Frederik J Simons

Frederik J Simons
Princeton University | PU · Department of Geosciences

Ph. D.

About

93
Publications
19,022
Reads
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4,542
Citations
Introduction
I am a geologically inspired, geophysically educated, computationally motivated and mathematically minded geoscientist interested in the seismic, mechanical, thermal and magnetic properties of the Earth's lithosphere --- and of the terrestrial planets and moons.
Additional affiliations
July 2017 - present
Princeton University
Position
  • Professor
July 2013 - June 2017
Princeton University
Position
  • Professor
September 2006 - June 2013
Princeton University
Position
  • Professor
Education
August 1996 - August 2002
September 1994 - June 1996
KU Leuven
Field of study
  • Geology
September 1992 - June 1994
KU Leuven
Field of study
  • Geology

Publications

Publications (93)
Article
Full-text available
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...
Article
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...
Article
Full-text available
The interaction of ocean surface waves produces pressure fluctuations at the seafloor capable of generating seismic waves in the solid Earth. The accepted mechanism satisfactorily explains secondary microseisms of the Rayleigh type, but it does not justify the presence of transversely polarized Love waves, nevertheless widely observed. An explanati...
Article
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...
Article
Full-text available
Earth models in which seismic wavespeeds vary only with depth are sufficientlywell constrained to accurately locate earthquakesand calculate the paths followed byseismic rays [Engdahl et al., 1998]. The differencesbetween observations and theoreticalpredictions of seismograms in such one-(hyphen)dimensionalEarth models can be used toreconstruct the...
Article
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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...
Article
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...
Article
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...
Conference Paper
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
From early 2003 to mid-2013, the total mass of ice in Greenland declined at a progressively increasing rate. In mid-2013, an abrupt reversal occurred, and very little net ice loss occurred in the next 12–18 months. Gravity Recovery and Climate Experiment (GRACE) and global positioning system (GPS) observations reveal that the spatial patterns of th...
Article
Full-text available
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,...
Chapter
Full-text available
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...
Article
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...
Article
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-...
Conference Paper
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...
Article
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...
Article
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...
Article
Full-text available
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...
Article
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...
Chapter
Full-text available
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...
Chapter
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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.
Chapter
Full-text available
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...
Chapter
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Conference Paper
Full-text available
We utilize a new, maximum likelihood-based technique to estimate elastic thickness and loading characteristics of the venusian lithosphere.
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Conference Paper
Full-text available
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...
Article
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
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...
Conference Paper
Full-text available
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.