Efficient seismic forward modeling using simultaneous random sources and sparsity

Overview of Simultaneous Vibroseis Acquisition Methods

The high cost of simulating densely sampled seismic forward modeling data arises from activating sources one at a time in sequence.Toincreaseefficiency,onecouldleveragerecentinnovations in seismic field-data acquisition and activate several e.g., 2‐6 sources simultaneously during modeling. However, such approaches would suffer from degraded data quality because of the interference between the model’s responses to the simultaneoussources.Twonewefficientsimultaneous-sourcemodeling approachesareproposedthatrelyonthenoveltandemuseofrandomness and sparsity to construct almost noise-free model response to individual sources. In each approach, thefirst step is to measure the model’s cumulative response with all sources activated simultaneously using randomly scaled band-limited impulses or continuous band-limited random-noise waveforms. In the second step, the model response to each individual source is estimated from the cumulative receiver measurement by exploiting knowledge of the random source waveforms and the sparsity of the model response to individual sources in a known transformdomaine.g.,curveletdomain.Theefficiencyachievable by the approaches is primarily governed by the sparsity of the model response. By invoking results from the field of compressive sensing, theoretical bounds are provided that assert that the approaches would need less modeling time for sparser i.e., simpler or more structured model responses.Asimulated modelingexampleisillustratedthatshowsthatdatacollectedwithas manyas8192sourcesactivatedsimultaneouslycanbeseparated into the 8192 individual source gathers with data quality comparable to that obtained when the sources were activated sequentially.Theproposedapproachescouldalsodramaticallyimprove seismic field-data acquisition efficiency if the source signatures actuallyprobingtheearthcanbemeasuredaccurately.

Seismic data acquisition in marine environments is a costly process that calls for the adoption of simultaneous‐source or randomized acquisition ‐ an emerging technology that is stimulating both geophysical research and commercial efforts. Simultaneous marine acquisition calls for the development of a new set of design principles and post‐processing tools. In this paper, we discuss the properties of a specific class of randomized simultaneous acquisition matrices and demonstrate that sparsity‐promoting recovery improves the quality of reconstructed seismic data volumes. We propose a practical randomized marine acquisition scheme where the sequential sources fire airguns at only randomly time‐dithered instances. We demonstrate that the recovery using sparse approximation from random time‐dithering with a single source approaches the recovery from simultaneous‐source acquisition with multiple sources. Established findings from the field of compressive sensing indicate that the choice of the sparsifying transform that is incoherent with the compressive sampling matrix can significantly impact the reconstruction quality. Leveraging these findings, we then demonstrate that the compressive sampling matrix resulting from our proposed sampling scheme is incoherent with the curvelet transform. The combined measurement matrix exhibits better isometry properties than other transform bases such as a non‐localized multidimensional Fourier transform. We illustrate our results with simulations of ‘ideal’ simultaneous‐source marine acquisition, which dithers both in time and space, compared with periodic and randomized time‐dithering.

Randomized marine acquisition with compressive sampling matrices

A model of nonlinearity of the contact between the vibrator baseplate and the ground is proposed to describe the distortion of vibroseis signals in the near-field. A thin layer between the baseplate and the soil exhibits a strong nonlinear response because of the difference in its rigidity between the compression and tension phases. The model allows for a quantitative description of the transmission of seismic energy into the ground, including the observed harmonic distortion. However, the contact nonlinearity does not lead to the dependence of wave traveltimes on the amplitude of the force applied to the ground. This fact can be used in field observations to localize the source of the observed harmonic distortion.

J.S. May

Papers

High Fidelity Vibratory Seismic (HFVS) Method For Acquiring Seismic Data