Numerical Methods of Exploration Seismology

Margrave, Gary F.; Lamoureux, Michael P.

doi:10.1017/9781316756041

Cited by 56 publications

(58 citation statements)

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“…The method is based on data migration using fast Fourier transforms, which can easily be performed on current hand-held systems of the size of smart phones. As such, this paper demonstrates the applicability of the fast imaging technique in the frequency-wavenumber domain by Stolt [6], [9] to image single focal point data, by using the virtual point source concept [10]- [12]. A comparison to the postprocessing method in time-space domain by Kortbek et al [10] is made in this paper.…”

Section: Introductionmentioning

confidence: 76%

“…Our technique particularly addresses the second stage, which processes the single-focused image into an overall focused image. The first stage of line-based delay-and-sum has been described thoroughly in many text books [3], [6].…”

Section: Concept and Theorymentioning

confidence: 99%

“…Many imaging algorithms exist in the seismic research field to process such a dataset into an image [6], [15]- [18], which motivates our choice for the change of origin in the first place. The algorithms include delay-and-sum algorithms based on geometrical paths, and full-wave imaging algorithms based on migration of the source plane and receiver plane.…”

Section: Concept and Theorymentioning

confidence: 99%

“…The algorithms include delay-and-sum algorithms based on geometrical paths, and full-wave imaging algorithms based on migration of the source plane and receiver plane. A fast and accurate algorithm is proposed by Stolt [6], [18]. The algorithm processes the data in the wavenumber-frequency domain based on the linear wave equation assuming constant speed of sound in the medium.…”

Section: Concept and Theorymentioning

confidence: 99%

“…We follow the derivation of Margrave [6], which we repeat here for consistency. A similar derivation can be found in [9].…”

Section: B Theorymentioning

confidence: 99%

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F– k Domain Imaging for Synthetic Aperture Sequential Beamforming

Vos

Neer

Mota

et al. 2016

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Spatial resolution in medical ultrasound images is a key component in image quality and an important factor for clinical diagnosis. In early systems, the lateral resolution was optimal in the focus but rapidly decreased outside the focal region. Improvements have been found in, e.g., dynamic-receive beamforming, in which the entire image is focused in receive, but this requires complex processing of element data and is not applicable for mechanical scanning of single-element images. This paper exploits the concept of two-stage beamforming based on virtual source-receivers, which reduces the front-end computational load while maintaining a similar data rate and frame rate compared to dynamic-receive beamforming. We introduce frequency-wavenumber domain data processing to obtain fast second-stage data processing while having similarly high lateral resolution as dynamic-receive beamforming and processing in time-space domain. The technique is very suitable in combination with emerging technologies such as application-specific integrated circuits (ASICs), hand-held devices, and wireless data transfer. The suggested method consists of three steps. In the first step, single-focused RF line data are shifted in time to relocate the focal point to a new origin t' = 0, z' = 0. This new origin is considered as an array of virtual source/receiver pairs, as has been suggested previously in literature. In the second step, the dataset is efficiently processed in the wavenumber-frequency domain to form an image that is in focus throughout its entire depth. In the third step, the data shift is undone to obtain a correct depth axis in the image. The method has been tested first with a single-element scanning system and second in a tissue-mimicking phantom using a linear array. In both setups, the method resulted in a −6-dB lateral point spread function (PSF) which was constant over the entire depth range, and similar to dynamic-receive beamforming and synthetic aperture sequential beamforming. The signal-to-noise ratio increased by 6 dB in both the near field and far field. These results show that the second-stage processing algorithm effectively produces a focused image over the entire depth range from a single-focused ultrasound field.

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Section: Introductionmentioning

confidence: 76%

Section: Concept and Theorymentioning

confidence: 99%

Section: Concept and Theorymentioning

confidence: 99%

Section: Concept and Theorymentioning

confidence: 99%

“…We follow the derivation of Margrave [6], which we repeat here for consistency. A similar derivation can be found in [9].…”

Section: B Theorymentioning

confidence: 99%

See 3 more Smart Citations

F– k Domain Imaging for Synthetic Aperture Sequential Beamforming

Vos

Neer

Mota

et al. 2016

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Constraining attenuation uncertainty in common midpoint radar surveys of ice sheets

et al. 2016

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For common offset radar data, there is no clear way to disentangle path effects from reflector characteristics, so efforts to determine the physical properties at the bed using reflection amplitude are inherently limited by the constraints on englacial attenuation. In this study, we identify the theoretical considerations required for interpreting bistatic radar surveys and use data collected on the Northeast Greenland Ice Stream and Kamb Ice Stream to compute local attenuation profiles. We found that failing to correct for angle‐dependent controls on return power (including antenna directivity, the reflection coefficient, and refractive focusing) can bias the computed attenuation rates as much as 30 dB/km for reflectors at 1 km depth. Because the radiation characteristics are the dominant source of uncertainty in our data, we recommend either a simplified survey design for the future (where the antennae are decoupled from the ice surface) or additional data collection to constrain the near‐field permittivity and its effect on the radiation pattern. Depth‐averaged attenuation rates computed using common midpoint methods for deep reflectors yield values >10 dB/km higher than attenuation rates computed using common offset techniques with the same data. We attribute these anomalously high attenuation rates to additional wavenumber‐dependent (and therefore, angle‐dependent) interferences between subwavelength reflectors.

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