velocity accuracy estimators.Key words: seismic cone penetration testing (SCPT), downhill simplex method (DSM), forward modeling, Fermat's principle, weighted least squares (l2 norm), cost function.

THE REFRACTION SEISMOGRAPH IN THE ALBERTA FOOTHILLS

Geophysics ◽  
1956 ◽  
Vol 21 (3) ◽  
pp. 828-838 ◽  
Author(s):  
G. J. Blundun
Keyword(s):  
Operating Conditions ◽  
Radio Communication ◽  
Interval Velocity ◽  
Mississippian Limestone ◽  
Interval Velocities ◽  
Definition Of ◽  
Characteristic Interval ◽  
Consequent Improvement ◽  
Continuous Determination

In the Alberta foothills the most valuable use of the refraction seismograph is for the definition of overthrust faulting in the Mississippian limestone which is overlain by a faulted, overthrust, and overturned Cretaceous section. Normally, two refracted arrivals are recorded with characteristic interval velocities of 14,000 ft/sec and 21,000 ft/sec, the former arising from an unknown Cretaceous marker, and the latter from the Mississippian. In contrast to a shot‐range of 65,000 ft required to record the refracted arrival from the Mississippian at a depth of 10,000 ft as the first event, a range of 20,000 ft permits recording it as the later event, with consequent improvement in the quality and reliability of the data, reduces the amount of surveying required together with smaller dynamite charges, and improves radio communication. A geophone spread of 6,300 ft with single geophones at 300 ft intervals recorded on 22 traces is recommended. Both in‐line and broadside refraction with the Mississippian arrival recorded as the later event have been used successfully with certain advantages to each method. The former permits continuous determination of the interval velocity of the refracted events as well as providing two‐way control; the latter is considerably faster, and often faulting may be observed directly on the seismograms without reduction of the data. Specimen seismograms are included to illustrate the two methods. Field operating conditions pertaining to survey tolerances, shot formation, size of dynamite charges, the weathering shot as a polarity check, filtering, geophone frequency, and costs are discussed.

SEISMIC SIGNATURES OF SEDIMENTATION MODELS

Geophysics ◽  
1972 ◽  
Vol 37 (1) ◽  
pp. 45-58 ◽  
Author(s):  
J. C. Harms ◽  
P. Tackenberg
Keyword(s):  
Cross Sections ◽  
Quality Data ◽  
Interval Velocity ◽  
Reflection Seismic ◽  
Depositional Processes ◽  
Velocity Changes ◽  
Interval Velocities ◽  
Processing Techniques ◽  
Direct Location ◽  
Stratigraphic Sequences

Seismic techniques have been used mainly for structural interpretation, but mounting interest in stratigraphic applications is evident. Estimation of sand‐shale ratios from seismically derived average velocities is a recent example of a stratigraphic application. Except in the case of tall pinnacle reefs, today direct location of stratigraphic traps by reflection methods is restricted, at best, to areas of very high quality data and abundant well control. However, it may be possible to interpret some useful stratigraphic characteristics from seismic reflections, the interpretation being based upon the concept of sedimentation models. Most stratigraphic sequences are not random stacks of various lithologies. Commonly, they are well organized and have units with characteristic contacts, thicknesses, lateral extents, lateral facies changes, and vertical sequence. These orderly characteristics are summarized in sedimentation models, where the control of lithologic distribution by dominant depositional processes is emphasized. Three sedimentation models for sandstone and shale sequences are presented. For each, one example is described and converted to a synthetic reflection seismic cross‐section. These cross‐sections are each distinct in terms of reflection polarities, areal changes in reflection amplitudes, continuity of events, and lateral interval velocity changes. The simplified models, although limited in their scope, suggest that additional stratigraphic information can be gleaned from reflection seismic data. To exploit this promise, record processing techniques that emphasize recognition of reflection polarities, amplitudes, continuity, and interval velocities must be developed or improved. It is also necessary to improve our knowledge of seismic boundaries in a variety of stratigraphic sequences. Though difficult, these valuable goals appear attainable.

INTERVAL VELOCITIES FROM SURFACE MEASUREMENTS IN THE THREE‐DIMENSIONAL PLANE LAYER CASE

Geophysics ◽  
1976 ◽  
Vol 41 (2) ◽  
pp. 233-242 ◽  
Author(s):  
Peter Hubral
Keyword(s):  
Three Dimensional ◽  
Normal Incidence ◽  
Plane Layer ◽  
Three Dimensions ◽  
Seismic Parameters ◽  
Interval Velocity ◽  
Common Depth Point ◽  
Measured Time ◽  
Surface Measurements ◽  
Interval Velocities

The basic requirements to recover plane layers of constant interval velocity, arbitrary dip and strike from common depth point (CDP) recordings are the following four quantities related to the primary event of each reflector at the common midpoint of a CDP profile: a) Two‐way normal time b) Normal moveout velocity within one arbitrary CDP profile c) Time slope of normally reflected rays within the profile d) Time slope of normally reflected rays in some other direction. The solution of the inverse problem is obtained directly. The moveout velocity is expressed in terms of seismic parameters along the normal incidence path in three dimensions and the direction of the profile within the free surface. A formula connecting dip and strike of the emerging normal ray with the measured time gradients is given and discussed. The method includes, as a special case, the Dix formulas for plane parallel layers.

scholarly journals Adaptive Fifth-Degree Cubature Information Filter for Multi-Sensor Bearings-Only Tracking

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3241 ◽  
Author(s):  
Haonan Jiang ◽  
Yuanli Cai
Keyword(s):  
Information Filtering ◽  
Estimation Procedure ◽  
Estimation Accuracy ◽  
Selection Strategy ◽  
Bayesian Filtering ◽  
Process Noise ◽  
Covariance Matching ◽  
Information Filter ◽  
Cubature Kalman Filter ◽  
Noise Covariance

Standard Bayesian filtering algorithms only work well when the statistical properties of system noises are exactly known. However, this assumption is not always plausible in real target tracking applications. In this paper, we present a new estimation approach named adaptive fifth-degree cubature information filter (AFCIF) for multi-sensor bearings-only tracking (BOT) under the condition that the process noise follows zero-mean Gaussian distribution with unknown covariance. The novel algorithm is based on the fifth-degree cubature Kalman filter and it is constructed within the information filtering framework. With a sensor selection strategy developed using observability theory and a recursive process noise covariance estimation procedure derived using the covariance matching principle, the proposed filtering algorithm demonstrates better estimation accuracy and filtering stability. Simulation results validate the superiority of the AFCIF.

Velocity analysis without picking

Geophysics ◽  
1989 ◽  
Vol 54 (2) ◽  
pp. 191-199 ◽  
Author(s):  
John L. Toldi
Keyword(s):  
Field Data ◽  
Velocity Model ◽  
Point Of View ◽  
Velocity Analysis ◽  
Lateral Variation ◽  
Data Set ◽  
Initial Interval ◽  
Analysis Algorithm ◽  
Interval Velocity ◽  
Interval Velocities

Conventionally, interval velocities are derived from picked stacking velocities. The velocity‐analysis algorithm proposed in this paper is also based on stacking velocities; however, it eliminates the conventional picking stage by always considering stacking velocities from the point of view of an interval‐velocity model. This view leads to a model‐based, automatic velocity‐analysis algorithm. The algorithm seeks to find an interval‐velocity model such that the stacking velocities calculated from that model give the most powerful stack. An additional penalty is incurred for models that differ in smoothness from an initial interval‐velocity model. The search for the best model is conducted by means of a conjugate‐gradient method. The connection between the interval‐velocity model and the stacking velocities plays an important role in the algorithm proposed in this paper. In the simplest case, stacking velocity is assumed to be equal to rms velocity. For the more general case, a linear theory is developed, connecting interval velocity and stacking velocity through the intermediary of traveltime. When applied to a field data set, the method produces an interval‐velocity model that explains the lateral variation in both stacking velocity and traveltime.

1-D seismic inversion of dual wavefield data: Part I, Nonuniqueness and stability

Geophysics ◽  
1994 ◽  
Vol 59 (5) ◽  
pp. 782-788 ◽  
Author(s):  
Steve T. Hildebrand ◽  
George A. McMechan
Keyword(s):  
Seismic Inversion ◽  
Inversion Method ◽  
Velocity Analysis ◽  
Dominant Wavelength ◽  
Parameter Estimator ◽  
Interval Velocity ◽  
Problem Resolution ◽  
Impedance Response ◽  
Variance Estimate ◽  
Interval Velocities

The inversion problem for determining seismic impedance is nonunique and nonstable because of limited recording aperture, data bandwidth, and data noise. For large reflection angles, small errors in the reflection coefficients give rise to arbitrarily large errors in the seismic impedance estimates. Spatial resolution of the seismic impedance response is controlled by the dominant wavelength corresponding to the source time wavelet; aperture limitations control the resolution of material impedance and interval velocity. Analysis of a linearization‐approximation approach shows that this method degenerates into a single‐parameter estimator for material impedance when using only small‐offset data and for velocity when using only far‐offset data. A nonlocal inversion method is introduced to estimate the material impedance and interval velocity by exploring interval velocity space and computing an associated variance estimate surface. Using this method, the resolution of the material impedance and compressional and shear interval velocities is shown to be poor in the elastic case because of a “valley” feature in the variance estimate surface; in the acoustic problem, resolution of the material impedance and interval velocity is excellent.

scholarly journals Real-time determination of sarcomere length of a single cardiomyocyte during contraction

2013 ◽  
Vol 304 (6) ◽  
pp. C519-C531 ◽  
Author(s):  
Pearu Peterson ◽  
Mari Kalda ◽  
Marko Vendelin
Keyword(s):  
Real Time ◽  
Sarcomere Length ◽  
Accurate Determination ◽  
Region Of Interest ◽  
Estimation Procedure ◽  
Accurate Method ◽  
Estimation Accuracy ◽  
Rat Cardiomyocytes ◽  
Image Pixels ◽  
Microscopy Images

Sarcomere length of a cardiomyocyte is an important control parameter for physiology studies on a single cell level; for instance, its accurate determination in real time is essential for performing single cardiomyocyte contraction experiments. The aim of this work is to develop an efficient and accurate method for estimating a mean sarcomere length of a contracting cardiomyocyte using microscopy images as an input. The novelty in developed method lies in 1) using unbiased measure of similarities to eliminate systematic errors from conventional autocorrelation function (ACF)-based methods when applied to region of interest of an image, 2) using a semianalytical, seminumerical approach for evaluating the similarity measure to take into account spatial dependence of neighboring image pixels, and 3) using a detrend algorithm to extract the sarcomere striation pattern content from the microscopy images. The developed sarcomere length estimation procedure has superior computational efficiency and estimation accuracy compared with the conventional ACF and spectral analysis-based methods using fast Fourier transform. As shown by analyzing synthetic images with the known periodicity, the estimates obtained by the developed method are more accurate at the subpixel level than ones obtained using ACF analysis. When applied in practice on rat cardiomyocytes, our method was found to be robust to the choice of the region of interest that may 1) include projections of carbon fibers and nucleus, 2) have uneven background, and 3) be slightly disoriented with respect to average direction of sarcomere striation pattern. The developed method is implemented in open-source software.

scholarly journals HYBRID INVERSION OF INTERVAL VELOCITIES IN MULTISCALE APPROACH

2017 ◽  
Vol 35 (4) ◽  
pp. 237
Author(s):  
Rodrigo de S. Santos ◽  
Milton J. Porsani
Keyword(s):  
Simulated Annealing ◽  
Hybrid Algorithm ◽  
Seismic Waves ◽  
Optimization Method ◽  
Multiscale Approach ◽  
Velocity Inversion ◽  
Interval Velocity ◽  
The Earth ◽  
Very Fast Simulated Annealing ◽  
Interval Velocities

ABSTRACT. The understanding of the interior of the planet by using the seismic method of reflection requires knowledge of the velocities with which the seismic waves propagate in the subsurface of the Earth. This work presents strategies to obtain the velocity intervals using RMS velocity inversion. Using a hybrid algorithm that combines the Very Fast Simulated Annealing (VFSA) global optimization method and the Fletcher-Reeves local search method, we have sought to reduce the dependence between the accuracy of the results and the model by which the optimization process begins. The main innovative contribution of this study was the development and presentation of the named inversion strategy of multiscale parameters. This technique allows the use of the VFSA method in inversion problems in which the number of variables is significantly large. The hybrid algorithm with multiscale approach was used to solve 1D and 2D problems, estimating models with high degrees of accuracy, which allowed to confirm the efficiency of the proposed method.Keywords: inversion, parameter multiscale, interval velocity, Very Fast Simulated Annealing, Fletcher-Reeves, hybrid.RESUMO. O entendimento do interior do planeta por meio do método sísmico de reflexão requer o conhecimento das velocidades com que as ondas sísmicas se propagam na subsuperfície da Terra. Este trabalho apresenta estratégias para a obtenção das velocidade intervalares por uso inversão de velocidades RMS. Utilizando um algoritmo híbrido, que combina o método de otimização global Very Fast Simulated Annealing (VFSA), e o método de busca local Fletcher-Reeves, buscou-se reduzir a dependência entre a acurácia dos resultados e o modelo pelo qual o processo de otimização se inicia. A principal contribuição inovadora deste estudo foi o desenvolvimento e apresentação da estratégia de inversão nomeada de multiescala de parâmetros. Esta técnica possibilita o uso do método VFSA em problemas de inversão em que o número de variáveis é significativamente grande. O algoritmo híbrido com abordagem multiescala foi usado para solucionar problemas 1D e 2D, estimando modelos com elevado grau de acurácia, o que permitiu confirmar a eficiência do método proposto.Palavras-chave: inversão, multiescala de parâmetros, velocidade intervalar, Very Fast Simulated Annealing, Fletcher-Reeves, híbrido.

Traveltime inversion using transmitted waves of offset VSP data

Geophysics ◽  
1990 ◽  
Vol 55 (8) ◽  
pp. 1089-1097 ◽  
Author(s):  
Myung W. Lee
Keyword(s):  
Seismic Profile ◽  
Inversion Method ◽  
Earth Model ◽  
Computationally Efficient ◽  
Arrival Times ◽  
Traveltime Inversion ◽  
Interval Velocity ◽  
Vsp Data ◽  
First Arrival ◽  
Interval Velocities

Estimation of layer parameters such as interval velocity, reflector depth, and dip can be formulated as a generalized linear inverse problem using observed arrival times. Based on a 2-D earth model, a computationally efficient and accurate formula is derived for traveltime inversion. This inversion method is applied to offset vertical seismic profile (VSP) data for estimating layer parameters using only transmitted first‐arrival times. As opposed to a layer‐stripping method, this method estimates all layer parameters simultaneously, thus reducing the cumulative error resulting from the errors in the upper layers. This investigation indicates (1) at least two source locations are required to estimate layer parameters properly, and (2) accurate arrival times are essential for computing the dip of a layer reliably. Bulk time shifts, such as static shifts, do not affect the parameter estimation significantly if the amount of shift is not too large. The result of real and modeled VSP data inversions indicates that traveltime inversion using transmitted first‐arrival times from at least two source locations is a viable method for estimating interval velocities, reflector depths, and reflector dips.

Sign in / Sign up

Export Citation Format

Share Document