scholarly journals Low-frequency acoustic signal created by rising air-gun bubble

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. P119-P128
Author(s):  
Daniel Wehner ◽  
Martin Landrø
Keyword(s):  
Acoustic Signal ◽  
Field Experiments ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Frequency Signal ◽  
Low Frequencies ◽  
Air Bubble ◽  
Rising Bubble ◽  
Air Gun ◽  
Different Depths

In the seismic industry, there is increasing interest in generating and recording low frequencies, which leads to better data quality and can be important for full-waveform inversion. The air gun is a seismic source with a signal that consists of the (1) main impulse, (2) oscillating bubble, and (3) rising of this air bubble. However, there has been little investigation of the third characteristic. We have studied a low-frequency signal that could be created by the rising air bubble and find the contribution to the low-frequency content in seismic acquisition. We use a simple theory and modeling of rising spheres in water and compute the acoustic signal created by this effect. We conduct tank and field experiments with a submerged buoy that is released from different depths and record the acoustic signal with hydrophones along the rising path. The experiments simulate the signal from the rising bubble separated from the other two effects (1 and 2). Furthermore, we use data recorded below a single air gun fired at different depths to investigate if we can observe the proposed signal. We find that the rising bubble creates a low-frequency signal. Compared with the main impulse and the oscillating bubble effect of an air-gun signal, the contribution of the rising bubble is weak, on the order of 1/900 depending on the bubble size. By using large air-gun arrays tuned to create one big bubble, the contribution of the signal can be increased. The enhanced signal can be important for deep targets or basin exploration because the low-frequency signal is less attenuated.

scholarly journals On low frequencies emitted by air guns at very shallow depths — An experimental study

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. P61-P71 ◽  
Author(s):  
Daniel Wehner ◽  
Martin Landrø ◽  
Lasse Amundsen
Keyword(s):  
Large Volume ◽  
Field Experiments ◽  
Field Measurements ◽  
Seismic Source ◽  
Sea Surface ◽  
Frequency Signal ◽  
Low Frequencies ◽  
Air Gun ◽  
Seismic Acquisition ◽  
Marine Seismic

In marine seismic acquisition, the enhancement of frequency amplitudes below 5 Hz is of special interest because it improves imaging of the subsurface. The frequency content of the air gun, the most commonly used marine seismic source, is mainly controlled by its depth and the volume. Although the depth dependency on frequencies greater than 5 Hz has been thoroughly investigated, for frequencies less than 5 Hz it is less understood. However, recent results suggest that sources fired very close to the sea surface might enhance these very low frequencies. Therefore, we conduct dedicated tank experiments to investigate the changes of the source signal for very shallow sources in more detail. A small-volume air gun is fired at different distances from the water-air interface, including depths for which the air bubble bursts directly into the surrounding air. The variations of the oscillating bubble and surface disturbances, which can cause changes of the reflected signal from the sea surface, are explored to determine whether an increased frequency signal below 5 Hz can be achieved from very shallow air guns. The results are compared with field measurements of a large-volume air gun fired close to the sea surface. The results reveal an increased signal for frequencies below 5 Hz of up to 10 and 20 dB for the tank and field experiments, respectively, for the source depth at which the air gun bubble bursts directly into the surrounding air. For large-volume air guns, an increased low-frequency signal might also be achieved for sources that are slightly deeper than this bursting depth. From these observations, new design considerations in the geometry of air-gun arrays in marine seismic acquisition are suggested.

A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 854-859 ◽  
Author(s):  
Xiao Ming Tang
Keyword(s):  
Elastic Wave ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Finite Size ◽  
Low Frequency ◽  
Frequency Range ◽  
Multiple Reflections ◽  
Low Frequencies ◽  
The Time Domain ◽  
Attenuation Values

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

Denoising for full-waveform inversion with expanded prediction-error filters

Geophysics ◽  
2021 ◽  
pp. 1-54
Author(s):  
Milad Bader ◽  
Robert G. Clapp ◽  
Biondo Biondi
Keyword(s):  
High Frequency ◽  
Prediction Error ◽  
Signal To Noise Ratio ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Frequency Data ◽  
Signal To Noise ◽  
Frequency Signal ◽  
Full Waveform

Low-frequency data below 5 Hz are essential to the convergence of full-waveform inversion towards a useful solution. They help build the velocity model low wavenumbers and reduce the risk of cycle-skipping. In marine environments, low-frequency data are characterized by a low signal-to-noise ratio and can lead to erroneous models when inverted, especially if the noise contains coherent components. Often field data are high-pass filtered before any processing step, sacrificing weak but essential signal for full-waveform inversion. We propose to denoise the low-frequency data using prediction-error filters that we estimate from a high-frequency component with a high signal-to-noise ratio. The constructed filter captures the multi-dimensional spectrum of the high-frequency signal. We expand the filter's axes in the time-space domain to compress its spectrum towards the low frequencies and wavenumbers. The expanded filter becomes a predictor of the target low-frequency signal, and we incorporate it in a minimization scheme to attenuate noise. To account for data non-stationarity while retaining the simplicity of stationary filters, we divide the data into non-overlapping patches and linearly interpolate stationary filters at each data sample. We apply our method to synthetic stationary and non-stationary data, and we show it improves the full-waveform inversion results initialized at 2.5 Hz using the Marmousi model. We also demonstrate that the denoising attenuates non-stationary shear energy recorded by the vertical component of ocean-bottom nodes.

scholarly journals Deep learning for low-frequency extrapolation from multioffset seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R989-R1001 ◽  
Author(s):  
Oleg Ovcharenko ◽  
Vladimir Kazei ◽  
Mahesh Kalita ◽  
Daniel Peter ◽  
Tariq Alkhalifah
Keyword(s):  
Deep Learning ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Low Frequencies ◽  
Seismic Surveys ◽  
Full Waveform ◽  
Frequency Components ◽  
Marine Seismic

Low-frequency seismic data are crucial for convergence of full-waveform inversion (FWI) to reliable subsurface properties. However, it is challenging to acquire field data with an appropriate signal-to-noise ratio in the low-frequency part of the spectrum. We have extrapolated low-frequency data from the respective higher frequency components of the seismic wavefield by using deep learning. Through wavenumber analysis, we find that extrapolation per shot gather has broader applicability than per-trace extrapolation. We numerically simulate marine seismic surveys for random subsurface models and train a deep convolutional neural network to derive a mapping between high and low frequencies. The trained network is then tested on sections from the BP and SEAM Phase I benchmark models. Our results indicate that we are able to recover 0.25 Hz data from the 2 to 4.5 Hz frequencies. We also determine that the extrapolated data are accurate enough for FWI application.

scholarly journals Time-domain full-waveform inversion of exponentially damped wavefield using the deconvolution-based objective function

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. R77-R88 ◽  
Author(s):  
Yunseok Choi ◽  
Tariq Alkhalifah
Keyword(s):  
Objective Function ◽  
Frequency Band ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Low Frequencies ◽  
Full Waveform ◽  
Adjoint State ◽  
Recorded Data ◽  
Adjoint State Method

Full-waveform inversion (FWI) suffers from the cycle-skipping problem when the available frequency-band of data is not low enough. We have applied an exponential damping to the data to generate artificial low frequencies, which helps FWI to avoid cycle skipping. In this case, the least-squares misfit function does not properly deal with the exponentially damped wavefield in FWI because the amplitude of traces decays almost exponentially with increasing offset in a damped wavefield. Thus, we use a deconvolution-based objective function for FWI of the exponentially damped wavefield. The deconvolution filter includes inherently a normalization between the modeled and observed data; thus, it can address the unbalanced amplitude of a damped wavefield. We specifically normalize the modeled data with the observed data in the frequency-domain to estimate the deconvolution filter and selectively choose a frequency-band for normalization that mainly includes the artificial low frequencies. We calculate the gradient of the objective function using the adjoint-state method. The synthetic and benchmark data examples indicate that our FWI algorithm generates a convergent long-wavelength structure without low-frequency information in the recorded data.

scholarly journals Low-frequency seismic: the next revolution in resolution

2014 ◽  
Vol 54 (1) ◽  
pp. 69
Author(s):  
Andrew Long ◽  
Cyrille Reiser
Keyword(s):  
New Technologies ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Seismic Inversion ◽  
Reservoir Properties ◽  
Well Control ◽  
Velocity Models ◽  
The Earth ◽  
Air Gun ◽  
Band Limited

Ultra-low seismic frequencies less than about 7 Hz cannot be produced by conventional air gun arrays, for any configuration and for any towing depth. There is a profound difference between improving low-frequency recovery by removing source and receiver ghosts (achievable) and improving low-frequency injection on the source side (an unrealised dream). If 1–7 Hz amplitudes could be usefully injected into the earth, it would be possible to facilitate much sharper seismic representation of geological contacts and internal features, and seismic inversion would yield robust and precise predictions of reservoir properties—without well control. The net result is fewer exploration and appraisal wells, greatly reduced exploration and development risks, and optimised recoverable reserves. Furthermore, an emerging seismic pursuit known as full waveform inversion (FWI) makes the bold promise that raw seismic field gathers can be directly used to invert for the highest achievable velocity models, almost without any human intervention. These models will bypass the traditional lack of low-frequency information in band-limited seismic data, and facilitate the aforementioned ambition of seismic inversion without well control. FWI, however, is confronted by the paradox that ultra-low-frequency seismic gathers are the necessary input for stable results. This paper describes new technologies that may enable the injection of strong 2–7 Hz amplitudes into the earth, and explains in simple terms how FWI can already be pursued as a robust complement to the prediction of accurate reservoir properties. The low-frequency revolution is already here.

scholarly journals Full-waveform inversion with extrapolated low-frequency data

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R339-R348 ◽  
Author(s):  
Yunyue Elita Li ◽  
Laurent Demanet
Keyword(s):  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Propagation Model ◽  
Full Waveform Inversion ◽  
Frequency Data ◽  
Local Minima ◽  
Bandwidth Extension ◽  
Low Frequencies ◽  
Full Waveform

The availability of low-frequency data is an important factor in the success of full-waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data less than 2 or 3 Hz from the field is a challenging and expensive task. We have explored the possibility of synthesizing the low frequencies computationally from high-frequency data and used the resulting prediction of the missing data to seed the frequency sweep of FWI. As a signal-processing problem, bandwidth extension is a very nonlinear and delicate operation. In all but the simplest of scenarios, it can only be expected to lead to plausible recovery of the low frequencies, rather than their accurate reconstruction. Even so, it still requires a high-level interpretation of band-limited seismic records into individual events, each of which can be extrapolated to a lower (or higher) frequency band from the nondispersive nature of the wave-propagation model. We have used the phase-tracking method for the event separation task. The fidelity of the resulting extrapolation method is typically higher in phase than in amplitude. To demonstrate the reliability of bandwidth extension in the context of FWI, we first used the low frequencies in the extrapolated band as data substitute, to create the low-wavenumber background velocity model, and then we switched to recorded data in the available band for the rest of the iterations. The resulting method, extrapolated FWI, demonstrated surprising robustness to the inaccuracies in the extrapolated low-frequency data. With two synthetic examples calibrated so that regular FWI needs to be initialized at 1 Hz to avoid local minima, we have determined that FWI based on an extrapolated [1, 5] Hz band, itself generated from data available in the [5, 15] Hz band, can produce reasonable estimations of the low-wavenumber velocity models.

Impedance inversion by using the low-frequency full-waveform inversion result as an a priori model

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R149-R164 ◽  
Author(s):  
Sanyi Yuan ◽  
Shangxu Wang ◽  
Yaneng Luo ◽  
Wanwan Wei ◽  
Guanchao Wang
Keyword(s):  
A Priori ◽  
Complex Structure ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Real Data ◽  
Well Logs ◽  
Low Frequencies ◽  
Impedance Model ◽  
Full Waveform ◽  
Impedance Inversion

Prestack acoustic full-waveform inversion (FWI) can provide long-wavelength components of the P-wave velocity by using low frequencies and long-offset direct/diving/refracted waves, which could be simulated via a large space grid, and it is weakly sensitive to density. Poststack impedance inversion can usually quickly yield high-resolution impedance, and it is sensitive to density. Therefore, we have combined these two methods to develop an FWI-driven impedance inversion. Our method first uses FWI to obtain the long-wavelength velocity with a guaranteed overlap between the high frequencies of the velocity and the low frequencies of the poststack data. Then, the fitting rock-physics relationship between the density and the velocity is adopted to translate the FWI velocity into the low-frequency impedance. Finally, the resulting low-frequency impedance is used to construct an a priori constraint for poststack impedance inversion. The method has the ability to solve the overlap between the FWI-based converted prior impedance model and poststack data, and it can thereby yield a broadband absolute impedance result. We adopt a Marmousi II model example and a real data case to test the performances of the FWI-driven impedance inversion and indicate its advantages compared with the conventional well-driven impedance inversion that uses well logs and interpreted horizons to build the prior impedance model. The synthetic data example demonstrates that well-driven impedance inversion produces a result with a relatively large deviation to the true impedance model at complex structure zones. However, FWI-driven impedance inversion favorably recovers all interesting sediment layers at complex structure zones. The real data example illustrates that well-driven impedance inversion yields a result with a distinct footprint of the prior model created from well logs and horizons. On the other hand, we find that FWI-driven impedance inversion yields a geologically reasonable solution, which not only conforms to the time-space variation trend of the well logs, but it also reveals a basin structural-depositional evolution.

scholarly journals Full-waveform inversion using a nonlinearly smoothed wavefield

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. R117-R127 ◽  
Author(s):  
Yuanyuan Li ◽  
Yunseok Choi ◽  
Tariq Alkhalifah ◽  
Zhenchun Li ◽  
Kai Zhang
Keyword(s):  
Objective Function ◽  
Global Minimum ◽  
Waveform Inversion ◽  
Gradient Methods ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Half Cycle ◽  
Low Frequencies ◽  
Full Waveform ◽  
Global Correlation

Conventional full-waveform inversion (FWI) based on the least-squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle-skipping phenomena. An initial model producing data that are at most a half-cycle away from the observed data is needed for convergence to the global minimum. Low frequencies are helpful in updating low-wavenumber components of the velocity model to avoid cycle skipping. However, low enough frequencies are usually unavailable in field cases. The multiplication of wavefields of slightly different frequencies adds artificial low-frequency components in the data, which can be used for FWI to generate a convergent result and avoid cycle skipping. We generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield, which is rich in low frequencies. The global correlation-norm-based objective function can mitigate the dependence on the amplitude information of the nonlinearly smoothed wavefield. Therefore, we have evaluated the use of this objective function when using the nonlinearly smoothed wavefield. The proposed objective function has much larger convexity than the conventional objective functions. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to that of the conventional FWI except for the adjoint source. We progressively reduce the smoothing width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.

On a Rectangular Pressure Distribution of Oscillating Strength Moving Over a Free Surface

1977 ◽  
Vol 21 (01) ◽  
pp. 11-23
Author(s):  
Hsao-Hsin Chen
Keyword(s):  
Free Surface ◽  
Pressure Distribution ◽  
Hydrodynamic Instability ◽  
Low Frequency ◽  
Wave Theory ◽  
Hydrodynamic Coefficients ◽  
Low Frequencies ◽  
Air Bubble ◽  
Negative Damping ◽  
Heave Motion

Through the application of linearized water-wave theory, a solution of the free surface due to the disturbance of a moving, oscillatory pressure distribution of rectangular form is obtained. Such a solution provides the basis for formulating the wave resistance of the moving pressure distribution just cited, as well as the hydrodynamic coefficients of a captured-air bubble of rectangular footprint in heave motion. Numerical methods are developed to compute the aforementioned resistance and hydrodynamic coefficients, the numerical examples of which are also presented. Of special interest is the occurrence of negative effectivemass at low frequencies for the two forward speeds considered in the present work. Another interesting feature is the hydrodynamic instability and the negative damping that occurs in the low-frequency range when the Froude number is very high.

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