Yingcai Zheng

Retrieving the exact Green’s function by wavefield crosscorrelation

Recent development on the Greens function retrieval by wavefield crosscorrelation has substantially advanced the physical research in a multidisciplinary and unprecedented fashion. However, the underlying assumption of the theory that the sources are in the far-field limits the technology to extracting only the high-frequency part of the Greens function in an open system. This critical approximation can be eliminated using the exact boundary integral equation method. A scheme involving the crosscorrelation kernel is proposed to recover the exact Greens function including all-frequency content. Symmetric difference kernels are analytically constructed for sources on a plane or on a circle and can be reduced to the known Dirac delta kernel under the far-field approximation.

Sequential approach to joint flow‐seismic inversion for improved characterization of fractured media

Seismic interpretation of subsurface structures is traditionally performed without any account of flow behavior. Here we present a methodology for characterizing fractured geologic reservoirs by integrating flow and seismic data. The key element of the proposed approach is the identification—within the inversion—of the intimate relation between fracture compliance and fracture transmissivity, which determine the acoustic and flow responses of a fractured reservoir, respectively. Owing to the strong (but highly uncertain) dependence of fracture transmissivity on fracture compliance, the modeled flow response in a fractured reservoir is highly sensitive to the geophysical interpretation. By means of synthetic models, we show that by incorporating flow data (well pressures and tracer breakthrough curves) into the inversion workflow, we can simultaneously reduce the error in the seismic interpretation and improve predictions of the reservoir flow dynamics. While the inversion results are robust with respect to noise in the data for this synthetic example, the applicability of the methodology remains to be tested for more complex synthetic models and field cases.

Double-beam stacking to infer seismic properties of fractured reservoirs

Summary We develop a theory for using 3D beam interference to infer scattering properties of a fractured reservoir using reflected seismic P data. For the sake of simplicity, we use Gaussian beams. The scattering properties are important to infer fracture spacing, orientation and compliance. The method involves the interference of two beams, one from the source region and the other from the receiver region. Each beam is formed by first windowing the data in space and time and then performing f-k filtering. The interference pattern depends on frequency, the incident angle, the reflection angle, and the azimuth. We try to interpret the interference pattern using local Born scattering in the target region. This interpretation is motivated by the observation that full-wave finite difference simulation of waves propagating through a set of vertical fractures using Schoenberg’s linear-slip boundary condition and fracture compliances consistent with those inferred from field and laboratory data shows that single scattering dominates in the reflection data. The methodology is versatile in that by adjusting the window sizes we can obtain plane wave interference as well as interference for a single shot or receiver gather. By suitable choice of pairs of source and receiver beams, the spatially varying fracture properties as well as the fracture orientation can be inferred.

Reverse Time Migration of Multiples

Multiple reflections have different wave propagation paths from primary reflections and thus can be used to complement the illumination where primary reflections from beneath the salt are not available. We propose to modify conventional reverse time migration (RTM) so that multiples can be used as constructive reflection energy for subsalt imaging. This new approach replaces the impulsive source wavelet with the recorded data containing both primaries and multiples and uses predicted multiples as the input data. In the RTM process, multiples recorded on the surface are extrapolated backward in time to each depth level, and the observed data with both primaries and multiples are extrapolated forward in time to the same depth level, followed by a cross-correlation imaging condition. A numerical test on the Sigsbee2B dataset shows that a wider coverage and a more balanced illumination of the subsurface area can be achieved by migration of multiples compared with conventional migration of primary reflections.

Theory of Transmission Fluctuations in Random Media with a Depth‐Dependent Background Velocity Structure

Abstract An extended theory on the coherence function of log amplitude and phase for waves passing through random media is developed for a depth‐dependent background medium using the WKBJ‐approximated Greens function, the Rytov approximation, and the stochastic theory of the random velocity field. The new theory overcomes the limitation of the existing theory that can only deal with constant background media. Our extended coherence functions depend jointly on the angle separation between two incident plane waves and the spatial lag between receivers. The theory is verified through numerical simulations using the iasp91 background velocity model with two layers of random media. The current theory has the potential to be used to invert for the depth‐dependent spectrum of heterogeneities in the Earth.

Nonlinear Signal Comparison and High‐Resolution Measurement of Surface‐Wave Dispersion

Abstract In surface‐wave dispersion measurement, we use cross correlation to compare the recorded signals at different stations to measure their phase difference. However, the measurement resolution is poor at low frequencies and the poor resolution was often incorrectly interpreted as large measurement errors. Here, we propose a new nonlinear signal comparison (NLSC) approach to achieve a uniform high‐resolution measurement across a wide frequency band. Furthermore, we can control the overall resolution in NLSC by an adjustable parameter. The traditional cross correlation is a special case of NLSC. We use both synthetic and recorded seismic data to demonstrate the effectiveness of NLSC by extracting surface Rayleigh‐wave phase‐velocity dispersion curves for different datasets, including synthetic multimode Rayleigh‐wave data, synthetic global Rayleigh waves of a Martian seismic model, and a real ambient noise correlation data processed from the USArray.

Nonlinear partial Functional Derivative and Nonlinear LS Seismic Inversion

Taylor expansion of the full nonlinear partial derivative (NLPD) operator is directly related to the full scattering series (Born series) which has a serious convergence problem for strong scattering. The renormalization procedure applied to the Taylor-Frechet series leads to the De wolf approximation of NLPD, which changes the Fredholm type series into a Volterra type series so that renormalized Frechet series has a guaranteed convergence. Numerical simulations demonstrate the different convergence behaviors of the two types of series for NLPD in the case of strong perturbations. Preliminary study on the LS inversion theory using the nonlinear kernel leads to an inversion scheme of simultaneous updating both the model parameters and propagators.

Seismic Interferometry Using Non-Far-Field Sources and Removing the Spurious Arrival

Abstract Seismic interferometry using far-field correlation is a technique to obtain the Green’s function between two receivers using passive wave-field recordings, and often it is under the theoretical assumption that sources are in the far field when in fact they may not be. Using a heterogeneous medium enclosed by a closed boundary on which the sources are fired, we offer two views on the meaning of the far-field correlation. In the intrinsic view, the validity of the far-field correlation is based on the far-field approximation for wave scattering, and it is investigated by comparing various physical dimensions in the heterogeneous interior, regardless of the exterior. However, the extrinsic view centers on the medium properties in the exterior only without considering the interior. Previous studies showed that, with the correct scattering model and complete source coverage, no spurious arrivals should be generated if the illuminating sources are in the far field. We investigate the case of near-field cross correlation. This problem is considered in the context of two-dimensional space with a single embedded scatterer that is represented by a cylindrical inclusion with small radius. An analytical solution for the scattered wave is computed. However, if the sources are not in the far field, the cross-correlation kernel must be used to eliminate the spurious arrival, in addition to the correct scattering model and full source aperture. The kernel accounts for the near-field illumination of the region.

Deep earthquakes in subducting slabs hosted in highly anisotropic rock fabric

Analysis of deep subduction-zone earthquakes, those at depths greater than 60 km, reveals the physical and chemical properties of a descending oceanic lithosphere at mantle depths. Over the past five decades, it has been observed that a large fraction of deep earthquakes has non-double-couple (non-DC) seismic radiation patterns. In contrast, shallow earthquakes tend to have DC radiation patterns due to mechanisms of shear faulting. These observations have been used to argue that deep earthquakes rupture differently from shallow earthquakes. Here we show that the observed global distribution of non-DC deep earthquakes could be caused by shear faulting mechanisms, but in a highly anisotropic laminated rock fabric that surrounds the deep earthquakes within subducted slabs. For intermediate-depth earthquakes (~60–300 km), we found a large shear-wave anisotropy of ~25%, possibly caused by laminated fabric or aligned melt pockets oriented parallel to the slab interface, which provides new supporting evidence for the metamorphic dehydration reactions in slabs. However, at deep-focus depths (>300 km), the putative metastable phase-change mechanism alone cannot explain the seismic anisotropy. Instead, our results and those from recent experiments suggest materials such as magnesite, or perhaps carbonatite melt, may play a role in generating deep-focus earthquakes.Radiation patterns for deep earthquakes could be a result of shear faulting mechanisms—similar to those for shallow earthquakes—but in highly anisotropic rock fabric, suggest seismic analyses.

Efficient Double-Beam Characterization for Fractured Reservoir

DEDICATED - Case Studies in Diffraction Imaging and Interpretation. We propose an efficient target-oriented method to characterize seismic properties of fractured reservoirs: the spacing between fractures and the fracture orientation. Based on the diffraction theory, the scattered wave vector is related to the incident wave vector computed from the source to the target using a background velocity model. Two Gaussian beams, a source beam constructed along the incident direction and a receiver beam along the scattered direction, interfere with each other. We then scan all possible fracture spacings and orientations and output an interference pattern as a function of the spacing and orientation from which the most likely fracture spacing and orientation can be inferred. Our method is adaptive for a variety of seismic acquisition geometries. If seismic sources (or receivers) are spatially sparse, we can shrink the source (or receiver) beam-width to zero and in this case, we achieve point-source-to-beam interference. We validate our algorithm using a synthetic dataset created by a finite difference scheme with the linear-slip boundary condition, which describes the wave-fracture interaction.