Seismic investigations of the Martian near- surface at the InSight … · 2020. 5. 4. · transfer from Mars to Earth and (2) reconstructing the original signals using a sparseness-constrained

Cedric Schmelzbach(1), Nienke Brinkman(1), David Sollberger(1), Sharon Kedar(2),Matthias Grott(3), FredrikAndersson(1), Johan Robertsson(1), Martin van Driel(1),

Simon Stähler(1), Jan ten Pierick(1), Troy L. Hudson(2), Kenneth Hurst(2), Domenico Giardini(1), Philippe Lognonné(4), W. Tom Pike(5), Tilman Spohn(3), W. Bruce Banerdt(2),

Lucile Fayon(4), Anna Horleston(6), Aaron Kiely(2), Brigitte Knapmeyer-Endrun(7), Christian Krause(3), Nicholas C. Schmerr(8), Pierre Delage(9), Nick Teanby(6), Christos Vrettos(10)

(1) ETH, Zurich, Switzerland; (2) Jet Propulsion Laboratory, California Institute of Technology, USA; (3) Deutsches Zentrum für Luft und Raumfahrt, Germany; (4) Institut de Physique du Globe de Paris, France; (5)

Imperial College, London, UK; (6) University of Bristol, Bristol, UK; (7) University of Cologne, Germany; (8) University of Maryland, USA; (9) Ecole des Ponts, France; (10) Technical University Kaiserslautern, Germany.

EGU2020-20481

Seismic investigations of the Martian near-surface at the InSight landing site

Motivation – “Active-source” near-surface seismic study

Credit: NASA/JPL

SEISHP3

Sol 124

Credit: NASA/JPL

May 1 2020Sol 508

• The Heat Flow and Physical Properties Package (HP3) was deployed close to seismometer package (SEIS) in mid-February 2019

• HP3 mole is a self hammering device producing seismic waves with each hammer stroke

• The seismic signals may allow infering on the shallow elastic properties to (Kedar et al., 2017):– Study the geological structure, composition and

history at the landing site– Understand the seismic noise recorded by SEIS– Provide regolith properties for future missions

1.18 m

Schmelzbach et al. (2020), EGU2020-20481

Proposed seismic analyses to study the near-surfaceSeismic traveltimes• The traveltime of the wave arriving first

at SEIS can provide information on the subsurface seismic velocity structure (Brinkman et al., 2019)

Subsurface reflection imaging• Reflected waves may be used to image

shallow interfaces analogoues to vertical seismic profiling (Golombek et al., 2018; Brinkman et al., 2020)

• Requires the mole to penetrate into the subsurface

Keary et al. (2002)

Vertical-seismic profiling (VSP)

HP3 SEIS

Golombek et al. (2018)

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Velocity model from a synthetic data test

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Seismic reflection imaging illustrated with synthetic data


Challenges of this opportunistic experiment

• The analysis of the HP3 seismic signals is an opportunistic experiment that was only conceived after the key hardware decisions were made (Kedar et al. 2017)

• Time-resolution challenge: the SEIS acquisition flow is designed for seismic signals with frequencies 100 Hz (Sollberger et al., 2020)

• Time-correlation challenge: SEIS and HP3 operate on independent clocks that need to be correlated to determine the traveltimes of the seismic waves precisely enough for the proposed analyses (Brinkman et al., 2019)


Reconstruction of information beyond Nyquist frequencyThe HP3 hammering seismic signals are observed to have a much broader frequency content then the nominal SEIS acquisition electronics is designed to record.

The first active seismic experiment on Mars to characterize the shallow subsurface structure

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Figure 4: Illustration of the reconstruction algorithm used to recover the high-frequency information from fully aliased seismicdata recorded during HP3 hammering. The example is from an actual analogue field experiment conducted in the Nevada desertwith a spare model of the mole. a) Input seismic data before passing through the on-board down-sampling flow. b) Aliased datadown-sampled to 100 Hz aligned to the hammering time. Note the quasi-random subsampling of the common-receiver gather. c)Sparse, fully-sampled Radon model of the data. d) Reconstructed signal.

100 Hz. To avoid aliasing, the data are passed through a dig-ital anti-aliasing FIR filter that only passes information below50 Hz. However, the HP3 mole is expected to generate seismicsignals at frequencies much higher than 50 Hz.

To record information >50 Hz that of the hammering signals,we designed a new FIR filter (in the following referred to asthe spike filter) that is uploaded to the lander during mole ham-mering. The spike filter has a flat frequency response and thuspasses all the information contained in the hammering signal.As a consequence, the down-linked data is aliased. The signalsneed to be reconstructed in post-processing to recover the highfrequency information.

We developed a compressed sensing inspired algorithm (e.g.Donoho, 2006; Candès et al., 2006) that allows to accuratelyrecover the high-frequency signals beyond the nominal Nyquistfrequency of 50 Hz (Sollberger et al., 2019). Compressedsensing allows the recovery of sparse signals way beyond theNyquist limit. The concept of the reconstruction algorithm isillustrated in Figure 4. Our reconstruction algorithm exploitsthe fact that the hammering signal of the mole is highly repeat-able. Thousands of very similar signals are recorded as themole slowly penetrates into the regolith. As a result, the datashow a linear structure when arranged in a common-receivergather with each hammer stroke aligned with respect to thehammer time (Figure 4a).

HP3 time samples are not identical to the time sample on SEIS.Each of the repeated signals is sub-sampled differently (Fig-ure 4b). This is an ideal prerequisite for compressed sensing.Due to the linear structure, the data has a sparse representationin the Radon transform domain. Instead of the conventionalRadon transform, we use the so-called deconvolutive Radontransform (Gholami, 2017), which allows for an even sparserrepresentation of the signal. Each linear event in the 2D data iseffectively compressed to a point in the deconvolutive Radondomain (Figure 4). Reconstruction is then achieved by findingthe sparsest model (the model with smallest `1-norm) that fits

the aliased data. This is achieved by solving a basis pursuit de-noising problem (BPDN). The reconstructed, up-sampled sig-nal can then simply be found in the time domain by applyingthe inverse deconvolutive Radon transform to the best-fittingRadon-domain model parameters (Figure 4).

SEISMIC-DATA PROCESSING

The reconstructed, up-sampled seismic data and accurate trig-ger times enable a high resolution analysis of the data. First-arrival P-wave travel times and the seismic waveforms are usedfor seismic tomography and reflection processing, respectively.

In order to test the imaging potential of the HP3-SEIS ac-tive seismic experiment, we demonstrate the processing ona synthetic dataset. We used finite-difference modelling togenerate a synthetic dataset using the petrophysical model ofthe shallow Martian subsurface (B. Knapmeyer-Endrun, per-sonal communication). We then picked the first-arriving P-wave travel times and applied a non-linear seismic traveltimetomography based on Bayesian inference which allows to quan-tify uncertainties and non-linearities in the model. The methodthat we applied is the reversible jump Markov chain MonteCarlo (rj-MCMC) algorithm which allows the model space tobe transdimensional. The parameterization of the model spaceis defined by Voronoi cells (Okabe et al., 2009). During eachiteration step of the Markov chain, four different perturbationsto the model are possible (Bodin and Sambridge, 2009). Threeof those perturbations imply a change in the parameterization,a ”birth” step creates a new Voronoi cell, a ”death” step re-moves a Voronoi cell and a ”move” step rearranges the Voronoicells. The fourth possible perturbation is a velocity step, whichproposes a velocity parameter and does not influence the pa-rameterization. The forward problem of the first-arrival trav-eltime computation is solved using the Fast Marching method(Rawlinson and Sambridge, 2004).

Figure 5a represents the posterior density functions (PDFs) in

We therefore developed an acquisition and signal reconstruction flow that includes (1) recording aliased data by omitting filters when downsampling the data for transfer from Mars to Earth and (2) reconstructing the original signals using a sparseness-constrained reconstruction algorithm that exploits the high repeatability of the hammering signalsand uncorrelated hammer time and sampling (Sollberger et al., 2020).

Brinkman et al. (2019)

Sollberger et al. (2020)


First results – Hammering session 4 (sol 158)

• The seismic data of the SEIS short period (SP) sensor were recorded in aliased fashion for several HP3hammering sessions

• First-arrival traveltimes were determined from the reconstructed data

• An apparent velocity of 124 ± 34 m/s was obtained for hammering session 4(Lognonné et al., 2020)

Figure S2-2: Schematic cross-section of the locations of HP3, the mole with the mole tip in red and SEIS with respect to each other. s is the travel path, x is the horizontal distance between SEIS and HP3, d is the depth of the mole and θ is the tilt of the mole with respect to the vertical.

(a) Hammer Session 3

(b) Hammer Session 3

(c)Hammer Session 4

(d) Hammer Session 4

Figure S2-3: (a) and (c): Seismic data recorded by the short period sensor (SP) of SEIS arranged as a common-receiver gather with time zero corresponding to the trigger time of each hammer hit. (b) and (d): Travel time and P-velocity analysis recorded by the SP.

S2-3: Convective vortex modelling

Convective vortices are characterized by a pressure drop, typically of a few tenths to a few Pa, that induces small deformations of the ground that can be felt by the sensitive VBB seismometer. On the vertical component, the quasi-static ground motion can be modeled based on the pressure and wind time series and the frequency-dependent ground compliance (the ratio between vertical velocity and pressure forcing). The frequency dependency is related to the sensitivity depth to elastic properties, which scales

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Figure S2-2: Schematic cross-section of the locations of HP3, the mole with the mole tip in red and SEIS with respect to each other. s is the travel path, x is the horizontal distance between SEIS and HP3, d is the depth of the mole and θ is the tilt of the mole with respect to the vertical.

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Figure S2-3: (a) and (c): Seismic data recorded by the short period sensor (SP) of SEIS arranged as a common-receiver gather with time zero corresponding to the trigger time of each hammer hit. (b) and (d): Travel time and P-velocity analysis recorded by the SP.

S2-3: Convective vortex modelling

Convective vortices are characterized by a pressure drop, typically of a few tenths to a few Pa, that induces small deformations of the ground that can be felt by the sensitive VBB seismometer. On the vertical component, the quasi-static ground motion can be modeled based on the pressure and wind time series and the frequency-dependent ground compliance (the ratio between vertical velocity and pressure forcing). The frequency dependency is related to the sensitivity depth to elastic properties, which scales

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Lognonné et al. (2020)Schmelzbach et al. (2020), EGU2020-20481

Interpretation• Observed low (~120 m/s) seismic P-wave velocity interpreted to represent

the bulk velocity of the volume between HP3 mole tip and SEIS

• Low velocity consistent with proposed near-surface stratigraphy (Golombek et al., 2020) of >3 m thick impact-fragmented regolith consisting of poorly sorted unconsolidated sands and rocks

• A near-surface velocity model is under construction based on the HP3-SEIS traveltime and compliance inversions using atmospheric pressure signals (Lognonné et al., 2020)

Credit: NASA/JPLSchmelzbach et al. (2020), EGU2020-20481

References• Brinkman et al. (2019), The first active-seismic experiment on Mars to characterize the

shallow subsurface structure at the InSight landing site, SEG Technical Program Expanded Abstracts 2019, 4756–4760, doi:10.1190/segam2019-3215661.1

• Golombek et al. (2020), Geology of the InSight landing site on Mars. Nature Communications 11, 1014 doi: 10.1038/s41467-020-14679-1

• Golombek et al. (2018), Geology and Physical Properties In- vestigations by the InSightLander, Space Science Review, 214(5), 84, doi: 10.1007/s11214-018-0512-7.

• Kedar et al. (2017), Analysis of Regolith Properties Using Seismic Signals Generated by InSight’s HP3 Penetrator. Space Science Reviews, 211, 315–337, doi: 10.1007/s11214-017-0391-3

• Lognonné et al. (2020), Constraints on the shallow elastic and anelastic structure of Mars from InSight seismic data, Nature Geoscience, 13(3), http://doi.org/10.1038/s41561-020-0536-y

• Sollberger et al. (2020), A reconstruction algorithm for temporally aliased seismic signals recorded by the InSight Mars lander, submitted to Earth and Space Science.


Documents

Seismic investigations of the Martian near- surface at the InSight … · 2020. 5. 4. · transfer from Mars to Earth and (2) reconstructing the original signals using a sparseness-constrained