Linear Least-squares Inversion Research Articles

Least-squares Gaussian beam migration in viscoacoustic media

Because of amplitude decay and phase dispersion of seismic waves, conventional migrations are insufficient to produce satisfactory images using data observed in highly attenuative geologic environments. We have developed a least-squares Gaussian beam migration method for viscoacoustic data imaging, which can not only compensate for amplitude decay and phase dispersion caused by attenuation, but it can also improve image resolution and amplitude fidelity through linearized least-squares inversion. We represent the viscoacoustic Green’s function by a summation of Gaussian beams, in which an attenuation traveltime is incorporated to simulate or compensate for attenuation effects. Based on the beam representation of the Green’s function, we construct the viscoacoustic Born forward modeling and adjoint migration operators, which can be effectively evaluated by a time-domain approach based on a filter-bank technique. With the constructed operators, we formulate a least-squares migration scheme to iteratively solve for the optimal image. Numerical tests on synthetic and field data sets demonstrate that our method can effectively compensate for the attenuation effects and produce images with higher resolution and more balanced amplitudes than images from acoustic least-squares Gaussian beam migration.

Micromechanics modelling for mineral volume fraction determination: application on a terrigenous formation

This work presents a non-linear Self-Consistent (SC) micromechanics method to model the observed physical elastic properties of a terrigenous formation with the purpose to obtain its depth mineral volume fractions profile. In this approach, it is first assumed that the observed physical elastic properties obtained from well logs, such as the density rho_{o} and the elastic compressional Vp_{o} and shear Vs_{o} velocities, are a non-linear relationship of the unknown mineral volume fractions alpha. Then, a gradient descent algorithm is implemented to seek for those volume fractions alpha for which differences between modelled and observed physical elastic properties are minimum. It is assumed that quartz, calcite and clay are the main comprising minerals of the formation. Obtained volume fractions profile follow the same general trends to those estimated by implementing the Linear Least-Squares Inversion LLSI method which is widely used in petrophysical analysis to obtain mineral concentrations from density rho_{o}, photoelectric effect Pe_{o} and compressional slowness Delta tp_{o} well logs. Results also show that calcite and clay volume fractions from these two methods are highly correlated while quartz volume fractions show low correlation. Further comparison between clay concentrations from SC method with clay concentrations calculated from direct measurements of gamma ray GR well logs used as a guideline also exhibits high correlation. These results suggest that the SC method is better suited to obtain clay and calcite volume fractions rather than quartz volume fractions. However, SC method can provide with insights about the general distribution of quartz along the borehole.

Origin and causes of complex magnetic anomalies of Dokdo and neighboring guyots

To identify the causes of complex magnetic anomalies on the three guyots located in the northeastern part of the Ulleung Basin, East Sea, a linear least-squares inversion method was implemented. Modeling under the assumption that the guyots are uniformly magnetized did not yield reliable results. However, an inhomogeneously-magnetized model shows relatively high goodness-of-fit parameters and low residual magnetic anomalies, indicating that these guyots are considerably nonuniformly magnetized. Our modeling results show that all three guyots show similar magnetic patterns. Magnetic anomalies north of guyots have different magnetic polarities at similar depths in the south, indicating that these magnetic anomalies were formed at different times. These results suggest that relatively short wavelengths and complicated magnetic anomalies in the study area are the compound result of different magnetic polarities. Paleomagnetic analysis on trachyandesite lavas and pyroclastic breccia indicates a thermo-chemical remagnetization activity after Reunion Subchron (2.138–2.122 Ma). This result also suggests that remagnetization contributes to the creation of complex magnetic anomalies to some extent as well. In addition, the upward continuation results up to 1500 m using a FFT routine show high positive magnetic anomalies with a linearly segmented shape at the base of guyots. These linear and positive magnetic anomalies are interpreted as volcanic eruptions along fissures because mafic lava should have much higher magnetic anomalies compared to continental crust, where guyots are located. Therefore, we interpret that the complex magnetic anomalies distributed in the study area are due to polarity reversals occurring at least twice, and were formed during the formation of the current guyots as volcanic eruptions derived from fissures.

Elastic model low- to intermediate-wavenumber inversion using reflection traveltime and waveform of multicomponent seismic data

Low-, intermediate-, and high-wavenumber components of P- and S-wave velocities jointly influence the elastic wave propagation and scattering in an isotropic medium. By taking advantage of all information in the data, elastic full-waveform inversion (E-FWI) has the potential to recover these model components. However, if the transmitted wave data are insufficient to illuminate the deeper part of the subsurface, we should rely on the solutions using reflection data. To reduce the nonlinearity of waveform inversion, we choose to decouple the effects of the model background and perturbation on the reflected waves within a linearized inversion framework. This resorts to three stages aiming to gradually fit the traveltimes and waveforms of the reflected PP and PS waves based on data or gradient preconditioning through P/S mode decomposition. For the first two stages, once the multicomponent seismograms have been separated into PP and PS reflection recordings, reflection traveltime inversion using an acoustic wave propagator (A-RTI) can successively recover the low-wavenumber components of P- and S-wave velocities. In the last stage, starting from the models having reliable low-wavenumber components, elastic reflection waveform inversion (E-RWI) can easily get out of the local minima and continue to retrieve the increasing wavenumber features sensitive to the waveform and amplitude variations. This is supported by gradient preconditioning through P/S mode decomposition of the extrapolated normal and adjoint wavefields, and alternately updating model background and high-wavenumber components in terms of linearized least-squares inversion. Numerical examples have demonstrated the performance of our E-RWI approach and the validity of the three-stage inversion workflow.

Geomagnetic and geoelectrical prospection for buried archaeological remains on the Upper City of Amorium, a Byzantine city in midwestern Turkey

On the basis of geophysical imaging surveys, including geomagnetic and geoelectrical resistivity, possible archaeological remains and their spatial parameters (i.e., location, extension, depth and thickness) were explored to provide useful data for future excavations on the Upper City of the ancient Amorium site, which comprises a large prehistoric man-made mound. The surveys were performed very close to the main axis of the Basilica, and the derived geophysical traces indicated some subsurface structures that appear to confirm that more-substantial brick and masonry buildings lie near the present-day surface of the mound. Analyzing the local gradients by total horizontal derivatives of pseudogravity data enhanced the edges of the magnetic sources. Additionally, a profile curvature technique, which has rarely been applied to potential field data sets, dramatically improved the magnetic-source body edges and the lineaments that may be associated with buried archaeological remains. The depths of these possible anthropogenic remains were estimated by applying the Euler deconvolution technique to the geomagnetic data set. The Euler solutions on tentative indices indicated that the depths of the source bodies are not more than about 3 m. Moreover, geoelectrical resistivity depth slices produced from the results of two- and three-dimensional linearized least-squares inversion techniques revealed high-resistivity anomalies within a depth of about 3 m from the ground surface, which is in close agreement with those obtained by applying the Euler deconvolution technique to the magnetic data. Based on the existence of some archaeological remains in the vicinity of the surveyed area, these geophysical anomalies were thought to be the possible traces of the buried remains and were suggested as targets for excavations. This study also emphasized that the data-processing techniques applied in this investigation should be suitable for providing an insight into the layout of the unexcavated parts of the Amorium site.

A simultaneous inversion for deformation rates and topographic errors of DInSAR data utilizing linear least square inversion technique

We demonstrate here a computer code for calculation of time series and also mean and linear deformation rates from a set of coregistered unwrapped differential interferograms using a linear least-squares inversion technique based on the small baseline subset (SBAS) algorithm. The computer code is written in C and uses a singular value decomposition (SVD) routine from the LAPACK library and the fast Fourier transform for spatial filtering from the FFTW library. Various offset estimation and topographic correction algorithms are implemented, including simultaneous inversion for deformation rates and residual topographic error. This approach is particularly useful when applied to ALOS PALSAR interferograms that are coherent even at large perpendicular baselines and acquired with orbital parameters correlated with the time of acquisition. This methodology is applied to produce time series of ground deformation at Tauhara and Wairakei geothermal fields (Taupo Volcanic Zone, North Island, New Zealand) from 12 ALOS PALSAR images acquired between July 2007 and December 2009. We also present here a high-resolution deformation map of the ground subsidence caused by the extraction of geothermal groundwater for power generation, with maximum rates of subsidence of about 7 cm/y.

Influence of inaccurate wavelet phase estimation on seismic inversion

On the assumption that the seismic wavelet amplitude spectrum is estimated accurately, a group of wavelets with different phase spectra, regarded as estimated wavelets, are used to implement linear least-squares inversion. During inversion, except for the wavelet phase, all other factors affecting inversion results are not taken into account. The inversion results of a sparse reflectivity model (or blocky impedance model) show that: (1) although the synthetic data using inversion results matches well with the original seismic data, the inverted reflectivity and acoustic impedance are different from that of the real model. (2) the inversion result reliability is dependent on the estimated wavelet Z transform root distribution. When the estimated wavelet Z transform roots only differ from that of the real wavelet near the unit circle, the inverted reflectivity and impedance are usually consistent with the real model; (3) although the synthetic data matches well with the original data and the Cauchy norm (or modified Cauchy norm) with a constant damping parameter has been optimized, the inverted results are still greatly different from the real model. Finally, we suggest using the L1 norm, Kurtosis, variation, Cauchy norm with adaptive damping parameter or/and modified Cauchy norm with adaptive damping parameter as evaluation criteria to reduce the bad influence of inaccurate wavelet phase estimation and obtain good results in theory.

Upper crustal P-wave velocity structure of Kii Peninsula, SW Japan by first-arrival traveltime inversion of the Kawachinagano-Kiwa refraction profile

SUMMARY We investigated the upper crustal P-wave velocity structure down to 5 km in the Kii Peninsula, SW Japan by a tomographic inversion of the first-arrival traveltimes from the seismic refraction experiment performed by the Research Group for Explosion Seismology (RGES) in 1988. The observations were carried out on a profile running in the N–S direction from Kawachinagano, Osaka Prefecture to Kiwa, Mie Prefecture. The profile extends for about 65 km across the major geological zones, which characterize the geological features of SW Japan. Six shots were fired and the generated seismic waves were recorded at 86 temporary observation sites. The inversion scheme was applied to 359 first-arrival times to delineate the velocity structure along the profile. In the tomographic scheme, velocity estimation was achieved by an iterative, linearized least-squares inversion. The Jacobian matrix was constructed via a finite-difference approximation by perturbing the slownesses of the cells instead of performing ray tracing. Traveltime calculations were carried out by using a fast finite-difference eikonal solver. Velocity updates were obtained by a matrix inversion algorithm using a conjugate gradient least-squares scheme. In addition, model covariance and model resolution matrices were obtained to assess the velocity image. Two low-velocity zones observed in the northern and southern parts of the profile are the most prominent features of the tomogram. The P-wave velocity structure is generally consistent with the surface geology, and the fault zones associated with the Median (MTL) and Gobo-Hagi (GHTL) tectonic lines across the peninsula.

Spatial and temporal evolution of a long term slow slip event: the 2006 Guerrero Slow Slip Event

The Guerrero 2006 Slow Slip Event (SSE), Mexico, one of the world's largest observed SSEs, was recorded at 15 continuous GPS stations. This event provides the opportunity to analyse in detail the spatial and temporal evolution of slip at depth, and to constrain the characteristics of a large SSE. We perform an inversion in two steps. First, we invert the cumulative GPS displacements to retrieve the total slip amplitude. Second, we invert for the initiation time and duration of the slip, using a linearized least-squares inversion procedure and assuming a functional form for the slip function. Our results show that the slip is located on a patch of 300 km × 150 km (parallel and perpendicular to the coast, respectively), and extends from the bottom of the seismogenic zone to the transition zone. This slow slip event has an equivalent moment magnitude of 7.5. The maximum slip over a length scale of 25 km is 15 cm and the mean slip is 5.5 cm. Its lateral extension coincides with the segmentation of the subduction. Our inversion scheme allows us to analyse the spatial variability of the rise time, rupture velocity and slip function. We obtain a continuous image of the spatial and temporal variations of slip on the fault plane. The rupture initiated at a depth of 40 km (transition zone), in the western part of the Guerrero gap. The rupture then propagated from the western to the eastern part of the Guerrero segment with an average velocity of 0.8 km d−1. Our results show that a slip dislocation pulse, characterized by a symmetric ramp function, can model the 2006 SSE. The rise time (local duration of slip) does not show large spatial variations and is equal to about 185 d. The local slip duration is compared to the total duration (11–12 months) of the event, suggesting a large interaction of a large part of the fault during the dynamic process. We find that our inverted slip model is well resolved on the shallow part of the fault and in the central section of the fault.

Seismic noise tomography in the Chile ridge subduction region

SUMMARY We used cross-correlation of ambient seismic noise recorded in the Chile Triple Junction (CTJ) region to estimate interstation surface wave time-domain Green’s functions, and then inverted traveltimes to obtain crustal surface wave velocity models. Interstation distances within the Chile Ridge Subduction Project (CRSP) temporary seismic network ranged from 40 to ∼100 km. We selected 365 d, and cross-correlated and stacked 24 hr of vertical component data at 38 stations pairs, resulting in nominally 703 traveltimes along assumed-straight interstation paths. Velocities in 2-D cells of 30 km × 30 km were calculated using a linear least-squares inversion of the Rayleigh wave group velocity traveltimes. Furthermore we performed a Rayleigh wave group velocity dispersion analysis to estimate the sensitivity of different period waves at depth and to calculate a 3-D shear velocity model of the Patagonian crust. The process was applied to cross correlation pairs determined in two period bands, 5–10 s, corresponding to shallow crustal velocities down to approximately 10 km depth, and 10–20 s, for velocities down to around 20 km. Our results show that cell velocities correlate well with known geological features. We find high-crustal velocities where the Patagonian Batholith outcrops or is likely present at depth, and low velocities correlate with the active volcanic arc of the Southern Volcanic Zone and the subducted Chile ridge in Taitao peninsula, where thermal activity of hot springs is present. High velocities in the mountainous portions of the southeastern study area appear to correlate with outcropping older metamorphic units. Low velocity in the east correlate with sequences of volcaniclastic deposits.

Turning-ray tomography using a low-spatial-frequency model parameterization

A linear least-squares inversion is applied to the turning-ray first-arrival times of a shallow-marine seismic reflection data set to estimate the slowly varying (laterally and vertically) components of the near-surface velocity field. The velocity model is represented with a low-spatial-frequency parameterization (2D cubic B-splines) designed specifically for the predicted components of the data. This model parameterization effectively decouples the slowly varying background from the higher spatial-frequency component of the velocity field produced by shallow, low-velocity, gas-charged sands and allows the solution to be obtained in a single iteration. The observed first-arrival times (background and shallow anomaly-induced perturbations) and the slowly varying first-arrival times related to the background velocity are inverted separately. Similar velocity-model estimates result, demonstrating the decoupling imposed by the B-spline model parameterization. The background velocity and the low-velocity anomalies are best treated as separate inverse problems using very different model parameterizations. Ray tracing a synthetic model containing local low-velocity anomalies embedded in a smooth background does not accurately predict the anomaly-induced first-arrival time perturbations seen in the field data. Acoustic finite-difference waveform modeling shows that reflections and diffractions from the anomalies interfere with the diving-wave first arrivals. First-arrival times picked from the full-waveform synthetics more accurately predict the field data first-arrival times.

Wavelet modelling of broad-band receiver functions

SUMMARY We present a wavelet modelling approach to invert for S-wave velocities from broad-band receiver functions. Taking spline function as the basic wavelet, the broad-band receiver function is decomposed into five resolution scales by Mallat's pyramid algorithm. The linearized least-squares inversion procedure is applied to every resolution scale. The fifth-scale approximation of receiver function is first inverted to recover the slowly varying background velocity variations with respect to a reference model. This solution is then taken as the initial model for fitting the fourth-scale wavelet coefficients of receiver function to further tune the solution to resolve sharper variations. This procedure is iteratively carried out up to the first-scale wavelet coefficients of receiver function. In this manner, the model neighbourhood containing the global minimum is first searched from the coarsest-scale receiver function, and the search gradually focuses on the global minimum by introducing finer-scale information of receiver function. Noise-free synthetic receiver function tests show that wavelet modelling of receiver functions can guide a certain range of initial models to converge to the true velocity distribution. Tests on actual data indicate that wavelet modelling can provide results very similar to those inferred by joint inversion of receiver function and surface wave dispersion.

Mapping northern land cover fractions using Landsat ETM+

The goal of fractional mapping is to obtain land cover fraction estimates within each pixel over a region. Using field, Ikonos and Landsat data at three sites in northern Canada, we evaluate a physical unmixing method against two modeling approaches to map five land cover fractions that include bare, grass, deciduous shrub, conifer, and water along an 1100 km north–south transect crossing the tree-line of northern Canada. Error analyses are presented to assess factors that affect fractional mapping results, including modeling method (linear least squares inversion (LLSI) vs. linear regression vs. regression trees), number of Landsat spectral bands (3 vs. 5), local and distant fraction estimation using locally and globally calibrated models, and spatial resolution (30 m vs. 90 m). The ultimate purpose of this study is to determine if reliable land cover fractions can be obtained for biophysical modeling over northern Canada from a three band, resampled 90 m Landsat ETM+ mosaic north of the tree-line. Of the three modeling methods tested, linear regression and regression trees with five spectral bands produced the best local fraction estimates, while LLSI produced comparable results when unmixing was sufficiently determined. However, distant fraction estimation using both locally and globally calibrated models was most accurate using the three spectral bands available in the Landsat mosaic of northern Canada at 30 m resolution, and only slightly worse at 90 m resolution. While local calibrations produced more accurate fractions than global calibrations, application of local calibration models requires stratification of areas where local endmembers and models are representative. In the absence of such information, globally calibrated linear regression and regression trees to estimate separate fractions is an acceptable alternative, producing similar root mean square error, and an average absolute bias of less than 2%.

S-wave velocity structure, mantle xenoliths and the upper mantle beneath the Kaapvaal craton

SUMMARY Inversion of two-station Rayleigh-wave fundamental-mode phase velocities across the undisturbed region of the southern Kaapvaal craton south of the Bushveld Province produces velocity-depth models quantitatively similar to those estimated from low-T mantle xenoliths brought to the surface in Cretaceous-age kimberlite pipes that erupted in the same region. The cratonic xenolith suite was previously analysed thermobarometrically and chemically to obtain the equilibrium P-T conditions from which the seismic velocities and density of the cratonic mantle to about 180 km depth were calculated. As the xenoliths represent a snapshot of the mantle at the time of their eruption, comparison with recently recorded seismic data provides an opportunity to compare and contrast the independently gained results. We form a composite reference velocity model using xenolith values for the depth range 50–180 km with an interpolated join to PREM for the depth range 220–500 km, and a regionally determined crustal model for the upper 35 km. This composite served as the starting model for a linearized least-squares inversion (LLSI) using fundamental-mode Rayleigh-wave phase velocities in the period range 18–171 s measured for five events along 16 two-station paths within the southern Kaapvaal craton. Based on xenolith data, we constrain the vP/vS ratio in the inversion to vary from about 1.72 in the uppermost mantle to 1.78 at 180 km depth. The velocity structures determined by surface-wave inversion are consistent with those derived from the xenolith data, suggesting that the velocity structure (i.e. thermal structure) of the mantle to a depth of 180 km beneath the Kaapvaal craton today is similar to that at ∼70–90 Ma, the time of kimberlite eruption. Results from both surface-wave inversion and xenolith calculations indicate that S-wave velocities decrease slightly with depth beneath the craton, from a value around 4.7 km s−1 in the uppermost mantle to about 4.60–4.65 km s−1 at a depth of 180–200 km. We performed tests based on a wide range of starting models, and found no models with a minimum vS in the mantle less than about 4.55 km s−1 down to a depth of 250 km within the resolution possible from an inversion based on fundamental-mode Rayleigh waves. Additional analysis of synthetic models, using a combination of LLSI and the neighbourhood algorithm, shows that if there was a low-velocity zone such as that reported by Priestley in 1999, our analysis procedure would have found it.

Comparison of Performance of Heuristic Search Methods for Phase Velocity Inversion in Shallow Surface Wave Method

Three heuristic search methods, Genetic Algorithm, Simulated Annealing and Tabu Search are implemented to invert Rayleigh wave phase velocity for shallow S-wave velocity profiling in seismic surface wave surveying. Unlike linearized least-squares inversion, they do not require derivative calculation, or an initial model, only the forward modeling calculation. In this study, the performances of the three heuristic techniques are compared with numerical experiments. With common paramerization and search limits, the three algorithms can accurately reconstruct shallow S-wave profiles with and without a velocity reversal from the synthetic data without any specific initial models. The Genetic Algorithms and the Simulated Annealing show fast convergence. However, the Simulated Annealing can find models with the smallest misfits. It is also found that the decrease of the misfits is the most gradual in the Tabu Search.

Inversion of electrical capacitance tomography data by simulated annealing: Application to real two-phase gas–oil flow imaging

In this work we apply a highly optimized simulated annealing (SA) inversion method to the reconstruction of permittivity images from real two-phase gas–oil flow electrical capacitance tomography (ECT) data. We test the SA inversion method using several flow regimes generated by varying gas and oil flow rates in a test loop facility. The SA-based permittivity inversions have some advantages over other reconstruction approaches based on linear least-squares inversion: they can find good solutions starting with poor initial models, can easily implement complex a priori information, and do not introduce smoothing effects in the final permittivity distribution model. A major disadvantage comes from the fact that SA is computationally very intensive and leads to relatively slow reconstructions when calculation of the forward problem is not very fast. In this work we employ a linearized and numerically improved forward model based on the use of a sensitivity matrix. We find this novel approach to be faster and more accurate than traditional linear methods.

Three-dimensional upper-mantleS-velocity model for the Eurasia-Africa plate boundary region

SUMMARY A new regional S-velocity study resolving the Eurasia‐Africa plate boundary region from the Azores to the eastern Mediterranean Sea is presented. The resolution of existing velocity models has been complemented by using new seismic broad-band data recorded by the temporary MIDSEA network and at permanent European seismic stations. Following the partitioned waveform inversion method, we interactively fitted the waveforms of S and Rayleigh wave trains of more than 1100 seismograms. The linear constraints on upper-mantle S velocity provided by the waveform fits have been combined with independent estimates of Moho depth in a linear damped least-squares inversion for S velocity and crustal thickness. The resulting S-velocity structure for the Mediterranean Sea shows strong lateral variations, confirming the complex evolution of this plate boundary region. The upper mantle along the Eurasia‐Africa suture zone is characterized by high-velocity material representing subducted oceanic lithosphere. This signature can be followed to depths of 300‐500 km, depending on the region and resolution. A high-velocity body, possibly representing a fragment of subducted lithosphere, has been imaged beneath eastern Spain at a depth between 250 and 500 km. Not only convergence has been recorded in the upper mantle, but extension also has its own signature beneath the

Constraints on the S wave velocity structure in a continental shield from surface wave data: Comparing linearized least squares inversion and the direct search Neighbourhood Algorithm

In their study of upper mantle structure beneath the Paraná Basin of SE Brazil, Snoke and James [1997] concluded, on the basis of a linearized least squares inversion (LLSI) of surface wave dispersion data, that a strong (5% contrast) low‐velocity zone (LVZ) beginning at a depth less than ∼150 km was not required to fit the data. They were unable to establish a quantitative estimate, however, on the maximum depth at which such a LVZ could be resolved by their data. Sambridge [1999a, 1999b] has introduced the Neighbourhood Algorithm (NA), a direct search method for nonlinear inversion which can be tuned to extract information from an ensemble of models in addition to finding a single best fit model. Applying NA to the Brazilian dispersion data quantifies the statistics of the ensemble of models classified as “acceptable” based on a data misfit criterion and a smoothness constraint. The NA best fit model is not significantly different from the LLSI best fit model, but the analysis of the ensemble of models provides new insights regarding how well constrained the model is. Synthetics runs show that for this data set, our modeling procedures could resolve a strong LVZ that began at a depth of 120 km but could not rule out such an LVZ beginning at a depth of 180 km.

Vertical profile of effective turbidity reconstructed from broadening of incoherent body-wave pulses-I. General approach and the inversion procedure

SUMMARY A method is developed for the reconstruction of a non-uniform distribution of scattering properties in the upper layers of the Earth using data on broadening of an incoherent body-wave group or pulse along a number of rays. The theoretical basis for this reconstruction is a linear integral formula after Bocharov (1985, 1988), which is employed to design a linear inversion procedure. The inversion is performed in terms of a single scalar parameter of eVective turbidity. This parameter presents an adequate generalization of the common turbidity parameter used in the isotropic scattering case; it describes, simultaneously, scattering attenuation, pulse broadening and backscattering or coda formation. As a preliminary step, necessary conditions of applicability of the transport equation approach for the analysis of regional high-frequency seismic waves are verified. A new compact derivation of Bocharov’s formula is then presented. A linear leastsquares inversion procedure for recovering a layered turbidity structure is proposed and tested on synthetic data of onset-to-peak delays of incoherent body-wave pulses. A few practical aspects of the application of the general approach to seismological data are analysed, including the correctness of the low-angle approximation, the use of peak delay observations instead of pulse centroid, the eVects of a realistic spatial spectrum of inhomogeneity field, the potential bias produced by intrinsic loss, and the distortions produced by a non-spherical (double dipole) source radiation pattern. The latter point is considered as critically important, as one can expect significant data contamination by nodal arrivals. An eYcient robust estimation procedure is designed and tested that is capable of suppressing distortions from nodal and near-nodal data.

Full waveform inversion of field sonar returns for a visco-acoustic Earth; a comparison of linearized and fully nonlinear methods

The techniques of linearized least squares inversion (LLSI) and simulated annealing (SA) are both used to invert a series of synthetic and real normal-incidence, geo-acoustic sonar returns for estimates of impedance versus two-way travel time in the top several meters of ocean floor sediment. The objective is to determine the better (faster, more accurate) method for inverting this class of data. LLSI uses an over parameterized earth, i.e., one composed of layers whose thickness corresponds to a travel time equal to the sample interval. This makes the inverse problem quite large, but also makes it nearly linear. SA uses a more efficient parameterization, one whose layers have variable thickness as well as variable impedance. Because of the relatively narrow frequency band (/spl sim/1 octave at 20 dB down from the peak) the time domain signal is oscillatory and inversion for layer thickness is nonlinear. Results show greater time efficiency in solving the large linear problem (LLSI) than in solving the small nonlinear problem (SA). However, in both cases almost all of the waveform energy was modeled, indicating that essentially all the information in the data had been successfully recovered. The inversions are applied to 10-20 kHz field data acquired offshore Florida, and several techniques are employed to enhance the effectiveness of each inversion method.