scholarly journals Tackling Lateral Variability Using Surface Waves: A Tomography-Like Approach

2021 ◽  
Author(s):  
Ilaria Barone ◽  
Jacopo Boaga ◽  
Alberto Carrera ◽  
Adrian Flores-Orozco ◽  
Giorgio Cassiani
Keyword(s):  
Inverse Problem ◽  
Surface Wave ◽  
Weighted Least Squares ◽  
Low Velocity ◽  
Lateral Velocity ◽  
Linear Inversion ◽  
Urban Waste ◽  
Near Surface ◽  
Velocity Variations ◽  
Waste Deposit

AbstractLateral velocity variations in the near-surface reflect the presence of buried geological or anthropic structures, and their identification is of interest for many fields of application. Surface wave tomography (SWT) is a powerful technique for detecting both smooth and sharp lateral velocity variations at very different scales. A surface-wave inversion scheme derived from SWT is here applied to a 2-D active seismic dataset to characterize the shape of an urban waste deposit in an old landfill, located 15 km South of Vienna (Austria). First, the tomography-derived inverse problem for the 2-D case is defined: under the assumption of straight rays at the surface connecting sources and receivers, the forward problem for one frequency reduces to a linear relationship between observed phase differences at adjacent receivers and wavenumbers (from which phase velocities are straightforwardly derived). A norm damping regularization constraint is applied to ensure a smooth solution in space: the choice of the damping parameter is made through a minimization process, by which only phase variations of the order of the average wavelength are modelled. The inverse problem is solved for each frequency with a weighted least-squares approach, to take into account the data error variances. An independent multi-offset phase analysis (MOPA) is performed using the same dataset, for comparison: pseudo-sections from the tomography-derived linear inversion and MOPA are very consistent, with the former giving a more continuous result both in space and frequency and less artefacts. Local dispersion curves are finally depth inverted and a quasi-2-D shear wave velocity section is retrieved: we identify a well-defined low velocity zone and interpret it as the urban waste deposit body. Results are consistent with both electrical and electromagnetic measurements acquired on the same line.

Turning‐ray tomography

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1917-1929 ◽  
Author(s):  
Joseph P. Stefani
Keyword(s):  
Velocity Structure ◽  
Initial Point ◽  
Real Data ◽  
Point Sources ◽  
Surface Velocity ◽  
Inversion Algorithm ◽  
Low Velocity ◽  
Linear Inversion ◽  
Near Surface ◽  
Velocity Inversion

Turning‐ray tomography is useful for estimating near‐surface velocity structure in areas where conventional refraction statics techniques fail because of poor data or lack of smooth refractor/velocity structure. This paper explores the accuracy and inherent smoothing of turning‐ray tomography in its capacity to estimate absolute near‐surface velocity and the statics times derived from these velocities, and the fidelity with which wavefields collapse to point diffractors when migrated through these estimated velocities. The method comprises nonlinear iterations of forward ray tracing through triangular cells linear in slowness squared, coupled with the LSQR linear inversion algorithm. It is applied to two synthetic finite‐ difference data sets of types that usually foil conventional refraction statics techniques. These models represent a complex hard‐rock overthrust structure with a low‐velocity zone and pinchouts, and a contemporaneous near‐shore marine trench filled with low‐ velocity unconsolidated deposits exhibiting no seismically apparent internal structure. In both cases velocities are estimated accurately to a depth of one‐ fifth the maximum offset, as are the associated statics times. Of equal importance, the velocities are sufficiently accurate to correctly focus synthetic wavefields back to their initial point sources, so migration/datuming applications can also use these velocities. The method is applied to a real data example from the Timbalier Trench in the Gulf of Mexico, which exhibits the same essential features as the marine trench synthetic model. The Timbalier velocity inversion is geologically reasonable and yields long and short wavelength statics that improve the CMP gathers and stack and that correctly align reflections to known well markers. Turning‐ray tomography estimates near‐surface velocities accurately enough for the three purposes of lithology interpretation, statics calculations, and wavefield focusing for shallow migration and datuming.

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.

scholarly journals Singular value decomposition of the velocity‐reflector depth tradeoff, Part 2: High‐resolution analysis of a generic model

Geophysics ◽  
1992 ◽  
Vol 57 (7) ◽  
pp. 933-943 ◽  
Author(s):  
Christof Stork
Keyword(s):  
Inverse Problem ◽  
Singular Value Decomposition ◽  
Circulant Matrix ◽  
Singular Value ◽  
Generic Model ◽  
Lateral Velocity ◽  
Block Circulant Matrix ◽  
Velocity Variations ◽  
Value Decomposition ◽  
Horizontal Wavelength

The symmetries of a block circulant matrix significantly reduce the computational expense of the singular value decomposition (SVD) of the variable velocity inverse problem for a generic reflection seismology model. As a result, the decomposition does not suffer from edge effects or parameterization artifacts that are associated with small model spaces. Using this approach, we study the eigenvector and eigenvalue characteristics for a generic model of a size as large as is used with a variety of iterative inversion techniques (>100 000 parameters). Singular value decomposition of the raypath inverse problem of a discretized generic seismic model having one reflector indicates that the eigenvalue distribution for the inverse problem is nonuniform, with a large concentration near 0 and a gap near 0.4. All but the long horizontal wavelength reflector‐depth variations cannot be uniquely resolved from velocity variations. Lateral velocity variations serve to significantly reduce the ability of seismic data to resolve reflector depth for most of the horizontal wavelength components shorter than twice the cable length. As a result, automatic velocity analysis methods may not be able to resolve reflector variations when the velocity field is allowed to take on an arbitrary structure.

Imaging near-surface sharp lateral variations with surface-wave methods — Part 1: Detection and location

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. EN93-EN111 ◽  
Author(s):  
Chiara Colombero ◽  
Cesare Comina ◽  
Laura Valentina Socco
Keyword(s):  
Surface Wave ◽  
Acoustic Impedance ◽  
Location Estimation ◽  
Single Shot ◽  
Low Velocity ◽  
Near Surface ◽  
Wave Methods ◽  
Geophone Spacing ◽  
Decay Exponent ◽  
Lateral Variations

Near-surface sharp lateral variations can be either a target of investigation or an issue for the reconstruction of reliable subsurface models in surface-wave (SW) prospecting. Effective and computationally fast methods are consequently required for detection and location of these shallow heterogeneities. Four SW-based techniques, chosen between available literature methods, are tested for detection and location purposes. All of the techniques are updated for multifold data and then systematically applied on new synthetic and field data. The selected methods are based on computation of the energy, energy decay exponent, attenuation coefficient, and autospectrum. The multifold upgrade is based on the stacking of the computed parameters for single-shot or single-offset records and improves readability and interpretation of the final results. Detection and location capabilities are extensively evaluated on a variety of 2D synthetic models, simulating different target geometries, embedment conditions, and impedance contrasts with respect to the background. The methods are then validated on two field cases: a shallow low-velocity body in a sedimentary sequence and a hard-rock site with two embedded subvertical open fractures. For a quantitative comparison, the horizontal gradients of the four parameters are analyzed to establish uniform criteria for location estimation. All of the methods indicate ability in detecting and locating lateral variations having lower acoustic impedance than the surrounding material, with errors generally comparable or lower than the geophone spacing. More difficulties are encountered in locating targets with higher acoustic impedance than the background, especially in the presence of weak lateral contrasts, high embedment depths, and small dimensions of the object.

Spatial variation of crustal seismic velocities in southern California

1981 ◽  
Vol 71 (3) ◽  
pp. 671-689
Author(s):  
Raymond A. Ergas ◽  
David D. Jackson
Keyword(s):  
Southern California ◽  
Arrival Time ◽  
Epicentral Distance ◽  
Seismic Velocities ◽  
Time Data ◽  
Error Statistics ◽  
Lateral Velocity ◽  
Offshore Area ◽  
Near Surface ◽  
Velocity Variations

abstract Arrival-time data for local earthquakes were used to study lateral velocity variations and error statistics for southern California. Crustal P velocities averaged over the major geomorphic provinces vary by only a few per cent. Regions of relatively high velocity include the Peninsular ranges, the Imperial valley, the Pomona basin, and the Colorado desert. The Santa Monica, southern Sierra, San Bernardino, and San Jacinto mountains are relatively slow, as is the offshore area. Near-surface station delays, which are unknown to within several tenths of a second, are a major source of uncertainty in the regional velocities. Arrival-time errors include two types: (1) small errors caused by imperfect timing and unmodeled velocity variations; and (2) larger errors apparently caused by improper identification of arrivals and by blunders. We found no reliable way to identify the latter errors unless they result in large arrival-time residuals. For a strongly edited catalog, the variance of arrival-time residuals appears to increase linearly with epicentral distance, as predicted for wave propagation in a randomly heterogeneous medium. The variance of residuals is strongly station dependent. Residuals are nearly Gaussian within the 70 per cent confidence interval, but not outside this interval. The 95 per cent confidence limit occurs at about three standard deviations.

Time-lapse monitoring of stress-field variations within the Lower Permian shales in Kansas

2020 ◽  
Vol 39 (5) ◽  
pp. 318-323 ◽  
Author(s):  
Sarah L. Morton ◽  
Richard D. Miller ◽  
Julian Ivanov ◽  
Shelby L. Peterie ◽  
Robert L. Parsons
Keyword(s):  
Surface Wave ◽  
Stress Field ◽  
Shear Wave ◽  
Time Lapse ◽  
Bulk Velocity ◽  
Low Velocity ◽  
Mining Operations ◽  
South Central ◽  
Cap Rock ◽  
Velocity Variations

Azimuthal stress-field variations in Permian shale overlying voids in salt appear related to localized void roof failure based on interpretations of time-lapse recordings of passive seismic surface-wave data. Salt-dissolution voids in south-central Kansas exist within the Hutchinson Salt Member as a result of solution mining operations early in the 20th century. Since shear-wave velocity can be estimated from surface-wave analysis and is directly related to the shear modulus, or material rigidity, it can be used to indicate shale cap-rock competency. Temporal bulk-velocity variations in bedrock acquired over a known void from 2013 to 2018 are consistent with cyclic stress-field behavior expected with repetitive localized failure within the shale cap rock. It was determined that roof failure and associated subsidence began prior to the 2013 surveys along a north–south failure plane with consistent progression from southwest to northeast until 2017. A low-velocity anomaly observed in 2014–2015 on both profiles indicated a load redistribution in the shale cap rock. This low-velocity region was gradually replaced by an increasing velocity field in subsequent years. These bulk-velocity variations are interpreted as representations of stoping, which occurs when overlying roof layers or sidewall segments progressively fail. As of 2018, the velocity trend in the affected area remained lower than the recorded baseline conditions, with no low-velocity anomalies observed since 2015. Shear-wave velocities are not likely to return to 2013 conditions due to loss of roof material and redistribution of load. Annual surveys will monitor for conditions consistent with the beginning of a stress buildup and roof collapse unless monitoring indicates a change in the subsurface that warrants invasive analysis or other actions.

Tomographic velocity analysis and wave-equation depth migration in an overthrust terrain: A case study from the Tuha Basin, China

2018 ◽  
Vol 6 (1) ◽  
pp. T1-T13
Author(s):  
Bin Lyu ◽  
Qin Su ◽  
Kurt J. Marfurt
Keyword(s):  
Wave Equation ◽  
Data Quality ◽  
Model Building ◽  
Velocity Model ◽  
Lateral Velocity ◽  
Near Surface ◽  
Depth Migration ◽  
Time Migration ◽  
Head Waves ◽  
Velocity Variations

Although the structures associated with overthrust terrains form important targets in many basins, accurately imaging remains challenging. Steep dips and strong lateral velocity variations associated with these complex structures require prestack depth migration instead of simpler time migration. The associated rough topography, coupled with older, more indurated, and thus high-velocity rocks near or outcropping at the surface often lead to seismic data that suffer from severe statics problems, strong head waves, and backscattered energy from the shallow section, giving rise to a low signal-to-noise ratio that increases the difficulties in building an accurate velocity model for subsequent depth migration. We applied a multidomain cascaded noise attenuation workflow to suppress much of the linear noise. Strong lateral velocity variations occur not only at depth but near the surface as well, distorting the reflections and degrading all deeper images. Conventional elevation corrections followed by refraction statics methods fail in these areas due to poor data quality and the absence of a continuous refracting surface. Although a seismically derived tomographic solution provides an improved image, constraining the solution to the near-surface depth-domain interval velocities measured along the surface outcrop data provides further improvement. Although a one-way wave-equation migration algorithm accounts for the strong lateral velocity variations and complicated structures at depth, modifying the algorithm to account for lateral variation in illumination caused by the irregular topography significantly improves the image, preserving the subsurface amplitude variations. We believe that our step-by-step workflow of addressing the data quality, velocity model building, and seismic imaging developed for the Tuha Basin of China can be applied to other overthrust plays in other parts of the world.

scholarly journals Physics-Based Relationship for Pore Pressure and Vertical Stress Monitoring Using Seismic Velocity Variations

2021 ◽  
Vol 13 (14) ◽  
pp. 2684
Author(s):  
Eldert Fokker ◽  
Elmer Ruigrok ◽  
Rhys Hawkins ◽  
Jeannot Trampert
Keyword(s):  
Pore Pressure ◽  
Seismic Velocity ◽  
Pressure Head ◽  
Groundwater Table ◽  
Surface Velocity ◽  
Seismic Velocities ◽  
Stress Monitoring ◽  
Near Surface ◽  
Velocity Variations ◽  
Velocity Changes

Previous studies examining the relationship between the groundwater table and seismic velocities have been guided by empirical relationships only. Here, we develop a physics-based model relating fluctuations in groundwater table and pore pressure with seismic velocity variations through changes in effective stress. This model justifies the use of seismic velocity variations for monitoring of the pore pressure. Using a subset of the Groningen seismic network, near-surface velocity changes are estimated over a four-year period, using passive image interferometry. The same velocity changes are predicted by applying the newly derived theory to pressure-head recordings. It is demonstrated that the theory provides a close match of the observed seismic velocity changes.

STACKING OF REFLECTIONS FROM COMPLEX STRUCTURES

Geophysics ◽  
1974 ◽  
Vol 39 (4) ◽  
pp. 427-440 ◽  
Author(s):  
Max K. Miller
Keyword(s):  
Deep Structure ◽  
Control Model ◽  
Layer Model ◽  
Low Velocity ◽  
Seismic Reflection Data ◽  
Near Surface ◽  
Static Correction ◽  
Reflection Data ◽  
Actual Field ◽  
Interval Velocities

Common‐depth‐point seismic reflection data were generated on a computer using simple ray tracing and analyzed with processing techniques currently used on actual field recordings. Constant velocity layers with curved interfaces were used to simulate complex geologic shapes. Two models were chosen to illustrate problems caused by curved geologic interfaces, i.e., interfaces at depths which vary laterally in a nonlinear fashion and produce large spatial variations in the apparent stacking velocity. A three‐layer model with a deep structure and no weathering was used as a control model. For comparison, a low velocity weathering layer also of variable thickness was inserted near the surface of the control model. The low velocity layer was thicker than the ordinary thin weathering layers where state‐of‐the‐art static correction methods work well. Traveltime, moveout, apparent rms velocities, and interval velocities were calculated for both models. The weathering introduces errors into the rms velocities and traveltimes. A method is described to compensate for these errors. A static correction applied to the traveltimes reduced the fluctuation of apparent rms velocities. Values for the thick weathering layer model were “over corrected” so that synclines (anticlines) replaced false anticlines (synclines) for both near‐surface and deep zones. It is concluded that computer modeling is a useful tool for analyzing specific problems of processing CDP seismic data such as errors in velocity estimates produced by large lateral variations in overburden.

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