Green’s functions are the impulse response of the medium, which contain all the information of the properties of the wave propagation between two locations. Therefore, estimation of the Green’s function is significant for understanding the medium and for the downward continuation for wavefield imaging. Marchenko redatuming enables the retrieval of the Green’s function using single-sided seismic reflection response in a 1D, 2D or 3D medium. The retrieved Green’s function contains accurate information of both primaries and multiples of the seismic waves. In this study, we investigate how to handle Marchenko redatuming in the 3D configuration. Based on stationary phase analysis, we propose an approach to economically determine the surface survey area and spacial sampling of the source/receiver pairs. Then with numerical examples, we demonstrate that Marchenko redatuming is successful to retrieve the Green’s function with both primaries and multiples in the case of the 3D earth models.
Presentation Date: Tuesday, October 16, 2018
Start Time: 1:50:00 PM
Location: 211A (Anaheim Convention Center)
Presentation Type: Oral
The linear sampling method is a shape-reconstruction technique that uses the total scattered wave to image the boundary of an inhomogeneity. In particular, the method solves a series of linear equations without making any weak scattering approximations or requiring any a priori information on the physical nature of the scatterer. Here, we present the fundamentals of the linear sampling method and illustrate its capabilities with a few numerical simulations.
Presentation Date: Thursday, October 18, 2018
Start Time: 8:30:00 AM
Location: 211A (Anaheim Convention Center)
Presentation Type: Oral
Then we introduce a method to find the optimal weighting parameters for a synthetic aperture source array. Finally, we present an example of applying the optimal weighted synthetic aperture to synthetic electromagnetic fields with noise added. WEIGHTED SYNTHETIC APERTURE We review the theory and history of weighted synthetic aperture and present new weighting formulation for applications to CSEM. Fan et al. (2010) first applied synthetic aperture to CSEM fields; however, the technique was developed earlier for radar (Barber, 1985). Currently, many fields use the technique, including radar, sonar, medical imaging, to increase resolution or detectability (Van Veen and Buckley, 1988; Barber, 1985; Jensen et al., 2006).
Time-reversal (TR) methods provide a simple and robust solution to source imaging problems. However, for recovering a well resolved image of the source, TR requires a balanced illumination of the target from all angles. When acquisition is incomplete and a balanced illumination is not possible, the TR solution may not be adequate. In a previous paper, by formulating source imaging as an optimization problem, we presented a method named Backus-Gilbert focusing (BG) to enhance the performance of TR in acoustic media despite incomplete acquisition. Here, we generalize the theory of Backus- Gilbert focusing for application in elastic media.
Knaak, Allison (Colorado School of Mines) | Snieder, Roel (Colorado School of Mines) | Fan, Yuanzhong (Shell International Exploration & Production) | Ramirez-Mejia, David (Shell International Exploration & Production)
Controlled-source electromagnetics (CSEM) is a geophysical electromagnetic method used to detect hydrocarbon reservoirs in marine settings. Synthetic aperture, a technique that increases the size of the source by combining multiple individual sources, has been applied to CSEM fields to increase the detectability of hydrocarbon reservoirs. We apply synthetic aperture to a 3D synthetic CSEM field with a 2D source distribution to evaluate the benefits of the technique. We present an optimized beamforming of the 2D source which increases the detectability of the reservoir. With only a portion of three towlines spaced 2km apart, we enhance the anomaly from the target by 80%. We also demonstrate the benefits of using the Poynting vector to view CSEM fields in 3D.
We retrieve reflected plane waves by applying seismic interferometry to the recorded ground motion from a cluster of earth- quakes. We employ upgoing/downgoing P/S wavefield decomposition, time windows, time reversal, and multi-dimensional deconvolution (MDD) to improve the quality of the extraction of reflected waves with seismic interferometry. Because MDD interferometry requires the separation of wavefields depending on the direction of wave propagation, almost no studies apply this technique to earthquake data observed at the surface to extract body waves. The wavefield separation and seismic interferometry based on MDD allow us to reconstruct PP, PS, SP, and SS reflected waves without unwanted crosstalk between P and S waves. From earthquake data, we obtain PP, PS, and SS reflected plane waves that reflect off the same reflector, and estimate P- and S-wave velocities.
Focusing waves inside a medium has applications in geophysics in areas such as imaging and microseismic event location. The goal in focusing is to concentrate the wave energy at a specific time and location inside a medium. Various techniques have been devised and used to achieve this goal. Time-reversal (TR) is a well-researched method that has been used routinely to focus waves. The ability of TR methods to focus wave fields inside heterogeneous media is bounded by limitations caused by imperfect acquisition, attenuation, and the diffraction limit. To go beyond these limitations, we present a solution by formulating wave focusing as an optimization problem. Solving this optimization problem gives the needed signals for transmission to the medium to get the best focus. These signals are optimized for the configuration of the injection points, velocity of the medium, and the focusing target.
We demonstrate a technique to enhance the ability of imaging the location of a microseismic event by improving both spatial and temporal focusing. The technique improves locating a microseismic event in a velocity model for which the interface boundaries are approximate but where it has the correct mean slowness. Our method designs a signal to be rebroadcasted from the receivers, using only the waves recorded at each receiver, such that the wave field has an optimal temporal focus at the source location. Additionally, this procedure leads to an improved spatial focus of the wave field. The numerical test shown include additive noise. This proposed technique only involves a simple preprocessing step to the recorded data and its cost is hence negligible compared to the total cost of microseismic imaging.
Similar to surface reflection data, microseismic data also contain multiply-scattered events. They are especially prevalent in borehole microseismic data because of low attenuation. These scattered events, if not imaged accurately, can lead to the spurious microseismic hypocenters. Here, we introduce an imaging algorithm that accurately images not only the primary arrivals but also the multiply scattered events. The algorithm uses the exact Green’s function computed using an iterative scheme based on inverse-scattering theory. Extraction of the Green’s function, however, requires surface reflection data and a background velocity model. Imaging of surface microseismic data involves computation of the Green’s function between the image point and the surface receivers and the application of an imaging condition to the data. Borehole-microseismic-data imaging, however, requires two additional steps – first, computation of the Green’s function between the borehole receivers and the surface and second, computation of the Green’s function between the image point and the borehole receivers using seismic interferometry. Tests on synthetic data show that our imaging algorithm not only locates the microseismic hypocenters accurately but also substantially reduces the number of spurious events.
Wapenaar, Kees (Delft University of Technology) | Slob, Evert (Delft University of Technology) | van der Neut, Joost (Delft University of Technology) | Thorbecke, Jan (Delft University of Technology) | Broggini, Filippo (Colorado School of Mines) | Snieder, Roel (Colorado School of Mines)
In recent work we showed with heuristic arguments that the Green's response to a virtual source in the subsurface can be obtained from reflection data at the surface. This method is called “Green's function retrieval beyond seismic interferometry”, because, unlike in seismic interferometry, no receiver is needed at the position of the virtual source. Here we present a formal derivation of Green's function retrieval beyond seismic interferometry, based on a 3-D extension of the Marchenko equation. We illustrate the theory with a numerical example and indicate the potential applications in seismic imaging and AVA analysis.