Since 1984, Geophysical Data Analysis has filled the need for a short, concise reference on inverse theory for individuals who have an intermediate background in science and mathematics. The new ...edition maintains the accessible and succinct manner for which it is known, with the addition of: MATLAB examples and problem setsAdvanced color graphicsCoverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervalsOnline data sets and MATLAB scripts that can be used as an inverse theory tutorial.
Additional material on probability, including Bayesian influence, probability density function, and metropolis algorithmDetailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studiesNumerous examples and end-of-chapter homework problems help you explore and further understand the ideas presentedUse as classroom text facilitated by a complete set of exemplary lectures in Microsoft PowerPoint format and homework problem solutions for instructorsCheck out the companion website: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123971609 and the Instructor website: http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123971609
Seismic attenuation exhibits strong geographic variability in northeastern North America, with the highest values associated with the previously recognized Northern Appalachian Anomaly (NAA) in ...southern New England. The shear wave quality factor at 100 km depth is 14 < QS < 25, the ratio of P wave and S wave quality factors is QP/QS = 1.2 ± 0.03 (95%), and the frequency dependence parameter is α = 0.39 ± 0.025 (95%). The high values of QP/QS and α are compatible with laboratory measurements of unmelted rock and, in the case of α, incompatible with widespread melting. The low QS implies high mantle temperatures (~1,550–1,650°C) at 100 km depth (assuming no melt). Small‐scale variations in attenuation suggest structural heterogeneity within the NAA, possibly due to lithospheric delamination caused by asthenospheric flow.
Key Points
High seismic attenuation implies temperatures of ~1,550–1,650°C at ~100 km depth in the vicinity of the Northern Appalachian Anomaly
The character of the attenuation is incompatible with the widespread presence of melt but might allow low melt concentrations (~0.1%)
Strong spatial variability of attenuation may be due to lithosphere delamination caused by northeast‐southwest asthenospheric flow
The cross‐correlation of multicomponent ambient seismic noise can reveal both the velocity and polarization of surface waves propagating between pairs of stations. We explore this property to develop ...a novel method for determining the horizontal orientation of ocean bottom seismometers (OBS) by analyzing the polarization of Rayleigh waves retrieved from ambient noise cross‐correlation. We demonstrate that the sensor orientations can be estimated through maximizing the correlation between the radial‐vertical component and the phase‐shifted vertical‐vertical component of the empirical Green's tensor. We apply this new method to the ELSC (Eastern Lau Spreading Center) OBS experiment data set and illustrate its robustness by comparing the obtained orientations with results from a conventional method utilizing teleseismic P and Rayleigh wave polarizations. When applied to a large OBS array, the ambient noise method provides a larger number of orientation estimates and better azimuthal coverage than typically is possible with traditional methods.
Key Points
A new method for determining OBS orientation from ambient noise correlation
Polarization of Rayleigh wave is retrieved by 3-component noise correlations
Data quantity and azimuth coverage increase with number of sensors in the array
Environmental Data Analysis with MatLab is for students and researchers working to analyze real data sets in the environmental sciences. One only has to consider the global warming debate to realize ...how critically important it is to be able to derive clear conclusions from often-noisy data drawn from a broad range of sources. This book teaches the basics of the underlying theory of data analysis, and then reinforces that knowledge with carefully chosen, realistic scenarios. MatLab, a commercial data processing environment, is used in these scenarios; significant content is devoted to teaching how it can be effectively used in an environmental data analysis setting. The book, though written in a self-contained way, is supplemented with data sets and MatLab scripts that can be used as a data analysis tutorial. Author's website: http://www.ldeo.columbia.edu/users/menke/edawm/index.htm Well written and outlines a clear learning path for researchers and students Uses real world environmental examples and case studies MatLab software for application in a readily-available software environment Homework problems help user follow up upon case studies with homework that expands them.
Abstract
Tectonic forces alone cannot drive rifting in old and thick continental lithosphere. Geodynamic models suggest that thermal weakening is critical for lithospheric extension, yet many active ...rifts lack volcanism, seeming to preclude this process. We focus on one such rift, the Tanganyika-Rukwa segment of the East African Rift System, where we analyze local seismicity for shear wave anisotropy and couple the results with numerical modeling. The strongest splitting measurements are from earthquakes with paths sampling lower crustal regions of high compressional-to-shear wave velocity ratios and have fast polarization directions parallel to the local mantle flow, implying the existence of oriented melt lenses. This lower crustal magmatism and observed high surface heat flow are consistent with substantial lithospheric weakening and explain the enigmatic relief and increasing strain accommodation along the rift axis. We conclude that progressive nonvolcanic rifting is assisted by deep crustal melts yet to breach the surface.
The generalized least squares (GLS) method uses both data and prior information to solve for a best-fitting set of model parameters. We review the method and present simplified derivations of its ...essential formulas. Concepts of resolution and covariance—essential in all of inverse theory—are applicable to GLS, but their meaning, and especially that of resolution, must be carefully interpreted. We introduce derivations that show that the quantity being resolved is the deviation of the solution from the prior model and that the covariance of the model depends on both the uncertainty in the data and the uncertainty in the prior information. On face value, the GLS formulas for resolution and covariance seem to require matrix inverses that may be difficult to calculate for the very large (but often sparse) linear systems encountered in practical inverse problems. We demonstrate how to organize the computations in an efficient manner and present MATLAB code that implements them. Finally, we formulate the well-understood problem of interpolating data with minimum curvature splines as an inverse problem and use it to illustrate the GLS method.
We solve an idealized version of the moment tensor—anisotropy inverse problem. The medium in which faulting occurs has general anisotropy described by 21 parameters. The data are a set of moment ...tensors for all possible configurations of a unit fault; that is, all combinations of strike, dip and rake (a very idealized assumption, for tectonic constraints may limit available configurations). We first ask whether the anisotropic parameters can be inferred uniquely from the moment tensors and arrive at the answer, “almost”. The data constrain only 20 linear combinations of the 21 parameters; the isotropic Lamé parameter
λ
cannot be determined. We provide an analytic solution algorithm, valid for both weak and strong anisotropy, that uses the data and a prior value of
λ
. We then ask whether measurements of the trace of the moment tensor and its smallest eigenvalue (proxies for its explosive and compensated linear vector dipole components, respectively) can determine uniquely the anisotropy. Here our analysis is limited to the weak anisotropy case. We find that these data are “almost” sufficient. They constrain only 19 linear combinations of the 21 parameters; the isotropic Lamé parameters
λ
and
μ
cannot be determined. We provide a semi-analytic algorithm for solving the inverse problem, given prior values of
λ
and
μ
. Numerical tests demonstrate that both solution methods work and can be used to assess the sensitivity of the solution to erroneous prior information. However, because the methods require data for all fault configurations, their application to the sparse data available for most seismic source regions is limited; they complement but do not supplant existing inversion techniques.
Quantifying volatile concentrations in magmas is critical for understanding magma storage, phase equilibria, and eruption processes. We present PyIRoGlass, an open-source Python package for ...quantifying concentrations of H2O and CO2 species in the transmission FTIR spectra of basaltic to andesitic glasses. We leverage a dataset of natural melt inclusions and back-arc basin basalts with volatiles below detection to delineate the fundamental shape and variability of the baseline underlying the CO32- and H2Om, 1635 peaks, in the mid-infrared region. All Beer-Lambert Law parameters are examined to quantify associated uncertainties. PyIRoGlass employs Bayesian inference and Markov Chain Monte Carlo sampling to fit all probable baselines and peaks, solving for best-fit parameters and capturing covariance to offer robust uncertainty estimates. Results from PyIRoGlass agree with independent analyses of experimental devolatilized glasses (within 6 %) and interlaboratory standards (10 % for H2O, 6 % for CO2). We determine new molar absorptivities for basalts, εH2Ot,3550 = 63.03 ± 4.47 L/mol · cm and εCO2−3,1515,1430 = 303.44 ± 9.20 L/mol · cm; we additionally update the composition-dependent parameterizations of molar absorptivities, with their uncertainties, for all H2O and CO2 species peaks. The open-source nature of PyIRoGlass ensures its adaptability and evolution as more data become available.
•The asthenosphere beneath the northern coast of the Gulf of Mexico is seismically slow.•The intensity of P and S travel time delays and their ratio indicate a thermal origin.•The feature extends up ...to 300 km inland and may be centered offshore.
Seismic measurements are used in a detailed investigation of a region of extremely low asthenospheric seismic velocities along the US Gulf Coast, first imaged in continental-scale geotomography, which we term the Northern Gulf Anomaly (NGA). Differential P- and S-wave arrival times from teleseisms at a variety of back-azimuths, observed on EarthScope Transportable Array stations near the US Gulf Coast, demonstrate that asthenospheric seismic velocities are 8-10% lower than the neighboring craton, and define the spatial extent and character of the anomaly. Travel time anomalies are calculated relative to the AK135 earth model and corrected to account for the effect of the kilometers-thick sedimentary cover in the region. The NGA is most intense at the southernmost coast of Louisiana and East Texas (with an eastern edge at 89°W) and smoothly tapers away in a triangular wedge that extends inland as far as 300 km. It has sharper edges and a smaller areal extent (by ∼50%) than previously-published geotomography has indicated. Both the magnitude and ratio of delays indicate that the NGA has a thermal origin, which may represent past or present-day small-scale convective upwelling near the southeastern edge of the North American continent. The NGA suggests that large-scale but poorly understood asthenospheric processes are at work beneath the US Gulf Coast, notwithstanding this region's reputation as an aseismic, passively-subsiding continental margin.
The Lau Basin displays large along-strike variations in ridge characters with the changing proximity of the adjacent subduction zone. The mechanism governing these changes is not well understood but ...one hypotheses relates them to interaction between the arc and back-arc magmatic systems. We present a 3D seismic velocity model of the shallow mantle beneath the Eastern Lau back-arc Spreading Center (ELSC) and the adjacent Tofua volcanic arc obtained from ambient noise tomography of ocean bottom seismograph data. Our seismic images reveal an asymmetric upper mantle low velocity zone (LVZ) beneath the ELSC. Two major trends are present as the ridge-to-arc distance increases: (1) the LVZ becomes increasingly offset from the ridge to the north, where crust is thinner and the ridge less magmatically active; (2) the LVZ becomes increasingly connected to a sub-arc low velocity zone to the south. The separation of the ridge and arc low velocity zones is spatially coincident with the abrupt transition in crustal composition and ridge morphology. Our results present the first mantle imaging confirmation of a direct connection between crustal properties and uppermost mantle processes at ELSC, and support the prediction that as ELSC migrates away from the arc, a changing mantle wedge flow pattern leads to the separation of the arc and ridge melting regions. Slab-derived water is cutoff from the ridge, resulting in abrupt changes in crustal lava composition and crustal porosity. The larger offset between mantle melt supply and the ridge along the northern ELSC may reduce melt extraction efficiency along the ridge, further decreasing the melt budget and leading to the observed flat and faulted ridge morphology, thinner crust and the lack of an axial melt lens.
•We perform ambient noise tomography on OBS data.•We present a 3D shear velocity model beneath the Eastern Lau Spreading Center.•Imaged a asymmetrical low velocity zone along the spreading center.•Ridge and arc melting regions change from connected to separated as ridge–arc distance increases.•Imaging confirmation of a direct connection between crustal and mantle processes.
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