Angelo Sajeva

Characterization of the seismic environment at the Sanford Underground Laboratory, South Dakota

An array of seismometers is being developed at the Sanford Underground Laboratory, the former Homestake mine, in South Dakota to study the properties of underground seismic fields and Newtonian noise, and to investigate the possible advantages of constructing a third-generation gravitational-wave detector underground. Seismic data were analyzed to characterize seismic noise and disturbances. External databases were used to identify sources of seismic waves: ocean-wave data to identify sources of oceanic microseisms and surface wind-speed data to investigate correlations with seismic motion as a function of depth. In addition, sources of events contributing to the spectrum at higher frequencies are characterized by studying the variation of event rates over the course of a day. Long-term observations of spectral variations provide further insight into the nature of seismic sources. Seismic spectra at three different depths are compared, establishing the 4100 ft level as a world-class low seismic-noise environment.

Comparison of Stochastic Optimization Methods on Two Analytic Objective Functions and on a 1D Elastic FWI

We compare the performance of three different stochastic optimization methods on two analytic objective functions varying the number of parameters, and on a 1D elastic full waveform inversion (FWI) problem. The three methods that we consider are the Adaptive Simulated Annealing (ASA), the Genetic Algorithm (GA), and the Neighbourhood Algorithm (NA) which are frequently used in seismic inversion. The application of these algorithms on the two analytic functions is aimed at evaluating the rate of convergence for different model space dimensions. The first function consists in a convex surface, and the second one is a multi-minima objective function which also permits to verify the ability of each method to escape from entrapment in local minima. Our study shows that among the three optimization methods GA displays the better scaling with the number of parameters. The ASA method is often the most efficient in case of low dimensional model spaces, whereas NA seems to perform less efficiently than the other two and to be more prone to get trapped in local minima. Tests of 1D elastic FWI on synthetic data, inverting for density, P and S-wave velocity for a total of 21 unknowns confirm the conclusions drawn from the previous examples.

Comparing the performances of four stochastic optimisation methods using analytic objective functions, 1D elastic full-waveform inversion, and residual static computation

We compare the performances of four different stochastic optimisation methods using four analytic objective functions and two highly non-linear geophysical optimisation problems: 1D elastic full-waveform inversion (FWI) and residual static computation. The four methods we consider, namely, adaptive simulated annealing (ASA), genetic algorithm (GA), neighbourhood algorithm (NA), and particle swarm optimisation (PSO), are frequently employed for solving geophysical inverse problems. Because geophysical optimisations typically involve many unknown model parameters, we are particularly interested in comparing the performances of these stochastic methods as the number of unknown parameters increases. The four analytic functions we choose simulate common types of objective functions encountered in solving geophysical optimisations: a convex function, two multi-minima functions that differ in the distribution of minima, and a nearly flat function. Similar to the analytic tests, the two seismic optimisation problems we analyse are characterized by very different objective functions. The first problem is a 1D elastic FWI, which is strongly ill-conditioned and exhibits a nearly flat objective function, with a valley of minima extended along the density direction. The second problem is the residual static computation, which is characterized by a multi-minima objective function produced by the so-called cycle-skipping phenomenon. According to the tests on the analytic functions and on the seismic data, GA generally displays the best scaling with the number of parameters. It encounters problems only in the case of irregular distribution of minima, that is, when the global minimum is at the border of the search space and a number of important local minima are distant from the global minimum. The ASA method is often the best-performing method for low-dimensional model spaces, but its performance worsens as the number of unknowns increases. The PSO is effective in finding the global minimum in the case of low-dimensional model spaces with few local minima or in the case of a narrow flat valley. Finally, the NA method is competitive with the other methods only for low-dimensional model spaces; its performance stability sensibly worsens in the case of multi-minima objective functions. This article is protected by copyright. All rights reserved

Two-grid stochastic full waveform inversion of 2D marine seismic data

We apply stochastic Full Waveform Inversion (FWI) to 2D marine seismic data to estimate the macro-model velocity field which can be a suitable input for subsequent local (gradient based) FWI. Genetic Algorithms are used as the global optimization method. Our two-grid representation of the subsurface, made of a coarse grid for the inversion and of a fine grid for the modeling, allows us to reduce the number of unknowns to an acceptable number for the given computer resources and to perform a stable and reliable finite difference modeling. Thus, notwithstanding the known high computational costs that characterize global inversion methods, we are able to reconstruct a smooth, low wavenumber, acoustic velocity model of the subsurface. The reliability of the estimated velocity macro-model is checked through the inspection of prestack depth migrated gathers and through the superposition of observed and modeled seismograms. The method we propose is less affected by the risk of being trapped in local minima of the misfit functional than gradient based FWI methods, and can be a viable alternative to estimate proper starting models for gradient based full waveform inversions.

Application of quaternion algorithms for multicomponent data analysis: a review

Summary We illustrate the applications on real data sets of three algorithms of multicomponent seismic processing implemented by means of quaternion algebra i.e.: velocity analysis, deconvolution, and Rayleigh wave extraction. First we present an application of quaternion velocity analysis on multicomponent traces, which results in an improved resolution and it allows us to discern on a single velocity panel the different wave trends (P, PS, converted waves) simultaneously. Then we present an application of quaternion deconvolution, that represents an extension of the classical Wiener deconvolution, and takes advantage of the vectorial nature of the wave-field, performing better than scalar filters. Finally, we show an application of a quaternion procedure that extracts a single Rayleigh wave mode on a multicomponent land data set.

Characterisation and extraction of a Rayleigh-wave mode in vertically heterogeneous media using quaternion SVD

We propose a method that identifies a mode of Rayleigh waves and separates it from body waves and from other modes, using quaternions to represent multi-component data. Being well known the abilities of quaternions to handle rotations in space, we use previous results derived from Le Bihan and Mars (2004) [1] to prove that a Rayleigh-wave mode recorded by an array of vector-sensors can be approximated by a sum of trace-by-trace rotating time signals. Our method decomposes the signal into narrow-frequency bands, which undergo both a velocity correction and a polarisation correction. The aim of these corrections is to reduce the mode of interest to a quasi-monochromatic wave packet with infinite apparent velocity and quasi-circular polarisation. Once written in quaternion notation, we refer to this wave packet as quaternion brick. Based on theoretical considerations, we prove that this quaternion brick maps into the first quaternion eigenimage of the quaternion singular value decomposition. We apply this method to synthetic datasets derived from two vertically heterogeneous models to extract the fundamental mode and we prove that it is correctly separated from either a higher mode of propagation or body waves with negligible residual. Results are presented in both timeoffset and frequencyphase slowness domains. HighlightsWe propose a compact mathematical model of a Rayleigh-wave mode based on quaternions.The Rayleigh-wave mode is modelled as a sum of narrow-band rotating signals.Each narrow-band rotating Rayleigh-wave mode is a rank-1 quaternion matrix.This property can be used to separate the Rayleigh-wave mode from other signals.

Surface-consistent Residual Statics Estimation with Genetic Algorithms - An Application to a Near-surface Seismic Survey

In this work we apply a Genetic Algorithm (GA) approach to the residual statics computation problem. This type of geophysical optimization problem is characterised by many local minima produced by the so-called cycle-skipping phenomenon. The application of a global optimization method is particularly suitable in this context as it is able to jump out from local minima where gradient-based methods can easily be entrapped. We use an analytical objective function to test the capability of GA in finding the global minimum in case of highly non-linear multi-minima objective function. Because the residual statics optimization problem involves many unknown model parameters, in this analytical test we are particularly interested in analysing the rate of convergence (that is the number of evaluated models required to reach the global minimum) as the dimension of the model space increases. We then show the use of this methodology on a field seismic reflection data set acquired for near surface investigations. The application of the residual statics derived by the GA method produces final CMP gathers with flatter reflectors and a final stack section in which the continuity of the observed events increases.

Low frequency seismic noise acquisition and analysis in the Homestake Mine with tunable monolithic horizontal sensors

In this paper we describe the scientific data recorded along one month of data taking of two mechanical monolithic horizontal sensor prototypes located in a blind-ended (side) tunnel 2000 ft deep in the Homestake (South Dakota, USA) mine chosen to host the Deep Underground Science and Engineering Laboratory (DUSEL). The two mechanical monolithic sensors, developed at the University of Salerno, are placed, in thermally insulating enclosures, onto concrete slabs connected to the bedrock, and behind a sound-proofing wall. The main goal of this experiment is to characterize the Homestake site in the frequency band 10-4 - 30Hz and to estimate the level of Newtonian noise in a deep underegropund laboratory. The horizontal semidiurnal Earth tide and the Petersons New Low Noise Model have been measured.

Long term seismic noise acquisition and analysis in the Homestake mine with tunable monolithic sensors

In this paper we describe the scientific data recorded along one month of data taking of two mechanical monolithic horizontal sensor prototypes located in a blind-ended (side) tunnel 2000 ft deep in the Homestake (South Dakota, USA) mine chosen to host the Deep Underground Science and Engineering Laboratory (DUSEL). The two mechanical monolithic sensors, developed at the University of Salerno, are placed, in thermally insulating enclosures, onto concrete slabs connected to the bedrock, and behind a sound-proofing wall. The main goal of this experiment is to characterize the Homestake site in the frequency band 10-4 ÷ 30 H z and to estimate the level of Newtonian noise, providing also the necessary preliminary information to understand the feasibility of underground gravitational-wave interferometers sensitive at 1 H z and below.