Alan R. Levander

Fourth-order finite-difference P-SV seismograms

I describe the properties of a fourth-order accurate space, second-order accurate time two-dimensional P-Sk’ finite-difference scheme based on the MadariagaVirieux staggered-grid formulation. The numerical scheme is developed from the first-order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses. The Madariaga-Virieux staggered-grid scheme has the desirable quality that it can correctly model any variation in material properties, including both large and small Poisson’s ratio materials, with minimal numerical dispersion and numerical anisotropy. Dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints/wavelength. The scheme can be used to accurately simulate wave propagation in mixed acoustic-elastic media, making it ideal for modeling marine problems. Explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free-surface or within a layer and to satisfy free-surface boundary conditions. Benchmark comparisons of finite-difference and analytical solutions to Lamb’s problem are almost identical, as are comparisons of finite-difference and reflectivity solutions for elastic-elastic and acoustic-elastic layered models.

Continuing Colorado plateau uplift by delamination-style convective lithospheric downwelling

The Colorado plateau is a large, tectonically intact, physiographic province in the southwestern North American Cordillera that stands at ∼1,800–2,000 m elevation and has long been thought to be in isostatic equilibrium. The origin of these high elevations is unclear because unlike the surrounding provinces, which have undergone significant Cretaceous–Palaeogene compressional deformation followed by Neogene extensional deformation, the Colorado plateau is largely internally undeformed. Here we combine new seismic tomography and receiver function images to resolve a vertical high-seismic-velocity anomaly beneath the west-central plateau that extends more than 200 km in depth. The upper surface of this anomaly is seismically defined by a dipping interface extending from the lower crust to depths of 70–90 km. The base of the continental crust above the anomaly has a similar shape, with an elevated Moho. We interpret these seismic structures as a continuing regional, delamination-style foundering of lower crust and continental lithosphere. This implies that Pliocene (2.6–5.3 Myr ago) uplift of the plateau and the magmatism on its margins are intimately tied to continuing deep lithospheric processes. Petrologic and geochemical observations indicate that late Cretaceous–Palaeogene (∼90–40 Myr ago) low-angle subduction hydrated and probably weakened much of the Proterozoic tectospheric mantle beneath the Colorado plateau. We suggest that mid-Cenozoic (∼35–25 Myr ago) to Recent magmatic infiltration subsequently imparted negative compositional buoyancy to the base and sides of the Colorado plateau upper mantle, triggering downwelling. The patterns of magmatic activity suggest that previous such events have progressively removed the Colorado plateau lithosphere inward from its margins, and have driven uplift. Using Grand Canyon incision rates and Pliocene basaltic volcanism patterns, we suggest that this particular event has been active over the past ∼6 Myr.

A stochastic view of lower crustal fabric based on evidence from the Ivrea Zone

Despite its complicated history the Ivrea Zone is considered to be a representative surface exposure of extended continental crust. We have digitized two standard 1:25,000 geological maps from this area and evaluated their structural statistics. Because of the subvertical orientation of the Ivrea Zone these maps can be considered as small-scale cross sections through the lower continental crust. The autocorrelation functions of the digitized lithologies measured from these maps show a clear self-similar or fractal rather than a Gaussian or deterministic trend. We found that an anisotropic von Karman correlation function with an aspect ratio around 4 and a Hurst number of 0.3, corresponding to a fractal dimension of 2.7, matches the observed data. Our results represent an explicit confirmation of previous indirect evidence for the fractal nature of lithospheric heterogeneities and provide the means to construct realistic crustal-scale seismic models of Ivrea-type lower continental crust.

Trans-Alaska Crustal Transect and continental evolution involving subduction underplating and synchronous foreland thrusting

We investigate the crustal structure and tectonic evolution of the North American continent in Alaska, where the continent has grown through magmatism, accretion, and tectonic under-plating. In the 1980s and early 1990s, we conducted a geological and geophysical investigation, known as the Trans-Alaska Crustal Transect (TACT), along a 1350-km-long corridor from the Aleutian Trench to the Arctic coast. The most distinctive crustal structures and the deepest Moho along the transect are located near the Pacific and Arctic margins. Near the Pacific margin, we infer a stack of tectonically underplated oceanic layers interpreted as remnants of the extinct Kula (or Resurrection) plate. Continental Moho just north of this underplated stack is more than 55 km deep. Near the Arctic margin, the Brooks Range is underlain by large-scale duplex structures that overlie a tectonic wedge of North Slope crust and mantle. There, the Moho has been depressed to nearly 50 km depth. In contrast, the Moho of central Alaska is on average 32 km deep. In the Paleogene, tectonic underplating of Kula (or Resurrection) plate fragments overlapped in time with duplexing in the Brooks Range. Possible tectonic models linking these two regions include flat-slab subduction and an orogenic-float model. In the Neogene, the tectonics of the accreting Yakutat terrane have differed across a newly interpreted tear in the subducting Pacific oceanic lithosphere. East of the tear, Pacific oceanic lithosphere subducts steeply and alone beneath the Wrangell volcanoes, because the overlying Yakutat terrane has been left behind as underplated rocks beneath the rising St. Elias Range, in the coastal region. West of the tear, the Yakutat terrane and Pacific oceanic lithosphere subduct together at a gentle angle, and this thickened package inhibits volcanism.

Crustal and uppermost mantle structure along the Deep Probe seismic profile

The Rocky Mountain region has undergone a complex tectonic history that includes Proterozoic accretion to form the North American craton, late Paleozoic deformation, Cretaceous to early Tertiary shortening, and Oligocene to Recent extension. Understanding the effects of these events on lithospheric structure was the primary goal of the Deep Probe seismic experiment. This is a lithospheric-scale study of the Rocky Mountain region that attempted to image crust and upper mantle structures up to 500 km depth to provide insights on the effect of various tectonic events on todays continental structure. To accomplish this goal, instruments were deployed along a 2400-km-long transect from New Mexico to Canada to record explosions 10 times more powerful than those employed in conventional crustal studies. The Deep Probe results provide new constraints on the location and geometry of the Archean–Proterozoic boundary near the Colorado–Wyoming border, as well as new information on crustal thickness, and uppermost mantle velocities along the profile. Geophysical modeling of the profile used well log and geologic data to evaluate the composition and structure of the uppermost crust. Seismic refraction and reflection, gravity, and receiver function studies were employed to constrain properties of the lower crust and upper mantle structure. The final model shows that seismic velocities along the Deep Probe profile range from 3.5 km/s in the basins to over 8.2 km/s in the upper mantle. At the southern end of the profile, the model indicates a crustal thickness of about 35 km beneath the Basin and Range province. The crust gradually thickens to about 40 to 45 km going north along the profile into the Colorado Plateau. An area of 50 km-thick crust under northwestern Colorado may reflect Proterozoic tectonism related to the suture zone between the Archean and Proterozoic terranes. Northwestward thinning of the crust to about 40 km under southern Wyoming is interpreted as evidence for a relict (2.0 Ga) passive continental margin. The crust in the Archean Wyoming province thickens to over 50 km going north, and then thins again under southern Canada. This thickening is due to a lowermost crustal layer that is about 20 km thick and is confined to the Archean Wyoming province. This lower crustal layer has velocities ranging from 7.05 to 7.3 km/s, which corresponds to a mafic composition. Thus, this layer is interpreted as mafic material that was probably underplated during the Archean. The uppermost mantle of the Archean Wyoming province has lower velocities (∼8.1 km/s) on average than typical cratonal areas, which is consistent with it being located in and adjacent to the North American Cordillera, which has undergone significant recent tectonism.

The crust as a heterogeneous "optical" medium" or "crocodiles in the mist"

Abstract Based on petrophysical data, geologic maps, and a well log, we present statistical descriptions of likely upper-, middle-, and lower-crustal rocks to characterize the fine-scale heterogeneity observed in crustal exposures and inferred from deep-crustal seismic data. The statistical models, developed for granitic and metamorphic upper crust, and for an extended metamorphic lower crust, are used to construct whole-crustal models of seismic velocity heterogenity. We present finite-difference synthetic CMP data from several models which compare favorably with field data. The statistical models also permit classification of the seismic reflection experiment and the crustal heterogeneity according to scattering regime. The “optical”, or scattering properties of importance for classification are the velocity fluctuation intensity, the horizontal and vertical correlation lengths of the medium, the correlation function of the medium, and the velocity population function. For the crustal properties we measured, the bandwidth of a typical deep crustal experiment overlaps from the weak to the strong scattering regime, with implications for crustal seismic data processing and imaging. Notably, deep-crustal signals are likely to have experienced multiple scattering, making common seismic imaging techniques of questionable value. Moreover, the details of the unmigrated CMP stacked section bears little resemblance to the underlying medium.

Modal fields: A new method for characterization of random seismic velocity heterogeneity

Geologically and petrophysically constrained synthetic random velocity fields are important tools for exploring (through the application of numerical codes) the seismic response of small-scale lithospheric heterogeneities. Statistical and geophysical analysis of mid- and lower-crustal exposures has demonstrated that the probability density function for some seismic velocity fields is likely to be discrete rather than continuous. We apply the term “modal” fields to describe fields of this sort. This letter details a methodology for generating synthetic modal fields which satisfy the von Karman covariance function. In addition, we explore some of the mathematics of “modality”, and define a modality parameter which quantifies the variation between end members binary and continuous fields.

Stochastic modeling of the reflective lower crust: Petrophysical and geological evidence from the Ivera Zone (northern Italy)

A method for the attainment of enhanced enantioselectivity in the reduction of 3-acyl derivatives of 1-(2-alkoxyethyl)-4-phenyl-imidazolin-2-ones to the optically active 3-acyl derivatives of 1-(2-alkoxyethyl)-4-phenyl-2-imidazolidones for use in the direct manufacture of levamisole, (-), 2, 3, 5, 6-tetrahydro-6-phenylimidazo-[2,1-b]-thiazole, useful as an anthelmintic has been discovered. The method involves the preferred use of iodide salts of Rh(I) complexes of optically active bis-tertiary phosphines to achieve maximum enantioselectivity. The methods for preparing the iodide salts are disclosed.

Small-scale heterogeneity and large-scale velocity structure of the continental crust

Since Conrad [1925] first identified a midcrustal refraction event in central Europe seismologists have developed layered models of the continental crust with velocity steps at various levels. Modern analysis of crustal refraction data, including automated inversion, relies on ray theoretical techniques or wave theory for plane layered media, which generally parameterize the Earth as a series of grossly horizontal layers. The bias toward layered models is in part based on physical and geologic intuition, but it is to a large measure a result of available interpretation methods, for example layer-based reflectivity and ray tracing methods. In contrast, reflection seismology has produced a picture of a highly heterogeneous crust, with wavelength-scale variations in velocity existing at different levels of the crust in different tectonic regimes. Finite difference modeling shows that zones of small amplitude random velocity fluctuations not only produce short discontinuous reflection segments as observed on deep seismic reflection data but also produce strong wide-angle reflections. Some of the events identified as crustal wide-angle reflections in field data may in fact be the result of scattering from wavelength-scale heterogeneities and need not result from reflection from a first- or second- order velocity discontinuity. Significant changes in the large-scale velocity structure associated with zones of random velocity fluctuations produce relatively small changes in the dynamic properties of the backscattered wave field. This observation is in disagreement with the common credo that the seismic refraction method is primarily sensitive to changes in the large-scale velocity structure. As a consequence, the ray theoretical interpretation of such wide-angle reflections as first-order discontinuities leads to crustal velocity structures that are nonunique and may be erroneous in detail, while correctly predicting average crustal velocity and thickness. We are not suggesting that crustal velocity does not change with depth on the large-scale; rather, we are proposing that crustal seismic events observed at intermediate and large offsets may be the result of scattering from wavelength-scale velocity fabric rather than specular reflection or refraction from first-order discontinuities.

Migration moveout analysis and depth focusing

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approa...