Browsing by Subject "Seismic attenuation"

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Multitaper spectral analysis of wide-angle refraction data from Costa Rica for t* estimation
(2007-12-22) Sood, Sanjay; Sen, Mrinal K.; Van Avendonk, Harm J. A.
The inputs and outputs of the Central American subduction zone have received attention from geoscientists of many disciplines in recent years. In order to have full understanding of subduction, it is important to have constraints on the nature of deep-seated magmatic processes and the composition of newly formed crust. In January to March and July 2005, I was associated with a group of scientists from the United States and Costa Rica that acquired two long seismic refraction lines parallel to and across the arc in Costa Rica to image the physical properties of the entire crust. Line1 runs almost SW-NE, across the arc in central Costa Rica from Pacific coast in the west to Atlantic coast in the east. We deployed 742 seismometers at nominal spacing of 200 m. Reftek “Texans” data loggers were used to record the data with a sampling interval of 4 msec. Twenty explosive shots ranging in size from 200 kg to 1025 kg were used. These sources were detonated at ~ 7.5 km interval along the profile to acquire seismic refraction data on this cross-section of the arc. The ultimate goal of the project is to infer subsurface temperature distribution that can be related to magmatic processes. One approach to estimating temperature distribution is to map seismic attenuation distribution. Towards this goal, I have used the data from this line to map the variation of t* (path integrated attenuation) values across the volcanic arc using a method based on spectral ratios. I have compared several spectrum estimating techniques and demonstrated that a multitaper method is able to obtain robust estimates of spectra. I estimated the source by summing the spectra from near offset stations, a weighted running average of spectra with one km radius was taken to enhance the signal to noise ratio and a Random sampling was used to obtain more realistic estimates of the errors in the spectra. Finally I used a Spectral Ratio’s method to calculate the slopes. Different frequency windows were used to calculate the least squares linear fit. My results show a large variation in the t* values. These fluctuations in the t* values are attributed to the large variations in the near site effects and scattering attenuation associated with them along the profile. Some anomalous t* values may be a result of focusing of seismic energy due to underlying velocity structure. The background noise plays an important role in the t* values as well. At larger source-receiver offsets the signal/noise ratio is lower. Consequently, we overestimate the amplitude of the higher frequency at large offsets. Contrary to the assumption of Spectral Ratio’s method, attenuation seems to be frequency dependent for this data set
Seismic modeling and imaging in complex media using low-rank approximation
(2016-12) Sun, Junzhe; Fomel, Sergey B.; Biros, George; Ghattas, Omar; Sen, Mrinal K.; Zhang, Yu
Seismic imaging in geologically complex areas, such as sub-salt or attenuating areas, has been one of the greatest challenges in hydrocarbon exploration. Increasing the fidelity and resolution of subsurface images will lead to a better understanding of geological and geomechanical properties in these areas of interest. Wavefield time extrapolation is the kernel of wave-equation-based seismic imaging algorithms, known as reverse-time migration. In exploration seismology, traditional ways for solving wave equations mainly include finite-difference and pseudo-spectral methods, which in turn involve finite-difference approximation of spatial or temporal derivatives. These approximations may lead to dispersion artifacts as well as numerical instability, therefore imposing a strict limit on the sampling intervals in space or time. This dissertation aims at developing a general framework for wave extrapolation based on fast application of Fourier integral operators (FIOs) derived from the analytical solutions to wave equations. The proposed methods are theoretically immune to dispersion artifacts and numerical instability, and are therefore desirable for applications to seismic imaging. First, I derive a one-step acoustic wave extrapolation operator based on the analytical solution to the acoustic wave equation. The proposed operator can incorporate anisotropic phase velocity, angle-dependent absorbing boundary conditions and further improvements in phase accuracy. I also investigate the numerical stability of the method using both theoretical derivations and numerical tests. Second, to model wave propagation in attenuating media, I use a visco-acoustic dispersion relation based on a constant-Q wave equation with decoupled fractional Laplacians, which allows for separable control of amplitude loss and velocity dispersion. The proposed formulation enables accurate reverse-time migration with attenuation compensation. Third, to further improve numerical stability of Q-compensation, I introduce stable Q-compensation operators based on amplitude spectrum scaling and smooth division. Next, for applications to least-squares RTM (LSRTM) and full-waveform inversion, I derive the adjoint operator of the low-rank one-step wave extrapolation method using the theory of non-stationary filtering. To improve the convergence rate of LSRTM in attenuating media, I propose Q-compensated LSRTM by replacing the adjoint operator in LSRTM with Q-compensated RTM. Finally, I extend the low-rank one-step wave extrapolation method to general elastic anisotropic media. Using the idea of eigenvalue decomposition and matrix exponential, I study the relationship between wave propagation and wave-mode decomposition. To handle the case of strong heterogeneity, I incorporate gradients of stiffnesses in wave extrapolation. Numerous synthetic examples in both 2D and 3D are used to test the practical application and accuracy of the proposed approaches.