The discrete prolate spheroidal sequences and a series expansion for seismic wavelets

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. V119-V132 ◽  
Author(s):  
Michael Greene
Keyword(s):  
Series Expansion ◽  
Seismic Data ◽  
Robust Method ◽  
Prolate Spheroidal ◽  
Seismic Wavelet ◽  
Ricker Wavelet ◽  
Band Limited ◽  
Well Data ◽  
Definition Of ◽  
Logical Extension

The discrete prolate spheroidal sequences (DPSSs) are a set of time-limited, band-limited, and mutually orthogonal sequences. I exploit their favorable properties to introduce a series expansion for seismic wavelets. By modifying the definition of the DPSSs, I generate new sequences that are tailored to the character of the seismic wavelet but retain the DPSSs’ favorable properties. I show that a series expansion composed of these new sequences can be thought of as a logical extension of a familiar practice, assuming the wavelet is a linear combination of a Ricker wavelet and its Hilbert transform ([Formula: see text] rotation). Two examples, one synthetic and one real, show how the series expansion can be used to tie well data to seismic data. This leads to a robust method to determine a wavelet. The examples also illustrate the properties of the series expansion, some of which can be related to familiar geophysical concepts such as thin-bed tuning. I conclude that this series expansion is a natural and useful way to describe the seismic wavelet.

Seismic-to-well tie of a field of the Nigerian Delta

2021 ◽  
Vol 19 (3) ◽  
pp. 125-138
Author(s):  
S. Inichinbia ◽  
A.L. Ahmed
Keyword(s):  
Seismic Data ◽  
Processing Parameters ◽  
Seismic Inversion ◽  
Seismic Wavelet ◽  
Statistical Measures ◽  
Convolution Model ◽  
Data Driven Approach ◽  
Well Data ◽  
Seismic Reflectors ◽  
Matching Techniques

This paper presents a rigorous but pragmatic and data driven approach to the science of making seismic-to-well ties. This pragmatic  approach is consistent with the interpreter’s desire to correlate geology to seismic information by the use of the convolution model,  together with least squares matching techniques and statistical measures of fit and accuracy to match the seismic data to the well data. Three wells available on the field provided a chance to estimate the wavelet (both in terms of shape and timing) directly from the seismic and also to ascertain the level of confidence that should be placed in the wavelet. The reflections were interpreted clearly as hard sand at H1000 and soft sand at H4000. A synthetic seismogram was constructed and matched to a real seismic trace and features from the well are correlated to the seismic data. The prime concept in constructing the synthetic is the convolution model, which represents a seismic reflection signal as a sequence of interfering reflection pulses of different amplitudes and polarity but all of the same shape. This pulse shape is the seismic wavelet which is formally, the reflection waveform returned by an isolated reflector of unit strength at the target  depth. The wavelets are near zero phase. The goal and the idea behind these seismic-to-well ties was to obtain information on the sediments, calibration of seismic processing parameters, correlation of formation tops and seismic reflectors, and the derivation of a  wavelet for seismic inversion among others. Three seismic-to-well ties were done using three partial angle stacks and basically two formation tops were correlated. Keywords: seismic, well logs, tie, synthetics, angle stacks, correlation,

Impact of phase rotation on reservoir characterization and implementation of seismic well tie technique for calibration offshore Nile Delta, Egypt

2020 ◽  
Vol 39 (5) ◽  
pp. 346-352
Author(s):  
Mohamed G. El-Behiry ◽  
Mohamed S. Al Araby ◽  
Ramy Z. Ragab
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Nile Delta ◽  
Seismic Wavelet ◽  
Well Location ◽  
Formation Behavior ◽  
Dynamic Components ◽  
Well Data ◽  
Phase Amplitude ◽  
Seismic Anomalies

Seismic wavelets are dynamic components that result in a seismic trace when convolved with reflectivity series. The seismic wavelet is described by three components: amplitude, frequency, and phase. Amplitude and frequency are considered static because they mainly affect the appearance of a seismic event. Phase can have a large effect on seismic appearance by changing the way it describes the subsurface. Knowing the wavelet properties of certain seismic data facilitates the process of interpretation by providing an understanding of the appearance of regional geologic markers and hydrocarbon-bearing formation behavior. The process through which seismic data wavelets are understood is called seismic well tie. Seismic well tie is the first step in calibrating seismic data in terms of polarity and phase. It ensures that the seismic data are descriptive to regional markers, well markers, and discoveries (if they exist). The step connects well data to seismic data to ensure that the seismic correctly describes well results at the well location. It then extends the understanding of seismic behavior to the rest of the area covered by the seismic data. Good seismic well tie will greatly reduce uncertainties accompanying seismic interpretation. One important outcome of the seismic well tie process is understanding the phase of seismic data, which affects how seismic data will reflect a known geologic marker or hydrocarbon-bearing zone. This understanding can be useful in quantifying discoveries attached to seismic anomalies and extending knowledge from the well location to the rest of the area covered by seismic data.

Joint inversion of seismic data for acoustic impedance

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 994-1004 ◽  
Author(s):  
Li‐Yun Fu
Keyword(s):  
Neural Network ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Joint Inversion ◽  
Signal Reconstruction ◽  
Optimal Estimation ◽  
Data Sets ◽  
Seismic Wavelet ◽  
Model Based ◽  
Band Limited

I propose a joint inversion scheme to integrate seismic data, well data, and geological knowledge for acoustic impedance estimation. I examine the problem of recovering acoustic impedance from band‐limited seismic data. Optimal estimation of impedance can be achieved by combined applications of model‐based and deconvolution‐based methods. I incorporate the Robinson seismic convolutional model (RSCM) into the Caianiello neural network for network mapping. The Caianiello neural network provides an efficient approach to decompose the seismic wavelet and its inverse. The joint inversion consists of four steps: (1) multistage seismic inverse wavelets (MSIW) extraction at the wells, (2) the deconvolution with MSIW for initial impedance estimation, (3) multistage seismic wavelets (MSW) extraction at the wells, and (4) the model‐based reconstruction of impedance with MSW for improving the initial impedance model. The Caianiello neural network offers two algorithms for the four‐step process: neural wavelet estimation and input signal reconstruction. The frequency‐domain implementation of the algorithms enables control of the inversion on different frequency scales and facilitates an understanding of reservoir behavior on different resolution scales. The test results show that, with well control, the joint inversion can significantly improve the spatial description of reservoirs in data sets involving complex continental deposits.

scholarly journals Deblending by direct inversion

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. A9-A12 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Jan Thorbecke
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Iterative Procedure ◽  
Inversion Process ◽  
Direct Inversion ◽  
Source Data ◽  
Band Limited ◽  
Blended Data ◽  
Simultaneous Source ◽  
Additional Constraints

Deblending of simultaneous-source data is usually considered to be an underdetermined inverse problem, which can be solved by an iterative procedure, assuming additional constraints like sparsity and coherency. By exploiting the fact that seismic data are spatially band-limited, deblending of densely sampled sources can be carried out as a direct inversion process without imposing these constraints. We applied the method with numerically modeled data and it suppressed the crosstalk well, when the blended data consisted of responses to adjacent, densely sampled sources.

scholarly journals Characterizing Seismo-stratigraphic and Structural Framework of Late Cretaceous-Recent succession of offshore Indus Pakistan

2018 ◽  
Vol 10 (1) ◽  
pp. 174-191 ◽  
Author(s):  
Majid Khan ◽  
Yike Liu ◽  
Asam Farid ◽  
Muhammad Owais
Keyword(s):  
Seismic Data ◽  
Late Eocene ◽  
Indian Plate ◽  
Processing Scheme ◽  
Structural Growth ◽  
Seismic Records ◽  
Exploratory Wells ◽  
Well Data ◽  
Seismic Reflection Profiles ◽  
Push Up

Abstract Regional seismic reflection profiles and deep exploratory wells have been used to characterize the subsurface structural trends and seismo-stratigraphic architecture of the sedimentary successions in offshore Indus Pakistan. To improve the data quality, we have reprocessed the seismic data by applying signal processing scheme to enhance the reflection continuity for obtaining better results. Synthetic seismograms have been used to identify and tie the seismic reflections to the well data. The seismic data revealed tectonically controlled, distinct episodes of normal faulting representing rifting during Mesozoic and transpression at Late Eocene time. A SW-NE oriented anticlinal type push up structure is observed resulted from the basement reactivation and recent transpression along Indian Plate margin. The structural growth of this particular pushup geometry was computed. Six mappable seismic sequences have been identified on seismic records. In general, geological formations are at shallow depths towards northwest due to basement blocks uplift. A paleoshelf is also identified on seismic records overlain by Cretaceous sediments, which is indicative of Indian-African Plates rifting at Jurassic time. The seismic interpretation reveals that the structural styles and stratigraphy of the region were significantly affected by the northward drift of the Indian Plate, post-rifting, and sedimentation along its western margin during Middle Cenozoic. A considerable structural growth along the push up geometry indicates present day transpression in the margin sediments. The present comprehensive interpretation can help in understanding the complex structures in passive continental margins worldwide that display similar characteristics but are considered to be dominated by rifting and drifting tectonics.

Joint time-variant spectral analysis — Part 1: Forward modeling the effects of thin-bed layering

2018 ◽  
Vol 6 (4) ◽  
pp. T967-T983
Author(s):  
Ramses G. Meza ◽  
J. Antonio Sierra ◽  
John P. Castagna ◽  
Umberto Barbato
Keyword(s):  
Seismic Data ◽  
Seismic Isolation ◽  
Forward Modeling ◽  
Destructive Interference ◽  
Constructive Interference ◽  
Phase Component ◽  
Time Frequency ◽  
Seismic Wavelet ◽  
Specific Frequency ◽  
Net To Gross

Using time-frequency and time-phase analysis we found that for an isolated thin bed in a binary-impedance setting, there is no observable sensitivity in preferential illumination as layered net-to-gross (NTG) changes within the isolated thin bed, regardless of the way the internal layering is distributed — either uniformly or semirandomly. The NTG signature is observed on the amplitude (magnitude) responses, rather than any specific frequency or phase component. On the other hand, external mutual thin-bed interference can significantly change the preferred phase component for each participating target. This phenomenon is largely driven by the embedded seismic wavelet that determines the nominal seismic response of an isolated thin layer and what phase component would preferentially illuminate it. For vertical separations between mutually interfering and elastically comparable thin beds in which mutual constructive interference is achieved, the target bed will be preferentially illuminated at a phase component that is very close to that of a total seismic isolation, whereas the occurrence of mutual destructive interference will cause a significant departure on the phase preferential illumination from that of an isolated seismic thin bed. All these observations can provide an avenue to yield more robust stratigraphic interpretations of seismic data and enhance the confidence on subsurface description.

Robust wavelet estimation and blind deconvolution of noisy surface seismics

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. V37-V46 ◽  
Author(s):  
Mirko van der Baan ◽  
Dinh-Tuan Pham
Keyword(s):  
Blind Deconvolution ◽  
General Purpose ◽  
Sufficient Accuracy ◽  
Wiener Filtering ◽  
Challenging Problem ◽  
Limited Data ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Principal Frequency ◽  
Band Limited

Robust blind deconvolution is a challenging problem, particularly if the bandwidth of the seismic wavelet is narrow to very narrow; that is, if the wavelet bandwidth is similar to its principal frequency. The main problem is to estimate the phase of the wavelet with sufficient accuracy. The mutual information rate is a general-purpose criterion to measure whiteness using statistics of all orders. We modified this criterion to measure robustly the amplitude and phase spectrum of the wavelet in the presence of noise. No minimum phase assumptions were made. After wavelet estimation, we obtained an optimal deconvolution output using Wiener filtering. The new procedure performs well, even for very band-limited data; and it produces frequency-dependent phase estimates.

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