Jerry Krebs

Efficient seismic forward modeling using simultaneous random sources and sparsity

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.

Encoded Simultaneous Source Full-Wavefield Inversion For Spectrally Shaped Marine Streamer Data

In this paper, we apply encoded simultaneous source fullwavefield inversion (FWI) to marine streamer data. FWI of large scale 3D data is a challenging problem, especially constraining the inversion using the high frequencies available in exploration seismic data. Two methodologies that make high-frequency FWI feasible for field data are: (a) applying encoded simultaneous source full-wavefield inversion (ESSFWI) and (b) shaping the data to provide a preferential weighting to the low-frequency components of the data. These two methods in combination provide us with the computational efficiencies needed for large 3D runs. To date, most encoded simultaneous source methods have been applied to fixed-receiver data; i.e., each receiver records data from all shots in the survey. We developed an approach that enables us to apply ESSFWI to marine streamer data that are non-fixed spread. The approach uses a normalized cross-correlation objective function with multiple realizations of the encoded data at each iteration of the nonlinear FWI. The method can be applied to 2D/3D data with any survey geometry. Here we demonstrate the methodology and discuss its details with synthetic examples. Although not presented here our initial investigations on 3D field streamer data look encouraging.

Simultaneous full‐waveform inversion for source wavelet and earth model

The theory of full-waveform inversion developed by Tarantola (1988) included inversion for the source wavelet. Source-wavelet inversion has been performed in the time domain by Zhou et al. (1997) and in the frequency domain by Pratt (1999). Minkoff and Symes (1997) performed simultaneous inversion for reflectivity and source based on primary reflections in a layered earth. Since we believe a synthetic study of the stability and accuracy of source inversion to be important to both seismic acquisition and inversion communities, we performed a simultaneous fullwaveform inversion for the source wavelet and model parameters (P-wave velocity in this test).

Subsurface parameter estimation in full wavefield inversio n and reverse time migration

We develop a method for directly estimating subsurface medium parameter updates from the gradient equations in full wavefield inversion. This is achieved by accounting for the effects of source and receiver illuminations, background medium properties, and seismic resolution volume in the gradient equations. Using this method, we directly compute the subsurface seismic parameters needed to minimize the difference between the measured and modeled seismic field. It is shown that this method, when used to precondition the gradients in iterative inversion processes, yields faster convergence than when gradients are used without preconditioning. It is also shown that this method can be used for inversion of amplitudes in reverse time migration into the difference bulk modulus of subsurface.

Role of Simultaneous Source Technology in Seismic Industry

Simultaneous source method has been investigated in the past in the context of efficient seismic data acquisition; however recently due to its computational efficiency in imaging, simulation and inversion the momentum in this field has increased. At ExxonMobil, simultaneous source technology has been an active research topic for many years in several areas ranging from acquisition, imaging and recently in full-wavefield inversion (FWI).