Estimation of reflection coefficients from zero‐offset field data

1991 ◽  
Author(s):  
B. Arntsen ◽  
Bjørn Ursin
Keyword(s):  
Field Data ◽  
Reflection Coefficients ◽  
Zero Offset

Estimation of reflection coefficients from zero‐offset field data

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1634-1645 ◽  
Author(s):  
Børge Arntsen ◽  
Bjørn Ursin
Keyword(s):  
Point Source ◽  
Least Squares ◽  
Seismic Data ◽  
Field Data ◽  
Model Fitting ◽  
Seismic Survey ◽  
Reflection Coefficients ◽  
Data Set ◽  
Seismic Experiment ◽  
Zero Offset

The classical one‐dimensional (1-D) inverse problem consists of estimating reflection coefficients from surface seismic data using the 1-D wave equation. Several authors have found stable solutions to this problem using least‐squares model‐fitting methods. We show that the application of these plane‐wave solutions to seismic data generated with a point source can lead to errors in estimating reflection coefficients. This difficulty is avoided by using a least‐squares model fitting scheme describing vertically traveling waves originating from a point source. It is shown that this method is roughly equivalent to deterministic deconvolution with built‐in multiple removal and compensation for spherical spreading. A true zero‐offset field data set from a specially designed seismic experiment is then used as input to estimate reflection coefficients. Stacking velocities from a conventional seismic survey were used to estimate spherical spreading. The resulting reflection coefficients are shown to correlate well with an available well log.

VELOCITY STRATIFICATION AS AN AID TO CORRELATION

Geophysics ◽  
1940 ◽  
Vol 5 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Roland F. Beers
Keyword(s):  
Experimental Data ◽  
Historical Development ◽  
Field Data ◽  
Reflection Coefficients ◽  
Stratigraphic Correlation ◽  
Seismic Reflections

This paper outlines the historical development of the concept “velocity stratification” from the field data of refraction and reflection seismographs. The concept is shown to form the basis of the phenomenon known as “seismic reflections.” Experimental data are interpreted to show approximately the magnitude of reflection coefficients. Employment of velocity stratification as a means of stratigraphic correlation is suggested. Means whereby data for these correlations may be collected are discussed. Finally the use of the method for attack on stratigraphic problems is outlined.

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.

Velocity estimation by image-focusing analysis

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. U49-U60 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
New York ◽  
Seismic Data ◽  
Field Data ◽  
Velocity Estimation ◽  
Data Set ◽  
Velocity Function ◽  
Curvature Correction ◽  
Velocity Information ◽  
Zero Offset ◽  
Inherent Ambiguity

Migration velocity can be estimated from seismic data by analyzing, focusing, and defocusing of residual-migrated images. The accuracy of these velocity estimates is limited by the inherent ambiguity between velocity and reflector curvature. However, velocity resolution improves when reflectors with different curvatures are present. Image focusing is measured by evaluating coherency across structural dips, in addition to coherency across aperture/azimuth angles. The inherent ambiguity between velocity and reflector curvature is directly tackled by introducing a curvature correction into the computation of the semblance functional that estimates image coherency. The resulting velocity estimator provides velocity estimates that are (1) unbiased by reflector curvature and (2) consistent with the velocity information that is routinely obtained by measuring coherency over aperture/azimuth angles. Applications to a 2D synthetic prestack data set and a 2D field prestack data set confirm that the proposed method provides consistent and unbiased velocity information. They also suggest that velocity estimates based on the new image-focusing semblance may be more robust and have higher resolution than estimates based on conventional semblance functionals. Applying the proposed method to zero-offset field data recorded in New York Harbor yields a velocity function that is consistent with available geologic information and clearly improves the focusing of the reflectors.

True‐amplitude transformation to zero offset of data from curved reflectors

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 112-129 ◽  
Author(s):  
Norman Bleistein ◽  
Jack Cohen ◽  
Herman Jaramillo
Keyword(s):  
General Context ◽  
Reflection Coefficients ◽  
Geometrical Spreading ◽  
Curvature Effects ◽  
Multiplicative Factor ◽  
Amplitude Factor ◽  
Amplitude Versus Offset ◽  
Zero Offset ◽  
The Cost ◽  
Amplitude Versus

Transformation to zero offset (TZO), alternatively known as migration to zero offset (MZO), or the combination of normal moveout and dip moveout (NMO/DMO), is a process that transforms data collected at finite offset between source and receiver to a pseudozero offset trace. The kinematic validity of NMO/DMO processing has been well established. The TZO integral operators proposed here differ from their NMO/DMO counterparts by a simple amplitude factor. (The form of the operator depends on how the input and output variables are chosen from among the combinations of midpoint or wavenumber with time or frequency.) With this modification in place, the dynamical validity for planar reflectors of the proposed TZO operators of this paper have been established in earlier studies. This means that the traveltime and geometrical spreading terms of the finite offset data are transformed to their counterparts for zero offset data, while the finite offset reflection coefficient is preserved. The main purpose of this study is to show that dynamical validity of the TZO operator extends to the case of curved reflectors in the 2.5-D limit. Thus, at the cost of a simple additional multiplicative factor in any standard NMO/DMO operator to produce the corresponding TZO operator, the amplitude factor attributed to curvature effects in finite offset data is transformed by this TZO processing to the corresponding curvature factor for zero offset data. This problem has also been addressed in a more general context by Tygel and associates. However, in the generality, some of the specifics and interpretations of the simpler problem are lost. Thus, we see some value in presenting this analysis where one can carry out all calculations explicitly and see specific quantities that are more familiar and accessible to users of DMO. Furthermore, in this paper, we show how processing of the input data with a second TZO operator allows for the extraction of the cosine of the preserved specular angle, a necessary piece of information for amplitude versus angle (AVA) analysis. We then discuss the possibility of using the output of our processing formalism at multiple offsets to create a table of angularly dependent reflection coefficients and attendant incidence angles as a function of offset. This is the basis of a proposed amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of the pseudozero offset traces. Finally, we describe the modifications of Hale DMO and Gardner/Forel DMO to obtain true amplitude output equivalent to ours and also how to extract the cosine of the specular angle for these forms of DMO. This last does not depend on true amplitude processing, but only on processing two DMO operators with slightly different kernels and then taking the quotient of their peak amplitudes.

Prestack Bayesian statistical inversion constrained by reflection features

Geophysics ◽  
2020 ◽  
pp. 1-98
Author(s):  
Bo Yu ◽  
Hui Zhou ◽  
Lingqian Wang ◽  
Wenling Liu
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Posterior Probability ◽  
Probability Distributions ◽  
Seismic Profile ◽  
Inversion Method ◽  
Reflection Coefficients ◽  
Geological Structures ◽  
Practical Applications ◽  
Geological Information

Bayesian statistical inversion can integrate diverse datasets to infer the posterior probability distributions of subsurface elastic properties. However, certain existing methods may suffer from two issues in practical applications, namely spatial discontinuities and the uncertainty caused by the low-quality seismic traces. These limitations are evident in prestack statistical inversion since some traces in prestack angle gathers may be missing or low-quality. We propose a prestack Bayesian statistical inversion method constrained by reflection features to alleviate these issues. Based on a Bayesian linearized inversion framework, the proposed inversion approach is implemented by integrating the prestack seismic data with reflection features. The reflection features are captured from the poststack seismic profile, and they represent the relationships of the reflection coefficients between different traces. By utilizing the proposed approach, we are able to achieve superior inversion results and to evaluate inversion uncertainty simultaneously even with the low-quality prestack seismic data. The results of the synthetic and field data tests confirm the theoretical and practical effects of the reflection features on improving inversion continuity and accuracy and reducing inversion uncertainty. Moreover, this work gives a novel way to integrate the information of geological structures in statistical inversion methods. Other geological information, which can be linearized accurately or approximately, can be utilized in this manner.

Waveform-based estimation of Q and scattering properties for zero-offset vertical seismic profile data

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. R365-R379
Author(s):  
Rie Nakata ◽  
David Lumley ◽  
Gary Hampson ◽  
Kurt Nihei ◽  
Nori Nakata
Keyword(s):  
Field Data ◽  
Estimation Method ◽  
Spectral Ratio ◽  
Seismic Profile ◽  
Ratio Method ◽  
Vsp Data ◽  
Spectral Ratio Method ◽  
Band Limited ◽  
Zero Offset ◽  
Negative Formula

Estimating [Formula: see text] using downgoing waves in zero-offset vertical seismic profiles (VSPs) can be challenging when scattered waves from near-borehole heterogeneities interfere with direct arrivals. In any [Formula: see text] estimation method that assumes a downgoing plane wave, constructive and destructive wave-mode interference can cause errors in the estimate. For example, in the spectral-ratio method, such interference modulates the amplitude spectra introducing significant variations and even nonphysical negative [Formula: see text] (amplification) estimates. We have investigated this phenomenon using synthetic and field data sets from offshore Australia and developed a two-step waveform-based method to characterize scattering anomalies and improve [Formula: see text] estimates. Waveform information is key to deal with closely spaced band-limited seismic events. First, we solve an inverse problem to locate and characterize scatterers by minimizing the traveltime and waveform misfits. Then, using the estimated parameters, we model the scatterers’ contribution to the VSP data and remove it from the observed waveforms. The resulting spectra resemble those that would have been acquired in the absence of the scatterers and are much more suitable for the spectral-ratio method. By assuming a 1D medium and a simple scatterer shape (i.e., circular), we parameterize a scattering heterogeneity using five parameters (depth, distance, size, velocity, and density) and seek a solution using a grid search to handle the nonuniqueness of the VSP inversion. Instead, adaptive subtraction is required to fine-tune the modeled interference to better fit the observation. We successfully use this method to characterize and mitigate the strongest wave interference in the field data. The final [Formula: see text] estimates contain milder variations and much less nonphysical negative [Formula: see text]. Our results demonstrate that the proposed method, readily extendible to multiple scatterer cases, can locate discrete scatterers, remove the effects of their interference, and thus significantly improve the [Formula: see text] estimates from VSP data.

Apparent layering in common‐midpoint stacked images of two‐dimensionally heterogeneous targets

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1466-1477 ◽  
Author(s):  
Bruce S. Gibson ◽  
Alan R. Levander
Keyword(s):  
Field Data ◽  
Synthetic Data ◽  
Reflection Coefficients ◽  
Random Structure ◽  
Fine Scale ◽  
Spatial Bias ◽  
Apparent Increase ◽  
Model Studies ◽  
Seismic Image ◽  
Random Target

Model studies with finite‐difference synthetic data demonstrate a fundamental spatial bias in the appearance of common‐midpoint (CMP) stacked images. The CMP stack of data recorded over a target having 2-D random variations in velocity shows numerous short reflection segments; similar reflection patterns in field data are often interpreted in terms of 1-D fine‐scale layering. The stacked image appears layered because of enhanced lateral continuity attributable to the well‐known dip filter of the stacking process. The stack filter can be characterized using the formulation of Bolondi et al. (1982). Lateral correlation in the target and its seismic image is quantified with a measure based on the spectral coefficient of coherence. Broadband primary reflectivity (defined as the vertical‐incidence, primaries‐only reflection coefficients of the 2-D target) is often taken as an ideal seismic image. The primary reflectivity section of a 2-D random target, however, shows greater apparent lateral correlation than is present in the random structure. This apparent increase in lateral continuity is attributable to the fact that reflectivity measured from the surface depends on the vertical derivative of velocity but depends on horizontal changes in velocity directly. The dip‐filtering effects of stacking cannot be reversed by poststack migration; the synthetic data demonstrate the necessity of migration before stack or equivalent processing (such as dip moveout correction). A field data example illustrates the effects of CMP stack filtering using lateral coherence functions measured on stacked and unstacked sections.

Euclid and the art of wavelet estimation, Part I: Basic algorithm for noise‐free data

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1931-1938 ◽  
Author(s):  
Eike Rietsch
Keyword(s):  
Field Data ◽  
Polynomial Algebra ◽  
Common Factors ◽  
Reflection Coefficients ◽  
Basic Algorithm ◽  
Wavelet Estimation ◽  
Free Data ◽  
The Common

An algorithm borrowed from polynomial algebra for finding the common factors of two or more polynomials can be used to find the wavelet that several seismic traces have in common. In the implementation described in this first part of a two‐part work, a matrix is constructed from the autocorrelations and crosscorrelations of these seismic traces. The number of zero eigenvalues of this matrix is equal to the number of samples of the wavelet, and the eigenvectors associated with these eigenvalues are related to the reflection coefficients. The method, which works well if the noise is not too high, is illustrated by means of a synthetic example. Part II of this two‐part work shows how this method is affected by noise and gives field‐data examples.

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