DISCUSSION ON: LATERAL VELOCITY VARIATIONS NEAR BOREHOLES

Geophysics ◽  
1959 ◽  
Vol 24 (3) ◽  
pp. 461-462
Author(s):  
J. A. Brooks
Keyword(s):  
High Velocity ◽  
Travel Times ◽  
Lateral Velocity ◽  
Travel Path ◽  
Cumulative Error ◽  
Velocity Variations

The requirement that integrated vertical times from a continuous velocity log check to within some small percent the vertical times computed from the observed travel times of a geophone survey in the same borehole is to me unreasonable. Although we geophysicists know that there are inherent errors in the results of geophone surveys because of possible errors in weathering velocity corrections, datum velocity corrections, depth of shot corrections, and especially seismic travel‐path assumptions, we have presumed the cumulative error in all but unusual surveys to be within the limits of accuracy of reflection seismograph interpretation. The usual seismic travel path assumption, particularly in areas of high velocity stringers or velocity inversions, can be very treacherous in the computation of vertical times. Consequently, I cannot understand why some of our colleagues insist that the log results are incorrect unless they check very closely with the computed vertical shot times. Maybe the computed times are wrong!

Including Lateral Velocity Variations Into True-Amplitude Wave-Equation Migration

2009 ◽  
Author(s):  
D. Amazonas ◽  
R. Aleixo ◽  
J. Schleicher ◽  
J. Costa ◽  
A. Novais ◽  
...  
Keyword(s):  
Wave Equation ◽  
Lateral Velocity ◽  
Amplitude Wave ◽  
Velocity Variations

The Interpretation of Seismic Reflection Data from the Western Platform Region of Taranaki Basin

1988 ◽  
Vol 6 (2) ◽  
pp. 136-150 ◽  
Author(s):  
Glenn P. Thrasher
Keyword(s):  
Travel Time ◽  
Seismic Reflection ◽  
Time Data ◽  
Lateral Velocity ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Travel Time Data ◽  
Velocity Variations ◽  
Thickness Variations ◽  
Reflection Characteristics

The western-most region of Taranaki Basin, the Western Platform, has a stratigraphy which permits subdivision into major seismic units. The reflectors separating these units are easily identifiable. Each of the units and reflectors has typical reflection characteristics which are often correlatable with the lithology of the unit. Lateral velocity variations, caused by lateral deposition and compaction variations in prograding sequences, area major problem in developing depth conversion models for this region. Analysis of travel time data from wells shows that velocity variations in both the Oligocene-Miocene and Pliocene-Pleistocene sequences are predictable from the thickness variations of the units (and hence from interval travel times). The imerval velocity variations of the Paleocene-Eocene transgressive sequence are dependent on the overburden history and lithology of the unit.

DISCUSSION ON: LATERAL VELOCITY VARIATIONS NEAR BOREHOLES

Geophysics ◽  
1959 ◽  
Vol 24 (3) ◽  
pp. 462-463
Author(s):  
E. Kaarsberg
Keyword(s):  
Structural Changes ◽  
Lateral Velocity ◽  
Actual Mechanism ◽  
Velocity Variations

The discrepancies between regular geophone‐type logs or surveys and continuous velocity surveys have been noted ever since the latter came into use. Hick’s speculations as to the cause of these discrepancies in terms of compositional and structural changes in the rock surrounding the borehole are, therefore, welcome. His description of the actual mechanism of alteration of shale velocity due to shale damage is, however, brief, and some additional and/or alternative causes, which could be considered, are given below.

Seismic depth migration with the Dirac equation

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 925-933 ◽  
Author(s):  
Ketil Hokstad ◽  
Rune Mittet
Keyword(s):  
Dirac Equation ◽  
Taylor Series ◽  
Rapid Expansion ◽  
Difference Operators ◽  
Square Root ◽  
Exact Linearization ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Spatial Derivatives ◽  
Velocity Variations

We demonstrate the applicability of the Dirac equation in seismic wavefield extrapolation by presenting a new explicit one‐way prestack depth migration scheme. The method is in principle accurate up to 90° from the vertical, and it tolerates lateral velocity variations. This is achieved by performing the extrapolation step of migration with the Dirac equation, implemented in the space‐frequency domain. The Dirac equation is an exact linearization of the square‐root wave equation and is equivalent to keeping infinitely many terms in a Taylor series or continued‐fraction expansion of the square‐root operator. An important property of the new method is that the local velocity and the spatial derivatives decouple in separate terms within the extrapolation operator. Therefore, we do not need to precompute and store large tables of convolutional extrapolator coefficients depending on velocity. The main drawback of the explicit scheme is that evanescent energy must be removed at each depth step to obtain numerical stability. We have tested two numerical implementations of the migration scheme. In the first implementation, we perform depth stepping using the Taylor series approximation and compute spatial derivatives with high‐order finite difference operators. In the second implementation, we perform depth stepping with the Rapid expansion method and numerical differentiation with the pseudospectral method. The imaging condition is a generalization of Claerbout’s U / D principle. For both implementations, the impulse response is accurate up to 80° from the vertical. Using synthetic data from a simple fault model, we test the depth migration scheme in the presence of lateral velocity variations. The results show that the proposed migration scheme images dipping reflectors and the fault plane in the correct positions.

Analytic synthetic seismograms for depth migration testing

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 697-700
Author(s):  
Samuel H. Gray ◽  
Chester A. Jacewitz ◽  
Michael E. Epton
Keyword(s):  
Velocity Field ◽  
Acoustic Velocity ◽  
Synthetic Seismograms ◽  
Lateral Velocity ◽  
Seismic Migration ◽  
Depth Migration ◽  
Circular Arcs ◽  
Velocity Variations ◽  
Migration Testing ◽  
Speed And Accuracy

By using the fact that raypaths in a linear acoustic velocity field are circular arcs, we analytically generate a number of distinct nontrivial synthetic seismograms. The seismograms yield accurate traveltimes from reflection events, but they do not give reflection amplitudes. The seismograms are useful for testing seismic migration programs for both speed and accuracy, in settings where lateral velocity variations can be arbitrarily high and dipping reflectors arbitrarily steep. Two specific examples are presented as illustrations.

Overthrust imaging with tomo‐datuming: A case study

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Xianhuai Zhu ◽  
Burke G. Angstman ◽  
David P. Sixta
Keyword(s):  
Velocity Model ◽  
Surface Velocity ◽  
Time Shift ◽  
Lateral Velocity ◽  
Prestack Depth Migration ◽  
Near Surface ◽  
Depth Migration ◽  
Static Corrections ◽  
Velocity Variations ◽  
Kirchhoff Method

Through the use of iterative turning‐ray tomography followed by wave‐equation datuming (or tomo‐datuming) and prestack depth migration, we generate accurate prestack images of seismic data in overthrust areas containing both highly variable near‐surface velocities and rough topography. In tomo‐datuming, we downward continue shot records from the topography to a horizontal datum using velocities estimated from tomography. Turning‐ray tomography often provides a more accurate near‐surface velocity model than that from refraction statics. The main advantage of tomo‐datuming over tomo‐statics (tomography plus static corrections) or refraction statics is that instead of applying a vertical time‐shift to the data, tomo‐datuming propagates the recorded wavefield to the new datum. We find that tomo‐datuming better reconstructs diffractions and reflections, subsequently providing better images after migration. In the datuming process, we use a recursive finite‐difference (FD) scheme to extrapolate wavefield without applying the imaging condition, such that lateral velocity variations can be handled properly and approximations in traveltime calculations associated with the raypath distortions near the surface for migration are avoided. We follow the downward continuation step with a conventional Kirchhoff prestack depth migration. This results in better images than those migrated from the topography using the conventional Kirchhoff method with traveltime calculation in the complicated near surface. Since FD datuming is only applied to the shallow part of the section, its cost is much less than the whole volume FD migration. This is attractive because (1) prestack depth migration usually is used iteratively to build a velocity model, so both efficiency and accuracy are important factors to be considered; and (2) tomo‐datuming can improve the signal‐to‐noise (S/N) ratio of prestack gathers, leading to more accurate migration velocity analysis and better images after depth migration. Case studies with synthetic and field data examples show that tomo‐datuming is especially helpful when strong lateral velocity variations are present below the topography.

Seismic structure of the Central Metasedimentary Belt, southern Grenville Province

1994 ◽  
Vol 31 (2) ◽  
pp. 243-254 ◽  
Author(s):  
C. A. Zelt ◽  
D. A. Forsyth ◽  
B. Milkereit ◽  
D. J. White ◽  
I. Asudeh ◽  
...  
Keyword(s):  
Seismic Data ◽  
High Velocity ◽  
Hanging Wall ◽  
New York State ◽  
Lake Ontario ◽  
Wide Angle ◽  
Seismic Structure ◽  
Lateral Velocity ◽  
Crust And Upper Mantle ◽  
Grenville Province

Crust and upper-mantle structure interpreted from wide-angle seismic data along a 260 km profile across the Central Metasedimentary Belt of the southern Grenville Province in Ontario and New York State shows (i) relatively high average crustal and uppermost mantle velocities of 6.8 and 8.3 km/s, respectively; (ii) east-dipping reflectors extending to 24 km depth in the Central Metasedimentary Belt; (iii) weak lateral velocity variations beneath 5 km; (iv) a mid-crustal boundary at 27 km depth; and (v) a depth to Moho of 43–46 km. The wide-angle model is generally consistent with the vertical-incidence reflectivity of an intersecting Lithoprobe reflection line. The mid-crustal boundary correlates with a crustal detachment zone in the Lithoprobe data and the depth extent of east-dipping wide-angle reflectors. Regional structure and aeromagnetic anomaly trends support the southwest continuity of Grenville terranes and their boundaries from the wide-angle profile to two reflection lines in Lake Ontario. A zone of wide-angle reflectors with an average apparent eastward dip of 13° has a surface projection that correlates spatially with the boundary between the Elzevir and Frontenac terranes of the Central Metasedimentary Belt and resembles reflection images of a crustal-scale shear zone beneath Lake Ontario. A high-velocity upper-crustal anomaly beneath the Elzevir–Frontenac boundary zone is positioned in the hanging wall associated with the concentrated zone of wide-angle reflectors. The high-velocity anomaly is coincident with a gravity high and increased metamorphic grade, suggesting northwest transport of mid-crustal rocks by thrust faulting consistent with the mapped geology. The seismic data suggest (i) a reflective, crustal-scale structure has accommodated northwest-directed tectonic transport within the Central Metasedimentary Belt; (ii) this structure continues southwest from the exposed Central Metasedimentary Belt to at least southern Lake Ontario; and (iii) crustal reflectivity and complexity within the eastern Central Metasedimentary Belt is similar to that observed at the Grenville Front and the western Central Metasedimentary Belt boundary.

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