scholarly journals Helmholtz tomography of ambient noise surface wave data to estimate Scholte wave phase velocity at Valhall Life of the Field

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. WA99-WA109 ◽  
Author(s):  
Aurélien Mordret ◽  
Nikolaï M. Shapiro ◽  
Satish S. Singh ◽  
Philippe Roux ◽  
Olav I. Barkved
Keyword(s):  
Phase Velocity ◽  
Ambient Noise ◽  
Waveform Inversion ◽  
Wave Model ◽  
P Wave ◽  
Data Set ◽  
Phase Velocities ◽  
Wave Phase ◽  
Wave Phase Velocity ◽  
Scholte Wave

We applied the Helmholtz tomography technique to 6.5 hours of continuous seismic noise record data set of the Valhall Life of Field network. This network, that has 2320 receivers, allows us to perform a multifrequency, high-resolution, ambient-noise Scholte wave phase velocity tomography at Valhall. First, we computed crosscorrelations between all possible pairs of receivers to convert every station into a virtual source recorded by all other receivers. Our next step was to measure phase traveltimes and spectral amplitudes at different periods from crosscorrelations between stations separated by distances between two and six wavelengths. This is done in a straightforward fashion in the Fourier domain. Then, we interpolated these measurements onto a regular grid and computed local gradients of traveltimes and local Laplacians of the amplitude to infer local phase velocities using a frequency dependent Eikonal equation. This procedure was repeated for all 2320 virtual sources and final phase velocities were estimated as statistical average from all these measurements at each grid points. The resulting phase velocities for periods between 0.65 and 1.6 s demonstrate a significant dispersion with an increase of the phase velocities at longer periods. Their lateral distribution is found in very good agreement with previous ambient noise tomography done at Valhall as well as with a full waveform inversion P-wave model computed from an active seismic data set. We put effort into assessing the spatial resolution of our tomography with checkerboard tests, and we discuss the influence of the interpolation methods on the quality of our final models.

Decoupling approximation of P- and S-wave phase velocities in orthorhombic media

Geophysics ◽  
2021 ◽  
pp. 1-74
Author(s):  
Bowen Li ◽  
Alexey Stovas
Keyword(s):  
Phase Velocity ◽  
P Wave ◽  
Wave System ◽  
S Wave ◽  
Phase Velocities ◽  
Wave Phase ◽  
Algebraic Expressions ◽  
Wave Phase Velocity ◽  
Independent Parameters ◽  
Velocity Approximation

Characterizing the kinematics of seismic waves in elastic orthorhombic media involves nine independent parameters. All wave modes, P-, S1-, and S2-waves, are intrinsically coupled. Since the P-wave propagation in orthorhombic media is weakly dependent on the three S-wave velocity parameters, they are set to zero under the acoustic assumption. The number of parameters required for the corresponding acoustic wave equation is thus reduced from nine to six, which is very practical for the inversion algorithm. However, the acoustic wavefields generated by the finite-difference scheme suffer from two types of S-wave artifacts, which may result in noticeable numerical dispersion and even instability issues. Avoiding such artifacts requires a class of spectral methods based on the low-rank decomposition. To implement a six-parameter pure P-wave approximation in orthorhombic media, we develop a novel phase velocity approximation approach from the perspective of decoupling P- and S-waves. In the exact P-wave phase velocity expression, we find that the two algebraic expressions related to the S1- and S2-wave phase velocities play a negligible role. After replacing these two algebraic expressions with the designed constant and variable respectively, the exact P-wave phase velocity expression is greatly simplified and naturally decoupled from the characteristic equation. Similarly, the number of required parameters is reduced from nine to six. We also derive an approximate S-wave phase velocity equation, which supports the coupled S1- and S2-waves and involves nine independent parameters. Error analyses based on several orthorhombic models confirm the reasonable and stable accuracy performance of the proposed phase velocity approximation. We further derive the approximate dispersion relations for the P-wave and the S-wave system in orthorhombic media. Numerical experiments demonstrate that the corresponding P- and S-wavefields are free of artifacts and exhibit good accuracy and stability.

High-frequency seismic interferometry: broadband measurements of surface-wave phase velocities using “large-N” arrays

2021 ◽  
Author(s):  
Yihe Xu ◽  
Sergei Lebedev ◽  
Raffaele Bonadio ◽  
Thomas Meier ◽  
Christopher Bean
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
High Frequency ◽  
Ambient Noise ◽  
Frequency Noise ◽  
Frequency Range ◽  
Velocity Measurements ◽  
Phase Velocities ◽  
Wave Phase ◽  
Large N

<p>High-frequency seismic surface waves sample the top few tens of meters to the top few kilometres of the subsurface. They can be used to determine three-dimensional distributions of shear-wave velocities and to map the depths of discontinuities (interfaces) within the crust. Passive seismic imaging, using ambient noise as the source of signal, can thus be an effective tool of exploration for mineral, geothermal and other resources, provided that sufficient high-frequency signal is available in the ambient noise wavefield and that accurate, high-frequency measurements can be performed on this signal. Ambient noise imaging using the ocean-generated noise at 5-30 s periods is now a standard method, but less signal is available at frequencies high enough for deposit-scale imaging (0.2-30 Hz), and few studies have reported successful measurements in broad frequency bands. Here, we develop a workflow for the measurement of high-frequency, surface-wave phase velocities in very broad frequency ranges. Our workflow comprises (1) a new noise cross-correlation procedure that accounts for the non-stationary properties of the high frequency noise sources, removes bandpass filtering, replaces temporal normalization with short time window stacking, and drops the explicit spectral normalization by adopting cross-coherence; (2) a new phase-velocity measurement method that extends the bandwidth of reliable measurements by exploiting the (resolved) 2π ambiguity of phase-velocity measurements; (3) interstation-distance-dependent quality control that uses the similarity of subgroups of dispersion curves to reject outliers and identify the frequency ranges with accurate measurements. The workflow is highly automated and applicable to large arrays. Applying our method to data from a large-N array that operated for one month near Marathon, Ontario, Canada, we use rectangular subarrays with 150-m station spacing and, typically, 1 hour of data and obtain Rayleigh-wave phase-velocity measurements in a 0.55-23.8 Hz frequency range, spanning over 5.4 octaves, nearly twice the typical frequency range of 1.5-3 octaves in previous studies. Phase-velocity maps and the subregion-average 1D velocity models they constrain show a high-velocity anomaly consistent with the known, west-dipping gabbro intrusions beneath the area. The new structural information can improve our understanding of the geometry of the gabbro intrusions, hosting the Cu-PGE Marathon deposit.</p>

Love-Wave Phase-Velocity Estimation from Array-Based Rotational Motion Microtremor

2020 ◽  
Author(s):  
Kunikazu Yoshida ◽  
Hirotoshi Uebayashi
Keyword(s):  
Phase Velocity ◽  
Rayleigh Waves ◽  
Love Wave ◽  
Velocity Estimation ◽  
Love Waves ◽  
Phase Velocities ◽  
Wave Phase ◽  
Wave Phase Velocity ◽  
Spatial Derivatives ◽  
Rotational Motions

ABSTRACT The most popular array-based microtremor survey methods estimate velocity structures from the phase velocities of Rayleigh waves. Using the phase velocity of Love waves improves the resolution of inverted velocity models. In this study, we present a method to estimate the phase velocity of Love waves using rotational array data derived from the horizontal component of microtremors observed using an ordinal nested triangular array. We obtained discretized spatial derivatives from a first-order Taylor series expansion to calculate rotational motions from observed array seismograms. Rotational motions were obtained from a triangular subarray consisting of three receivers using discretized spatial derivatives. Four rotational-motion time histories were calculated from different triangular subarrays in the nested triangular arrays. Phase velocities were estimated from the array of the four rotational motions. We applied the proposed Love-wave phase-velocity estimation technique to observed array microtremor data obtained using a nested triangular array with radii of 25 and 50 m located at the Institute for Integrated Radiation and Nuclear Science, Kyoto University. The phase velocities of rotational and vertical motions were estimated from the observed data, and results showed that the former were smaller than those of the latter. The observed phase velocities obtained from vertical and rotational components agreed well with the theoretical Rayleigh- and Love-wave phase velocities calculated from the velocity structure model derived from nearby PS logs. To show the ability of the rotation to obtain Love wave, we estimated apparent phase velocities from north–south or east–west components. The apparent velocities resulted in between the theoretical velocities of Rayleigh and Love waves. This result indicates that the calculated rotation effectively derived the Love waves from a combination of Love and Rayleigh waves.

Decoupled approximation and separate extrapolation of P- and SV-waves in transversely isotropic media

Geophysics ◽  
2021 ◽  
pp. 1-57
Author(s):  
Bowen Li ◽  
Alexey Stovas
Keyword(s):  
Phase Velocity ◽  
Wave Velocity ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Wave Phase ◽  
Wave Phase Velocity ◽  
Tti Media ◽  
Vti Media ◽  
Acoustic Approximation

Characterizing the kinematics of seismic waves in elastic vertical transversely isotropic (VTI) media involves four independent parameters. To reduce the complexity, the acoustic approximation for P-waves reduces the number of required parameters to three by setting the vertical S-wave velocity to zero. However, since only the SV-wave phase velocities parallel or perpendicular to the symmetry axis are indirectly set to zero, the acoustic approximation leads to coupled P-wave components and SV-wave artifacts. The new acoustic approximation suggests setting the vertical S-wave velocity as a phase angle-dependent variable so that the SV-wave phase velocity is zero at all phase angles. We find that manipulating this parameter is a valid way for P-wave approximation, but doing so inevitably leads to zero- or non-zero-valued spurious SV-wave components. Thus, we have developed a novel approach to efficiently approximate and thoroughly separate the two wave modes in VTI media. First, the exact P- and SV-wave phase velocity expressions are rewritten by introducing an auxiliary function. After confirming the insensitivity of this function, we construct a new expression for it and obtain simplified P- and SV-wave phase velocity expressions, which are three- and four-parameter, respectively. This approximation process leads to the same reasonable error for both wave modes. Accuracy analysis indicates that for the P-wave, the overall accuracy performance of our approach is comparable to that of some existing three-parameter approximations. We then derive the corresponding P- and SV-wave equations in tilted transversely isotropic (TTI) media and provide two available solutions, the hybrid finite-difference/pseudo-spectral scheme and the low-rank approach. Numerical examples illustrate the separability and high accuracy of the proposed P- and SV-wave simulation methods in TTI media.

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