Frederik J Simons

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• Ph. D.
• Professor at Princeton University

We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere, or, alternatively, of strictly spacelimited functions that are optimally concentrated within the...

While multiple data sources have confirmed that Antarctica is losing ice at an accelerating rate, different measurement techniques estimate the details of its geographically highly variable mass balance with different levels of accuracy, spatio-temporal resolution, and coverage. Some scope remains for methodological improvements using a single data...

Significance Secondary microseisms are the strongest background seismic vibrations of the Earth and represent the major part of global seismographic data. Secondary microseisms are generated by wind-driven ocean storms, whose energy couples with the solid Earth at the seafloor. State-of-the-art generation theories are unable to justify the presence...

We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are considered: (i) the spherical analogue of the one-dimensional (1-D) periodogram, (ii) the maximum likelihood method, and...

Earth models in which seismic wave speeds vary only with depth are sufficiently well constrained to accurately locate earthquakes and calculate the paths followed by seismic rays [ Engdahl et al ., 1998]. The differences between observations and theoretical predictions of seismograms in such onedimensional Earth models can be used to reconstruct th...

Elastic full-waveform inversion (EFWI) is a state-of-the-art seismic tomographic method. Recent advances in technology and instrumentation, combining crosstalk-free source-encoded FWI (SE-FWI) with multicomponent marine data acquisition using ocean-bottom nodes (OBNs), enable full-physics wave propagation and parameter inversion without the computa...

Floating seismometers (‘MERMAIDs’) operating in the noisy environment of the world’s oceans pose a challenge for picking the time of earthquake first arrivals. We report on an experiment to estimate the errors in picked arrivals from 49 MERMAIDS operating in the South Pacific, using two independent strategies. For 15 events, the same arrivals were...

Seismic tomography is a principal method for studying mantle structure, but imaging of Earth’s wavespeed anomalies is conditioned by seismic wave sampling. Global models use misfit criteria that may strive for balance between portions of the data set but can leave important regional domains underserved. We evaluate two full-waveform global tomograp...

We present a computational technique to model hydroacoustic waveforms from teleseismic earthquakes recorded by mid-column MERMAID floats deployed in the Pacific, taking into consideration bathymetric effects that modify seismo-acoustic conversions at the ocean bottom and acoustic wave propagation in the ocean layer, including reverberations. Our ap...

Crosstalk-free source-encoded elastic Full-Waveform Inversion (FWI) using time-domain solvers has demonstrated skill and efficiency at conducting seismic inversions involving multiple sources and receivers with limited computational resources. A drawback of common formulations of the procedure is that, by sweeping through the frequency domain rando...

The highly used Global Seismographic Network (GSN) is a pillar of the seismological research community and contributes to numerous groundbreaking publications. Despite its wide recognition, this survey found that the GSN is not consistently acknowledged in scientific literature and is underrepresented by roughly a factor of 3 in citation searches....

The eastern continental margin of North America, despite being a passive margin at present, records a comprehensive tectonic history of both mountain building and rifting events. This record is punctuated by several igneous events, including those associated with the Great Meteor and Bermuda hotspots. To gain a better understanding of the state of...

Seismic discontinuities in the mantle are indicators of its thermo-chemical state and offer clues to its dynamics. Ray-based seismic methods, though limited by the approximations made, have mapped mantle transition zone discontinuities in detail, but have yet to offer definitive conclusions on the presence and nature of mid-mantle discontinuities....

Passive seismic inversion at the reservoir scale offers the advantages of low cost, negligible environmental impact, and the ability to probe a target area with low-frequency energy not afforded by even the most modern active-source seismic technology. In order to build starting models suitable for full-waveform wavespeed tomography, characterizati...

We present the first 16 months of data returned from a mobile array of 16 freely-floating diving instruments, named MERMAID for Mobile Earthquake Recording in Marine Areas by Independent Divers, launched in French Polynesia in late 2018. Our 16 are a subset of the 50 MERMAIDs deployed over a number of cruises in this vast and understudied oceanic p...

A fleet of autonomously drifting profiling floats equipped with hydrophones, known by their acronym mermaid, monitors worldwide seismic activity from inside the oceans. The instruments are programmed to detect and transmit acoustic pressure conversions from teleseismic P wave arrivals for use in mantle tomography. Reporting seismograms in near-real...

To better understand earthquakes as a hazard and to better understand the interior structure of the Earth, we often want to measure the physical displacement, velocity, or acceleration at locations on the Earth’s surface. To this end, a routine step in an observational seismology workflow is the removal of the instrument response, required to conve...

Mobile Earthquake Recorder in Marine Areas by Independent Divers (MERMAID) is a passively drifting oceanic diving float that transmits acoustic pressure records from global earthquakes within hours or days of their rupture. The onboard algorithm used for the detection and identification of signals from the hydrophone prioritizes the recovery of ∼1...

Secondary microseisms are ubiquitous ambient noise vibrations due to ocean activity, dominating worldwide seismographic records at seismic periods between 3 and 10 s. Their origin is a heterogeneous distribution of pressure fluctuations along the ocean surface. In spherically symmetric Earth models, no Love surface waves are generated by such a dis...

The origin of the Bermuda rise remains ambiguous, despite, or perhaps because of, the existence of sometimes incongruous seismic wave‐speed and discontinuity models in the sub‐Bermudian mantle. Hence, whether Bermuda is the surface manifestation of a mantle plume remains in question. Using the largest data set of seismic records from Bermuda to dat...

Much like medical doctors who use X-rays or acoustic waves to make three-dimensional images of our insides, geophysicists use the elastic wavefield generated by earthquakes worldwide to scan the deep interior of our planet for subtle contrasts in the propagation speeds of seismic waves. To image the deep Earth using seismic tomography, over the yea...

We discuss the resolving power of three geophysical imaging and inversion techniques, and their combination, for the reconstruction of material parameters in the Earth’s subsurface. The governing equations are those of Newton and Poisson for gravitational problems, the acoustic wave equation under Hookean elasticity for seismology, and the geodynam...

Seismic tomography has arrived at the threshold of the era of big data. However, how to extract information optimally from every available time-series remains a challenge; one that is directly related to the objective function chosen as a distance metric between observed and synthetic data. Time-domain cross-correlation and frequency-dependent mult...

We describe an algorithm to pick event onsets in noisy records, characterize their error distributions, and derive confidence intervals on their timing. Our method is based on an Akaike information criterion that identifies the partition of a time series into a noise and a signal segment that maximizes the signal-to-noise ratio. The distinctive fea...

Mapping the Earth's uncharted interior through global seismic tomography is dependent on increasing the number of seismic stations in the oceans. We have developed a low-cost, autonomously floating hydrophone to capture earthquake signals suitable for the study of the interior of the Earth and the tectonically and magmatically active underwater rea...

One of Jupiter's most prominent atmospheric features, the Great Red Spot (GRS), has been observed for more than two centuries, yet little is known about its structure and dynamics below its observed cloud level. While its anticyclonic vortex appearance suggests it might be a shallow weather-layer feature, the very long time span for which it was ob...

We launched an array of nine freely floating submarine seismometers near the Galápagos islands, which remained operational for about two years. P and PKP waves from regional and teleseismic earthquakes were observed for a range of magnitudes. The signal-to-noise ratio is strongly influenced by the weather conditions and this determines the lowest m...

Significance The recent deglaciation of Greenland is a response to both oceanic and atmospheric forcings. From 2000 to 2010, ice loss was concentrated in the southeast and northwest margins of the ice sheet, in large part due to the increasing discharge of marine-terminating outlet glaciers, emphasizing the importance of oceanic forcing. However, t...

The Tibetan Plateau is the largest region of high elevation in the world. The source of water for a number of important rivers, the Himalayan region is vital to the billions of inhabitants of the Asian continent. Over the last fifty years, the climate in the region has warmed more rapidly than anywhere else at the same latitude. Causes and effects,...

Special function systems are reviewed that reflect particular properties of the Legendre polynomials, such as spherical harmonics, zonal kernels, and Slepian functions. The uncertainty principle is the key to their classification with respect to their localization in space and frequency/momentum. Methods of constructive approximation are outlined s...

Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth’s surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of...

When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are available, or when data quality varies strongly with geographic location, the inversion problem becomes severely ill-...

Full-waveform inversion (FWI) is a data fitting technique used to estimate properties of the Earth from seismic data by minimizing the misfit between observed and simulated seismograms. Because of very high computational cost, this technique has so far been used either in a 2D fully elastic formulation or in a 3D acoustic formulation, when applied...

We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systema...

We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systema...

Over the past several decades mountain glaciers and ice caps have been significant contributors to sea level rise. Here we estimate the ice mass changes in the Canadian Archipelago, the Gulf of Alaska, and Greenland since 2003 by analyzing time-varying gravimetry data from the Gravity Recovery and Climate Experiment. Prior to 2013, interannual ice...

We have developed a wavelet-multiscale adjoint scheme for the elastic full-waveform inversion of seismic data, including body waves (BWs) and surface waves (SWs). We start the inversion on the SW portion of the seismograms. To avoid cycle skipping and reduce the dependence on the initial model of these dispersive waves, we commence by minimizing an...

We present two high-resolution local models for the crustal magnetic field of the Martian south polar region. Models SP130 and SP130M were derived from three-component measurements made by Mars Global Surveyor at nighttime and at low altitude (<200 km). The availability area for these data covers the annulus between latitudes -76° and -87° and cont...

In the last few decades, a series of increasingly sophisticated satellite missions has brought us gravity and magnetometry data of ever improving quality. To make optimal use of this rich source of information on the structure of the Earth and other celestial bodies, our computational algorithms should be well matched to the specific properties of...

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is...

Our understanding of the internal dynamics of the Earth is largely based on images of seismic velocity variations in the mantle obtained with global tomography. However, our ability to image the mantle is severely hampered by a lack of seismic data collected in marine areas. Here we report observations made under different noise conditions (in the...

Lithospheric strength variations both influence and are influenced by many tectonic processes, including orogenesis and rifting cycles. The long, complex, and highly anisotropic histories of the continental lithosphere might lead to a natural expectation of widespread mechanical anisotropy. Anisotropy in the coherence between topography and gravity...

The software improves data analysis over small portions of a spherical planetary surface. Among other applications, it has helped track Greenland's ice loss over time.

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is...

In the last few decades, a series of increasingly sophisticated satellite missions has brought us gravity and magnetometry data of ever improving quality. To make optimal use of this rich source of information on the structure of the Earth and other celestial bodies, our computational algorithms should be well matched to the specific properties of...

Full-waveform seismic inversions based on minimizing the distance between observed and predicted seismograms are, in principle, able to yield better-resolved earth models than those minimizing misfits derived from traveltimes alone. Adjoint-based methods provide an efficient way of calculating the gradient of the misfit function via a sequence of f...

We present a realistic application of an inversion scheme for global seismic tomography that uses as prior information the sparsity of a solution, defined as having few nonzero coefficients under the action of a linear transformation. In this paper, the sparsifying transform is a wavelet transform. We use an accelerated iterative soft-thresholding...

We review the construction of three different Slepian bases on the sphere, and illustrate their theoretical behavior and practical use for solving ill-posed satellite inverse problems. The first basis is scalar, the second vectorial, and the third suitable for the vector representation of the harmonic potential fields on which we focus our analysis...

Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in spherical harmonics, basis functions with global support. For various reasons, however, inclined orbits are fa...

The last interglacial stage (LIG; ca. 130-115 ka) provides a relatively recent example of a world with both poles characterized by greater-than-Holocene temperatures similar to those expected later in this century under a range of greenhouse gas emission scenarios. Previous analyses inferred that LIG mean global sea level (GSL) peaked 6-9 m higher...

Global magnetic field models are typically expressed as spherical-harmonic expansion coefficients. Slepian functions are linear combinations of spherical harmonics that produce new basis functions, which vanish approximately outside chosen geographical boundaries but also remain orthogonal within the spatial region of interest. Hence, they are suit...

We utilize a new, maximum likelihood-based technique to estimate elastic thickness and loading characteristics of the venusian lithosphere.

We construct spherical vector bases that are bandlimited and spatially concentrated, or, alternatively, spacelimited and spectrally concentrated, suitable for the analysis and representation of real-valued vector fields on the surface of the unit sphere, as arises in the natural and biomedical sciences, and engineering. Building on the original app...

The melting of polar ice sheets is a major contributor to global sea-level rise. Early estimates of the mass lost from the Greenland ice cap, based on satellite gravity data collected by the Gravity Recovery and Climate Experiment, have widely varied. Although the continentally and decadally averaged estimated trends have now more or less converged...

The crustal remanent magnetic field of Mars remains enigmatic in many respects. Its heterogeneous surface distribution points to a complex history of formation and modification, and has been resistant to attempts at identifying magnetic paleopoles and constraining the geologic origin of crustal sources. We use a multitaper technique to quantify the...

The mean dynamic topography (MDT) can be computed as the difference between the mean sea level (MSL) and a gravimetric geoid. This requires that both data sets are spectrally consistent. In practice, it is quite common that the resolution of the geoid data is less than the resolution of the MSL data, hence, the latter need to be low-pass filtered b...

We pose and solve the analogue of Slepian's time-frequency concentration problem for vector fields on the surface of the unit sphere, to determine an orthogonal family of strictly bandlimited vector fields that are optimally concentrated within a closed region of the sphere or, alternatively, of strictly spacelimited functions that are optimally co...

The 27 February 2010 Mw 8.8 Maule, Chile, earthquake ruptured over 500 km along a mature seismic gap between 34° S and 38° S—the Concepción–Constitución gap, where no large megathrust earthquakes had occurred since the 1835 Mw ∼8.5 event. Notable discrepancies exist in slip distribution and moment magnitude estimated by various models inverted usin...

Topography and gravity are geophysical fields whose joint statistical structure derives from interface-loading processes modulated by the underlying mechanics of isostatic and flexural compensation in the shallow lithosphere. Under this dual statistical-mechanistic viewpoint an estimation problem can be formulated where the knowns are topography an...

Spaceborne gravimetry data from the Gravity Recovery And Climate Experiment (GRACE) are processed using spatio-spectral Slepian localization analysis enabling the high-resolution detection of permanent gravity change associated with both coseismic and postseismic deformation resulting from the great 11 March 2011 Mw 9.0 Tohoku-Oki earthquake. The G...

We propose a new probabilistic scheme for the automatic recognition of underwater acoustic signals generated by teleseismic P-waves recorded by hydrophones in the ocean. The recognition of a given signal is based on the relative distribution of its power among different frequency bands. The signal's power distribution is compared with a statistical...

Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree...

We pose and solve the analogue of Slepian's time-frequency concentration problem in the two-dimensional plane, for applications in the natural sciences. We determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the plane, or, alternatively, of strictly spacelimited functions that a...

We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies with position within the Earth. Our procedure is numerically efficient and can be implemented with parallel c...

The crust of Mars retains heterogenous remanent magnetism. Magnetic power spectra can provide constraints on the depths and strengths of magnetic sources. We use a spatiospectral windowing approach to map local variability across the planet.

The Neoproterozoic era was punctuated by the Sturtian (about 710 million years ago) and Marinoan (about 635million years ago) intervals of glaciation. In South Australia, the rocks left behind by the glaciations are separated by a succession of limestones and shales, which were deposited at tropical latitudes. Here we describe millimetre- to centim...

The thickness of continental lithosphere varies considerably from tectonically active to cratonic regions, where it can be as thick as 250–300 km. Embedded in the upper mantle like a ship, when driven to move by a velocity imposed at the surface, a continental keel is expected to induce a pressure gradient in the mantle. We hypothesize that the vis...

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is...

With polar temperatures approximately 3-5 degrees C warmer than today, the last interglacial stage (approximately 125 kyr ago) serves as a partial analogue for 1-2 degrees C global warming scenarios. Geological records from several sites indicate that local sea levels during the last interglacial were higher than today, but because local sea levels...

Frederik Simons, at Princeton University, discusses how he developed the Mobile Earthquake Recording in Marine Areas by Independent Divers (MERMAID) instrument. Frederik borrowed the technology called 'Sounding Oceanographic Lagrangian Observers,' (SOLO) floats from the ocean scientists. These can drift at depths of anywhere between the surface and...

While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of these naturally admit spectral representations, or they may need to be extracted from data collected globally,...

We describe the development and testing of an autonomous device designed to revolutionize Earth structure determination via global seismic tomography by detecting earthquakes at teleseismic distances in the oceans. One prototype MERMAID, short for Mobile Earthquake Recording in Marine Areas by Independent Divers, was constructed and tested at sea....

Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 35 (2008): L14310, doi:10.1029/2008GL033986. Earthquake Early Warning (EEW) algorithms estimate the magnitude of an...

We present a mathematical framework and a new methodology for the parameterization of surface-wave phase-speed models based on travel-time data. Our method is neither purely local like block-based approaches, nor is it purely global like those based on spherical harmonic basis functions. Rather, it combines the well-known theory and practical utili...

Regional mass fluxes owing to transport and adjustment within the Earth system that are implicitly contained in the monthly Gravity Recovery and Climate Experiment (GRACE) global geopotential coefficients are revealed by localizing global spectra using spatiospectrally concentrated window functions. We have analyzed 45 monthly global GRACE harmonic...

We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when only a portion of the data are available for analysis, or estimating the power spectrum from local data under...

Young researchers face a wide choice of scientific approaches and directions that may shape their careers. The Earth sciences,in particular, offer a broad range of topics to study and techniques to use that exceeds what any current scientist was exposed to at the schools they attended. At early stages of their careers, researchers need to gain conf...

Earthquake early warning systems must save lives. It is of great importance that networked systems of seismometers be equipped with reliable tools to make rapid determinations of earthquake magnitude in the few to tens of seconds before the damaging ground motion occurs. A new fully automated algorithm based on the discrete wavelet transform detect...

Geophysicists are often concerned with reconstructing subsurface properties using observations collected at or near the surface. For example, in seismic migration, we attempt to reconstruct subsurface geometry from surface seismic recordings, and in potential field inversion, observations are used to map electrical conductivity or density variation...

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. Here we show that the geodetic estimation problem has deep-seated connections to Slepian's...

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. Here we show that the geodetic estimation problem has deep-seated connections to Slepian's...

It is often advantageous to investigate the relationship between two geophysical data sets in the spectral domain by calculating admittance and coherence functions. While there exist powerful Cartesian windowing techniques to estimate spatially localized (cross-)spectral properties, the inherent sphericity of planetary bodies sometimes necessitates...

We derive estimates of temperature of the Australian continental mantle between 80 and 350 km depth from two published S-velocity models. Lithospheric temperatures range over about 1000 °C, with a large-scale correlation between temperature and tectonic age. In detail however, variations ranging from 200 to 700 °C occur within each tectonic provinc...

The first Meeting of Young Researchers in the Earth Sciences (MYRES-I), held in August of 2004, focused on “Heat, helium, hotspots, and whole mantle convection.” Biennial meetings, with MYRES-I as the first, are one of the ways the MYRES initiative is building an “international, interdisciplinary, open and unbiased community of colleagues who inter...

In early January 2004, one of us attended a workshop on ``science priorities and educational opportunities that can be addressed using ocean observatories.'' The attendees constituted a broad group-men and women, scientists, engineers, educators, representatives from the private and public sector-but lacked diversity in at least one important aspec...

We interpret the three-dimensional seismic wave-speed structure of the Australian upper mantle by comparing its azimuthal anisotropy to estimates of past and present lithospheric deformation. We infer the fossil strain field from the orientation of gravity anomalies relative to topography, bypassing the need to extrapolate crustal measures, and der...