We propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform. In a first pass, the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data. The aforementioned coefficients are divided into two groups of scales: alias-free and alias-contaminated scales. The alias-free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the alias-contaminated scale coefficients. The mask function is incorporated into the inversion via a minimum norm least-squares algorithm that determines the curvelet coefficients of the desired aliasfree data. Once the alias-free coefficients are determined, the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions. The proposed method can be used to reconstruct regularly and irregularly sampled seismic data. We believe that our exposition leads to a clear unifying thread between f-x and f-k beyond-alias interpolation methods and curvelet reconstruction. As in f-x and f-k interpolation, we stress the necessity of examining seismic data at different scales ͑frequency bands͒ to come up with viable and robust interpolation schemes. Synthetic and real data examples are used to illustrate the performance of the proposed curvelet interpolation method.
We use exponentially weighted recursive least squares to estimate adaptive prediction filters for frequency-space [Formula: see text] seismic interpolation. Adaptive prediction filters can model signals where the dominant wavenumbers vary in space. This concept leads to an [Formula: see text] interpolation method that does not require windowing strategies for optimal results. In other words, adaptive prediction filters can be used to interpolate waveforms that have spatially variant dips. The interpolation method’s performance depends on two parameters: filter length and forgetting factor. We pay particular attention to selection of the forgetting factor because it controls the algorithm’s adaptability to changes in local dip. Finally, we use synthetic- and real-data examples to illustrate the performance of the proposed adaptive [Formula: see text] interpolation method.
Linear prediction filters in the [Formula: see text] domain are widely used to interpolate regularly sampled data. We study the problem of reconstructing irregularly missing data on a regular grid using linear prediction filters. We propose a two-stage algorithm. First, we reconstruct the unaliased part of the data spectrum using a Fourier method (minimum-weighted norm interpolation). Then, prediction filters for all the frequencies are extracted from the reconstructed low frequencies. The latter is implemented via a multistep autoregressive (MSAR) algorithm. Finally, these prediction filters are used to reconstruct the complete data in the [Formula: see text] domain. The applicability of the proposed method is examined using synthetic and field data examples.
I introduce a unified approach for denoising and interpolation of seismic data in the frequency-wavenumber ([Formula: see text]) domain. First, an angular search in the [Formula: see text] domain is carried out to identify a sparse number of dominant dips, not only using low frequencies but over the whole frequency range. Then, an angular mask function is designed based on the identified dominant dips. The mask function is utilized with the least-squares fitting principle for optimal denoising or interpolation of data. The least-squares fit is directly applied in the time-space domain. The proposed method can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid. Synthetic and real data examples are provided to examine the performance of the proposed method.
The Metal Earth project acquired 927 km of deep seismic reflection profiles from August to November of 2017. Seismic data acquired in this early stage of the Metal Earth project benefited greatly from recent advances in the petroleum sector as well as those in mineral exploration. Vibroseis acquisition with receivers having a 5 Hz response (10 dB down) generated records from a sweep signal starting at 2 Hz, sweeping up to 150 Hz or 200 Hz. Not only does this broadband signal enhance reflections from the deepest to the shallowest crust, but it also helps the use of full waveform inversion (e.g., to mitigate cycle-skipping) and related techniques. Metal Earth regional-scale transects using over 5000 active sensors target mineralizing fluid pathways throughout the crust, whereas higher spatial-resolution reflection and full-waveform surveys target structures at mine camp scales. Because Metal Earth was proposed to map and compare entire Archean ore and geologically similar non-ore systems, regional sections cover the entire crust to the Moho in the Abitibi and Wabigoon greenstone belts of the Superior craton in central Canada. Where the new sections overlap with previous Lithoprobe surveys, a clear improvement in reflector detection and definition is observed. Improvements are here attributed to the increased bandwidth of the signal, better estimates of refraction and reflection velocities used in processing, and especially the pre-stack time migration of the data.
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