Linearized inversion of multioffset seismic reflection data in the ω-k domain: Depth‐dependent reference medium

Geophysics ◽  
1988 ◽  
Vol 53 (1) ◽  
pp. 50-64 ◽  
Author(s):  
L. T. Ikelle ◽  
J. P. Diet ◽  
A. Tarantola
Keyword(s):  
Inverse Problem ◽  
Linear System ◽  
Seismic Reflection ◽  
Synthetic Seismograms ◽  
Fourier Domain ◽  
Seismic Reflection Data ◽  
Spatial Variables ◽  
Reflection Data ◽  
Reference Medium ◽  
Set Up

The computation of synthetic seismograms can be linearized with respect to a reference medium that issno close to the actual medium. Using a least‐squares formulation, the inverse problem can then be set up as a problem of quadratic optimization. The inverse problem is greatly simplified if the reference medium is symmetric. For a homogeneous reference medium, a rigorous and economic solution can be obtained by Fourier transforming all spatial variables. In particular, the solution can be obtained through an explicit formula that does not require the resolution of any linear system (as is the case when not working in the Fourier domain). However, the assumption of a homogeneous reference medium is generally not realistic. In some situations, the reference medium can be depth‐dependent. It can then be shown that by Fourier transforming time and all spatial variables except depth, the inverse problem also has an elegant and economic solution. If [Formula: see text] is the (unknown) difference between the reference medium and the true (2-D) medium, the Fourier‐transformed solution [Formula: see text] can be obtained by solving, for each value of the horizontal wavenumber [Formula: see text] a linear system whose dimension equals the number of depth samples.

Retrieving both the impedance contrast and background velocity: A global strategy for the seismic reflection problem

Geophysics ◽  
1989 ◽  
Vol 54 (8) ◽  
pp. 991-1000 ◽  
Author(s):  
R. Snieder ◽  
M. Y. Xie ◽  
A. Pica ◽  
A. Tarantola
Keyword(s):  
Seismic Reflection ◽  
Gradient Methods ◽  
Synthetic Seismograms ◽  
Small Scale ◽  
Model Parameters ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Reference Velocity ◽  
Impedance Contrast

Recorded seismic reflection waveforms contain information as to the small‐scale variations of impedance and the large‐scale variations of velocity. This information can be retrieved by minimizing the misfit between the recorded waveforms and synthetic seismograms as a function of the model parameters. Because of the different physical characters of the velocity and the impedance, we update these parameters in an alternating fashion, which amounts to a relaxation approach to the minimization of the waveform misfit. As far as the impedance is concerned, this minimization can be performed efficiently using gradient algorithms. For the inversion for seismic velocities, gradient methods do not work nearly as well; therefore, we use different minimization methods for determining impedances and velocities. However, the determination of the impedance and the determination of the velocity are strongly coupled; relaxation is most effective when this coupling is as weak as possible. Weak coupling can be achieved partially by parameterizing the impedances not as a function of depth but as a function of traveltime. A nonlinear, nonlocal method is presented for determining the smooth reference velocity from seismic reflection data. This technique is applied both to synthetic seismograms and to real marine data. In both cases, the velocity information implicitly contained in the curvature of the reflection hyperbolas was fully retrieved using nonlinear waveform optimization. In this way, it is possible to reconstruct both the impedance contrast and the smooth reference velocity from band‐limited seismic reflection data using a single waveform‐fit criterion.

Inversion of seismic reflection data in the acoustic approximation

Geophysics ◽  
1984 ◽  
Vol 49 (8) ◽  
pp. 1259-1266 ◽  
Author(s):  
Albert Tarantola
Keyword(s):  
Inverse Problem ◽  
Bulk Modulus ◽  
Iterative Algorithm ◽  
Seismic Reflection ◽  
Current Model ◽  
Generalized Least Squares ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Acoustic Approximation

The nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation. The method is based on the generalized least‐squares criterion, and it can handle errors in the data set and a priori information on the model. Multiply reflected energy is naturally taken into account, as well as refracted energy or surface waves. The inverse problem can be solved using an iterative algorithm which gives, at each iteration, updated values of bulk modulus, density, and time source function. Each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation (backward in time) of the data residuals. The correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models. This shows, in particular, that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data, and commercially competitive with them.

High‐resolution seismic study in the Gas Hills uranium district, Wyoming

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1355-1374
Author(s):  
James K. Applegate ◽  
David A. Emilia ◽  
Edwin B. Neitzel ◽  
Paul R. Donaldson
Keyword(s):  
High Resolution ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Three Dimensional ◽  
Synthetic Seismograms ◽  
Seismic Reflection Data ◽  
Structural Controls ◽  
Reflection Data ◽  
Passive Seismic ◽  
Channel Deposits

A study was undertaken to evaluate the effectiveness of the high‐resolution seismic technique for the mapping of stratigraphic and structural controls in the Gas Hills uranium district, Wyoming. The test area is one in which uranium deposits are in Tertiary sediments which unconformably overlie a Mesozoic Paleozoic section. Paleochannels on the unconformity appear to control the localization of the uranium. Drilling in the area allows an evaluation of the effectiveness of the study. Using both sonic and density logs, we computed synthetic seismograms to evaluate the feasibility of predicting the success of the seismic reflection technique and to test this prediction using surface seismic methods. The field study was undertaken utilizing primarily two energy sources—a high‐frequency vibrator (40–350 Hz), and one‐pound dynamite charges shot in 10-ft holes. A limited amount of data was also acquired using detonating cord on the surface. Some three‐dimensional (3-D) data were also acquired, and a later study acquired passive seismic data. The seismic reflection data were successful not only in delineating the unconformable surface and in mapping paleodrainages on the unconformity, but also in defining channel deposits within the Tertiary section. Correlation with the logs shows the success of the study. Several areas were delineated where one would undertake tight drilling patterns, and other areas were delineated in which one might minimize or eliminate exploratory drilling. The synthetic seismograms also could have predicted the success of the seismic work.

The style of transverse faulting in the Dead Sea basin from seismic reflection data: The Amazyahu fault

2006 ◽  
Vol 55 (3) ◽  
pp. 129-139 ◽  
Author(s):  
Avihu Ginzburg ◽  
Moshe Reshef ◽  
Zvi Ben-Avraham ◽  
Uri Schattner
Keyword(s):  
Seismic Reflection ◽  
Dead Sea ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Dead Sea Basin ◽  
The Dead

Archive of digital boomer seismic reflection data collected offshore east-central Florida during USGS cruise 00FGS01, July 14-22, 2000

Data Series ◽  
10.3133/ds496 ◽  
2009 ◽  
Author(s):  
Janice A. Subino ◽  
Shawn V. Dadisman ◽  
Dana S. Wiese ◽  
Karynna Calderon ◽  
Daniel C. Phelps
Keyword(s):  
Seismic Reflection ◽  
Seismic Reflection Data ◽  
East Central ◽  
Central Florida ◽  
Reflection Data

Archive of digital CHIRP seismic reflection data collected during USGS cruise 06SCC01 offshore of Isles Dernieres, Louisiana, June 2006

Data Series ◽  
10.3133/ds259 ◽  
2007 ◽  
Author(s):  
Arnell S. Harrison ◽  
Shawn V. Dadisman ◽  
Nick F. Ferina ◽  
Dana S. Wiese ◽  
James G. Flocks
Keyword(s):  
Seismic Reflection ◽  
Seismic Reflection Data ◽  
Reflection Data
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