S11D-01
Body-Wave Attenuation Structure in Southern Mexico
Velocity spectra from moderate-sized earthquakes are used to investigate the body-wave attenuation structure in southern Mexico. In particular, we include local events with magnitudes in the range 4.0 < M < 6.2 and depths larger than 50 km recorded from July 2007 to present on the VEOX array, which consists of 47 broadband sensors from Pacific Coast to Gulf of Mexico, cross Oaxaca and Veracruz states in southern Mexico. By assuming a Brune-type source, a path-averaged frequency-independent Q is obtained for each seismogram in the frequency band 2 to 30 Hz, depending on the signal quality. P wave analyses show that waves from events deeper than 130 km and north of 16.5N generally attenuate more in the back arc than in the fore arc, while the waves from events shallower than 100 km do not show much distinctive feature. This indicates that the mantle wedge in this region is characterized by high attenuation, and the high-attenuation zone may lie approximately between the depths of 100 km and 130 km. Preliminary estimates show Q ~ 1000 in the crust and slab, and Q ~ 200 in the high-attenuation mantle wedge zone. The fact that waves from events to further south do not show a distinction between the back arc and fore arc is probably due to a 3D effect. We will present a detailed attenuation tomography model of this region, which then can be used to estimate variations in viscosity.
S11D-02
High Frequency Downhole Recordings of Sichuan Aftershocks
On June 6th, 2008, during nine hours of downhole recording with a three component borehole seismic array tool put in place to monitor a hydraulic fracture stimulation, recordings were made of several dozen natural earthquakes. The duration, frequency content and S-P arrival time difference of these events indicated that they were not related to the anticipated microseismic activity from the hydraulic stimulation about 1km away; rather they were coming from a distance of about 300km, about the distance to the M=7.9 Sichuan event of May 12th, 2008. The tool used in the recordings was a commercial borehole seismic array tool composed (in this case) of seven shuttles separated by 50m, each equipped with three component (3C) sensor packages coupled to the well casing and thereby to the formation via annular cement. Acoustic isolation of the 3C sensor package from the main body of each shuttle is accomplished via a retractable spring system. This tool design and the exceptionally quiet recording environment at 1500-1800m depth below ground level provide a very low noise floor and excellent vector fidelity. The geophones themselves are omni-tilt accelerometers, with particle displacements obtained through response function removal and (twice) time integration. These nine hours of downhole 3C array data present a unique set of high frequency earthquake recordings. Bandwidth extends from 1Hz to greater than 60Hz with 40dB signal-to-noise ratio between 3-10Hz. Processing is being carried out using a new technique developed for hydraulic fracture monitoring. This technique (Leaney (2008)) employs least-squares time reversal with a ray-trace Green's function and waveform fitting. Data analysis will include anisotropic model calibration using selected master events from assumed known locations, events location and source function determination. Other possibilities include reduced or constrained moment tensor inversion and interferometric (relative S/P) Q estimation. It is not yet known whether deep crustal reflections are present in the data.
S11D-03 INVITED
Seismic Absorption Estimation and Compensation
As seismic waves travel through the earth, visco-elasticity of the medium causes energy dissipation and waveform distortion. This phenomenon is referred to as seismic absorption. In hydrocarbon reservoir description, seismic absorption can be used as an important attribute to interpret fluid content. In seismic data processing, such information can be used to enhance seismic data resolution by means of absorption compensation. The absorptive property of a medium can be described by a quality factor, Q, which, together with the velocity, describes the propagation of seismic energy in the earth. In this presentation, we develop a basic approach which deals with the estimation and application of seismic absorption. By assuming that the amplitude spectrum of a seismic wavelet may be modeled as that of a Ricker wavelet, an analytical relation has been derived to estimate Q from seismic data peak frequency variation with time. Coarse resolution Q values can be estimated from prestack common midpoint (CMP) gathers, or from a poststack single trace based on event picking. To estimate interval Q's for reservoir description, a method, reflectivity-guided seismic attenuation analysis, is proposed. This approach first estimates peak frequencies at a common midpoint location, then correlates the peak frequency with sparsely- distributed reflectivities, and finally computes Q values from the peak frequencies at the reflectivity locations analytically. The peak frequency is estimated from the prestack CMP gather using peak frequency variation with offset (PFVO) analysis which is similar to amplitude variation with offset (AVO) analysis in implementation. Since the estimated Q section has the same layer boundaries as those of the acoustic impedance or other layer properties, the seismic attenuation property obtained with the guide of reflectivity is easy to interpret for the purpose of reservoir description. To overcome the instability problem of conventional inverse Q filtering, we formulate Q compensation as a least squares inverse problem in a Bayesian manner. To compensate for absorption in migrated seismic sections, we have developed a refocusing technique using nonstationary multidimensional deconvolution. We introduce a numerical method to calculate the blurring function in layered media, and use an n inverse scheme to remove the blurring effect in order to refocus the migrated image. This refocusing processing can be used as an alternative for regular migration with absorption compensation.
S11D-04
Waveform Tomography Strategies for Imaging 2D Attenuation Structure
Waveform Tomography, when implemented in the frequency-domain, potentially yields images of the intrinsic attenuation from seismic waveform data (Pratt et al., 1998). The attenuation (or its inverse, the seismic Q value) is strongly related to rheology, fluid flow, pore fluid content and fractures. Since phase and amplitude anomalies are also caused by velocity structure (due to geometrical and scattering effects), it is critical to assess inversion strategies as to their ability to resolve these effects. We compared two sets of strategies: first, velocity and attenuation models were updated jointly at each iteration ("simultaneous inversio"). In a second test, ("sequential inversion"), a velocity model alone was first inverted, followed by simultaneous inversion. While the predicted waveforms from both strategies agreed with the observed data, only the sequential inversion strategy imaged attenuation structure well in the presence of small-scale velocity heterogeneities. This highlights the strong dependence of attenuation imaging on the quality of the velocity model. We then tested the approach using a shallow seismic dataset collected on an engineered clay embankment at Seven Sisters Falls, Manitoba. The test embankment contained three targets composed of granitic rip- rap; these corresponded to higher velocities and higher scattering potential than the surrounding in-situ clays. Waveform Tomography was applied to long-offset refraction data collected over the embankment using 70 weight-drop shots and 48 geophones. The starting model was developed with traveltime tomography on the hand-picked first arrivals. The data were inverted between 20 Hz and 150 Hz, corresponding to wavelengths between approximately 100 m and 13 m. We were able to resolve sub- wavelength targets on the order of 3-4 m in cross-section using the final velocity model. Interpretation of the seismic-Q images along with the velocity allowed us to define the target positions. In order to assess the quality of our model fit, we compared synthetic results with the real data. A very good fit between model and observed data was achieved, indicating the reliability of the results.
S11D-05
Joint multi-frequency inversion of teleseismic P-wave amplitudes and traveltimes for 3-D velocity and attenuation structure under North America
We investigate amplitude anomalies of teleseismic body waves as a function of frequency and invert them using finite-frequency kernels. Applying our matched-filter cross-correlation technique (Sigloch and Nolet 2006) we obtain finite-frequency amplitude anomalies at dominant wave periods between 21 s and 2.7 s. This is equivalent to tstar measurements in that we sample the spectal slope at several frequencies, but in addition our method models spatial interference patterns (Fresnel zones). We correct for radiation patterns and deconvolve source time functions from broadband seismograms and correct for radiation patterns. For tomography, we use only amplitudes measured at 21, 15, and 10 s period (3 passbands, 160,000 recorded data in North America between 1999-2007). The same signal processing yields 420,000 traveltime measurements in seven passbands between 21 s and 2.7 s period (traveltimes can be fit more robustly at higher frequencies). We jointly invert amplitudes and traveltimes for 3-D P-velocity and attenuation structure of the mantle under North America. We focus our discussion on the western U.S. because the dense station coverage of USArray greatly facilitates the assessment of amplitudes and their comparison to the tomographic model. P-wave amplitude anomalies represent a clear, reproducible signal in many regards. At individual stations, amplitude anomalies cluster by source region. Variations are on the order of 10-20%. Amplitude dispersion on individual seismograms is often on the same order (10-20%) in the used frequency range of 0.05-0.1 Hz, but can be much larger when considering higher frequencies. Hence frequency dispersion is a strong effect in amplitudes. The variations are not always monotonous with frequency, which underscores the need for finite-frequency interpretation. Across USArray, we observe large-scale patterns of amplitude anomalies (station-averaged) that are spatially coherent over hundreds of kilometers. After source corrections, the tomographic velocity model predicts most of the observed amplitudes and their dispersion. This indicates that elastic focusing is the main cause of teleseismic P-wave amplitude anomalies. Amplitude predictions are good even when the velocity model was obtained from traveltimes only. The dominance of focusing is underscored by the fact that Vp models inverted from a) amplitudes only, and b) traveltimes only, are remarkably similar except between 200-400 km depth. Our 3-D Q-model is less robust, since attenuation is constrained by amplitudes only. Q anomalies are largely limited to the upper mantle. The magnitude of amplitude signal explained by Q structure is 2-3 times smaller than that explained by Vp. In addition, the Q model contains some suspect features (e.g., high Q under Yellowstone) that suggest "leakage" (focusing erroneously interpreted as attenuation). This ambiguity also manifests itself in resolution tests. Although Q inversions tell a cautionary tale, we envision improvements in robustness through coarser parametrization and improved signal processing. Once USArray moves into cratonic North America, we can also expect to target large-scale attenuation differences of greater magnitude than within the western U.S. alone.
S11D-06
Seismic Wave Propagation in Layered Viscoelastic Media
Advances in the general theory of wave propagation in layered viscoelastic media reveal new insights regarding seismic waves in the Earth. For example, the theory predicts: 1) P and S waves are predominantly inhomogeneous in a layered anelastic Earth with seismic travel times, particle-motion orbits, energy speeds, Q, and amplitude characteristics that vary with angle of incidence and hence, travel path through the layers, 2) two types of shear waves exist, one with linear and the other with elliptical particle motions each with different absorption coefficients, and 3) surface waves with amplitude and particle motion characteristics not predicted by elasticity, such as Rayleigh-Type waves with tilted elliptical particle motion orbits and Love-Type waves with superimposed sinusoidal amplitude dependencies that decay exponentially with depth. The general theory provides closed-form analytic solutions for body waves, reflection-refraction problems, response of multiple layers, and surface wave problems valid for any material with a viscoelastic response, including the infinite number of models, derivable from various configurations of springs and dashpots, such as elastic, Voight, Maxwell, and Standard Linear. The theory provides solutions independent of the amount of intrinsic absorption and explicit analytic expressions for physical characteristics of body waves in low-loss media such as the deep Earth. The results explain laboratory and seismic observations, such as travel-time and wide-angle reflection amplitude anomalies, not explained by elasticity or one dimensional Q models. They have important implications for some forward modeling and inverse problems. Theoretical advances and corresponding numerical results as recently compiled (Borcherdt, 2008, Viscoelastic Waves in Layered Media, Cambridge University Press) will be reviewed.
S11D-07
Seismic Waves In Dissipative Anisotropic Media
Wave propagation in dissipative anisotropic media is an important subject of contemporary seismology. We concentrate on three aspects of wave propagation in such media: on the so-called forbidden directions for inhomogeneous plane waves (for which real-valued and imaginary-valued parts of slowness vectors make a non-zero angle), on the specification of the quality factor Q for dissipative anisotropic media and on discussion of importance of consideration of inhomogeneous waves in heterogeneous dissipative media. We show that the problem of forbidden directions is caused by the use of attenuation angle (angle between real-valued and imaginary-valued parts of the slowness vector) for the specification of inhomogeneity of the plane wave. We propose use of the so-called inhomogeneity parameter, which avoids the problem. We define Q as the ratio of the densities of the time-averaged complete stored energy and dissipated energy. The quality factor is a real-valued positive, dimensionless, scalar, directionally dependent quantity. For weakly dissipative media, Q is independent of inhomogeneity of waves. Inhomogeneous waves are an important part of wavefields generated in heterogeneous dissipative media. They are generated even by a point source situated in a homogeneous anisotropic dissipative medium.
S11D-08 INVITED
Full Anelastic Waveform Tomography Including Model Uncertainty
We present a nonlinear adjoint waveform inversion method for determining the crustal velocity and intrinsic attenuation properties of sedimentary valleys in earthquake-prone regions. We formulate the inverse problem as a constrained optimization problem, where the constraints are the partial and ordinary differential equations governing the anelastic wave propagation from the source to the receivers. We employ a wave propagation model in which the intrinsic energy-dissipating nature of the soil medium is modeled by a set of standard linear solids. To represent the modeling uncertainties, given a prior model, we include an L2- normed weighting term, in addition to the data misfit term in our objective function, which quantifies the model estimation errors independent of the measured data. We illustrate the methodology with pseudo-data from two-dimensional sedimentary models of the San Fernando Valley obtained from the Southern California Earthquake Center (SCEC) Community Velocity Model using a source model with an antiplane slip function.