Center for Subsurface Imaging and Fluid Modeling (CSIM)
Recent Submissions

Superresolution Imaging Using Resonant Multiples(Society of Exploration Geophysicists, 20171222)A resonant multiple is defined as a multiple reflection that revisits the same subsurface location along coincident reflection raypaths. We show that resonant firstorder multiples can be migrated with either Kirchhoff or waveequation migration methods to give images with approximately twice the spatial resolution compared to poststack primaryreflection images. A moveoutcorrection stacking method is proposed to enhance the signaltonoise ratios (SNRs) of the resonant multiples before superresolution migration. The effectiveness of this procedure is validated by synthetic and field data tests.

Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves(Society of Exploration Geophysicists, 20171222)A robust imaging technology is reviewed that provide subsurface information in challenging environments: waveequation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method with synthetic seismograms and field data. The benefits of WD are that 1) there is no layered medium assumption, as there is in conventional inversion of dispersion curves, so that the 2D or 3D Svelocity model can be reliably obtained with seismic surveys over rugged topography, and 2) WD mostly avoids getting stuck in local minima. The synthetic and field data examples demonstrate that WD can accurately reconstruct the Swave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic media and the inversion of dispersion curves associated with Love wave. The liability is that is almost as expensive as FWI and only recovers the Vs distribution to a depth no deeper than about 1/2~1/3 wavelength.

Parsimonious Surface Wave Interferometry(Oxford University Press (OUP), 20171024)To decrease the recording time of a 2D seismic survey from a few days to one hour or less, we present a parsimonious surfacewave interferometry method. Interferometry allows for the creation of a large number of virtual shot gathers from just two reciprocal shot gathers by crosscoherence of trace pairs, where the virtual surface waves can be inverted for the Swave velocity model by waveequation dispersion inversion (WD). Synthetic and field data tests suggest that parsimonious waveequation dispersion inversion (PWD) gives Svelocity tomograms that are comparable to those obtained from a full survey with a shot at each receiver. The limitation of PWD is that the virtual data lose some information so that the resolution of the Svelocity tomogram can be modestly lower than that of the Svelocity tomogram inverted from a conventional survey.

Superresolution Nearfield Imaging with Surface Waves(Oxford University Press (OUP), 20171021)We present the theory for nearfield superresolution imaging with surface waves and time reverse mirrors (TRMs). Theoretical formulas and numerical results show that applying the TRM operation to surface waves in an elastic halfspace can achieve superresolution imaging of subwavelength scatterers if they are located less than about 1/2 of the shear wavelength from the source line. We also show that the TRM operation for a single frequency is equivalent to natural migration, which uses the recorded data to approximate the Green’s functions for migration, and only costs O(N4) algebraic operations for poststack migration compared to O(N6) operations for natural prestack migration. Here, we assume the sources and receivers are on an N × N grid and there are N2 trial image points on the free surface. Our theoretical predictions of superresolution are validated with tests on synthetic data. The fielddata tests suggest that hidden faults at the near surface can be detected with subwavelength imaging of surface waves by using the TRM operation if they are no deeper than about 1/2 the dominant shear wavelength.

Skeletonized waveequation Qs tomography using surface waves(Society of Exploration Geophysicists, 20170817)We present a skeletonized inversion method that inverts surfacewave data for the Qs quality factor. Similar to the inversion of dispersion curves for the Swave velocity model, the complicated surfacewave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleighwave arrivals. The optimal Qs model is then found that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradientbased waveequation optimization method. Solutions to the viscoelastic waveequation are used to compute the predicted Rayleighwave arrivals and the misfit gradient at every iteration. This procedure, denoted as waveequation Qs tomography (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to Q full waveform inversion (QFWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

Raytracing traveltime tomography versus waveequation traveltime inversion for nearsurface seismic land data(Society of Exploration Geophysicists, 20170511)Fullwaveform inversion of land seismic data tends to get stuck in a local minimum associated with the waveform misfit function. This problem can be partly mitigated by using an initial velocity model that is close to the true velocity model. This initial starting model can be obtained by inverting traveltimes with raytracing traveltime tomography (RT) or waveequation traveltime (WT) inversion. We have found that WT can provide a more accurate tomogram than RT by inverting the firstarrival traveltimes, and empirical tests suggest that RT is more sensitive to the additive noise in the input data than WT. We present two examples of applying WT and RT to land seismic data acquired in western Saudi Arabia. One of the seismic experiments investigated the watertable depth, and the other one attempted to detect the location of a buried fault. The seismic land data were inverted by WT and RT to generate the Pvelocity tomograms, from which we can clearly identify the water table depth along the seismic survey line in the first example and the fault location in the second example.

Resolution limits of migration and linearized waveform inversion images in a lossy medium(Oxford University Press (OUP), 20170310)The verticaland horizontalresolution limits Delta x(lossy) and Delta z(lossy) of poststack migration and linearized waveform inversion images are derived for lossy data in the farfield approximation. Unlike the horizontal resolution limit Delta x proportional to lambda z/L in a lossless medium which linearly worsens in depth z, Delta x(lossy) proportional to z(2)/QL worsens quadratically with depth for a medium with small Q values. Here, Q is the quality factor, lambda is the effective wavelength, L is the recording aperture, and loss in the resolution formulae is accounted for by replacing lambda with z/Q. In contrast, the lossy verticalresolution limit Delta z(lossy) only worsens linearly in depth compared to Delta z proportional to lambda for a lossless medium. For both the causal and acausal Q models, the resolution limits are linearly proportional to 1/Q for small Q. These theoretical predictions are validated with migration images computed from lossy data.

Imaging nearsurface heterogeneities by natural migration of backscattered surface waves: Field data test(Society of Exploration Geophysicists, 20170306)We have developed a methodology for detecting the presence of nearsurface heterogeneities by naturally migrating backscattered surface waves in controlledsource data. The nearsurface heterogeneities must be located within a depth of approximately onethird the dominant wavelength λ of the strong surfacewave arrivals. This natural migration method does not require knowledge of the nearsurface phasevelocity distribution because it uses the recorded data to approximate the Green’s functions for migration. Prior to migration, the backscattered data are separated from the original records, and the bandpassed filtered data are migrated to give an estimate of the migration image at a depth of approximately onethird λ. Each bandpassed data set gives a migration image at a different depth. Results with synthetic data and field data recorded over known faults validate the effectiveness of this method. Migrating the surface waves in recorded 2D and 3D data sets accurately reveals the locations of known faults. The limitation of this method is that it requires a dense array of receivers with a geophone interval less than approximately onehalf λ.

Parsimonious waveequation traveltime inversion for refraction waves(WileyBlackwell, 20170214)We present a parsimonious waveequation traveltime inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into O(N2) refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for waveequation traveltime inversion. Numerical results show that the parsimonious waveequation traveltime tomogram has about the same accuracy as the tomogram computed by standard waveequation traveltime inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.

Parsimonious Refraction Interferometry and Tomography(Oxford University Press (OUP), 20170204)We present parsimonious refraction interferometry and tomography where a densely populated refraction data set can be obtained from two reciprocal and several infill shot gathers. The assumptions are that the refraction arrivals are head waves, and a pair of reciprocal shot gathers and several infill shot gathers are recorded over the line of interest. Refraction traveltimes from these shot gathers are picked and spawned into O(N2) virtual refraction traveltimes generated by N virtual sources, where N is the number of geophones in the 2D survey. The virtual traveltimes can be inverted to give the velocity tomogram. This enormous increase in the number of traveltime picks and associated rays, compared to the many fewer traveltimes from the reciprocal and infill shot gathers, allows for increased model resolution and a better condition number with the system of normal equations. A significant benefit is that the parsimonious survey and the associated traveltime picking is far less time consuming than that for a standard refraction survey with a dense distribution of sources.

Opportunities and pitfalls in surfacewave interpretation(Society of Exploration Geophysicists, 20170121)Many explorationists think of surface waves as the most damaging noise in land seismic data. Thus, much effort is spent in designing geophone arrays and filtering methods that attenuate these noisy events. It is now becoming apparent that surface waves can be a valuable ally in characterizing the nearsurface geology. This review aims to find out how the interpreter can exploit some of the many opportunities available in surface waves recorded in land seismic data. For example, the dispersion curves associated with surface waves can be inverted to give the Swave velocity tomogram, the commonoffset gathers can reveal the presence of nearsurface faults or velocity anomalies, and backscattered surface waves can be migrated to detect the location of nearsurface faults. However, the main limitation of surface waves is that they are typically sensitive to Swave velocity variations no deeper than approximately half to onethird the dominant wavelength. For many exploration surveys, this limits the depth of investigation to be no deeper than approximately 0.51.0 km.

Waveequation dispersion inversion(Oxford University Press (OUP), 20161208)We present the theory for waveequation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by verticalcomponent geophones. Similar to waveequation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phasevelocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D Swave velocity models. This procedure, denoted as waveequation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycleskipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the Swave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

Parsimonious refraction interferometry(Society of Exploration Geophysicists, 20160906)We present parsimonious refraction interferometry where a densely populated refraction data set can be obtained from just two shot gathers. The assumptions are that the first arrivals are comprised of head waves and direct waves, and a pair of reciprocal shot gathers is recorded over the line of interest. The refraction traveltimes from these reciprocal shot gathers can be picked and decomposed into O(N2) refraction traveltimes generated by N virtual sources, where N is the number of geophones in the 2D survey. This enormous increase in the number of virtual traveltime picks and associated rays, compared to the 2N traveltimes from the two reciprocal shot gathers, allows for increased model resolution and better condition numbers in the normal equations. Also, a reciprocal survey is far less time consuming than a standard refraction survey with a dense distribution of sources.

Imaging nearsurface heterogeneities by natural migration of surface waves(Society of Exploration Geophysicists, 20160906)We demonstrate that nearsurface heterogeneities can be imaged by natural migration of backscattered surface waves in common shot gathers. No velocity model is required because the data are migrated onto surface points with the virtual Green's functions computed from the shot gathers. Migrating shot gathers recorded by 2D and 3D land surveys validates the effectiveness of detecting nearsurface heterogeneities by natural migration. The implication is that more accurate hazard maps can be created by migrating surface waves in land surveys.

Wave equation dispersion inversion using a difference approximation to the dispersioncurve misfit gradient(Elsevier BV, 20160726)We present a surfacewave inversion method that inverts for the Swave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamentalmode Rayleigh wave is inverted using finitedifference solutions to the multidimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal Swave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

Skeletonized inversion of surface wave: Active source versus controlled noise comparison(Society of Exploration Geophysicists, 20160714)We have developed a skeletonized inversion method that inverts the Swave velocity distribution from surfacewave dispersion curves. Instead of attempting to fit every wiggle in the surface waves with predicted data, it only inverts the picked dispersion curve, thereby mitigating the problem of getting stuck in a local minimum. We have applied this method to a synthetic model and seismic field data from Qademah fault, located at the western side of Saudi Arabia. For comparison, we have performed dispersion analysis for an active and controlled noise source seismic data that had some receivers in common with the passive array. The active and passive data show good agreement in the dispersive characteristics. Our results demonstrated that skeletonized inversion can obtain reliable 1D and 2D Swave velocity models for our geologic setting. A limitation is that we need to build layered initial model to calculate the Jacobian matrix, which is time consuming.

Extracting 220 Hz information from 55 Hz field data by nearfield superresolution imaging(Oxford University Press (OUP), 20160531)Field experiments are used to unequivocally demonstrate seismic superresolution imaging of subwavelength objects in the nearfield region of the source. The field test is for a conventional hammer source striking a metal plate near subwavelength scatterers and the seismic data are recorded by verticalcomponent geophones in the farfield locations of the sources. Timereversal mirrors (TRMs) are then used to refocus the scattered energy with subwavelength resolution to the position of the original source. A spatial resolution of lambda/10, where lambda is the dominant wavelength associated with the data, is seen in the field tests that exceeds the Abbe resolution limit of lambda/2.

Geotechnical Parameters from Seismic Measurements: Two Field Examples from Egypt and Saudi Arabia(GeoScienceWorld, 20160318)© 2016 EEGS. Geotechnical parameters were used to determine subsurface rock quality for construction purposes. We summarize the mathematical relationships used to calculate the geotechnical parameters from P and Swave velocities and density values. These relationships are applied to two field examples; the first is a regional seismic study in Egypt and the second is a 2D seismic profile recorded in Saudi Arabia. Results from both field examples are used to determine the subsurface rock quality and locate zones that should be avoided during construction. We suggest combining all geotechnical parameters into one map using a normalizedweighted relation, which helps to locate the zones with high versus low rock quality for engineering purposes.