Down-going Wavefield Research Articles

Fast least-squares imaging with surface-related multiples: Application to a North Sea data set

In marine seismic acquisition, surface-related multiples constitute a significant portion of the acquired data. Typically, multiples are removed during early-stage data processing because they can lead to phantom reflectors during migration that might result in erroneous geologic interpretations. However, if properly dealt with, multiples can provide valuable extra information and can complement primaries in illuminating the subsurface. Reverse time migration has limitations in imaging multiples. A computationally efficient inversion procedure is proposed which jointly maps primaries and multiples to the true reflectors and estimates the source function on the fly. As a result, high-quality, mostly artifact-free broad-band images are obtained in which the imprint of the source function is partly removed at a computationally affordable expense compared with the combined costs of wave-equation-based surface-related multiple elimination and reverse time migration. All this is achieved by including the total downgoing wavefields as areal sources in least-squares migration in combination with curvelet-domain sparsity promotion. The proposed method is applied to a shallow-water marine data set from the North Sea which contains abundant short-period surface-related multiples, and the efficacy of the method is shown in eliminating coherent imaging artifacts associated with multiples. The benefits of joint imaging of primaries and multiples are demonstrated compared with imaging these signal components separately.

Ocean-bottom cable data multiple suppression based on equipoise pseudo-multichannel matching filter

The effect of strong reflection interfaces, such as free surface, seabed, is strong; thus, the coupling of multiples and waves reduces the quality of ocean-bottom cable seismic data. Using the different polarity response of hydrophones and geophones to downgoing wave fields, dual-sensor summation can eliminate receiver-side multiples, enhance primaries, and improve the resolution of seismic data. We present a dual-sensor summation method based on the equipoise pseudo-multichannel adaptive matching filter. Compared with traditional methods, the proposed method is totally data driven and does not depend on the reflection coefficient; moreover, good results are obtained using synthetic and real data.

Autofocus Imaging: Image reconstruction based on inverse scattering theory

Conventional imaging algorithms assume single scattering and therefore cannot image multiply scattered waves correctly. The multiply scattered events in the data are imaged at incorrect locations resulting in spurious subsurface structures and erroneous interpretation. This drawback of current migration/imaging algorithms is especially problematic for regions where illumination is poor (e.g., subsalt), in which the spurious events can mask true structure. Here we discuss an imaging technique that not only images primaries but also internal multiples accurately. Using only surface-reflection data and direct-arrivals, we generate the up- and down-going wavefields at every image point in the subsurface. An imaging condition is applied to these up- and down-going wavefields directly to generate the image. Because the above algorithm is based on inverse-scattering theory, the reconstructed wavefields are accurate and contain multiply scattered energy in addition to the primary event. As corroborated by our synthetic examples, imaging of these multiply scattered energy helps eliminate spurious reflectors in the image. Other advantages of this imaging algorithm over existing imaging algorithms include more accurate amplitudes, target-oriented imaging, and a highly parallelizable algorithm.

A Fiber Optic Borehole Seismic Vector Sensor System for High Resolution CCUS Site Characterization and Monitoring

Abstract Seismic techniques are the dominant geophysical techniques for the characterization of subsurface structures and stratigraphy. The seismic techniques also dominate the monitoring and mapping of reservoir injection and production processes. Borehole seismology, of all the seismic techniques, despite its current shortcomings, has been shown to provide the highest resolution characterization and most precise monitoring results because it generates higher signal to noise ratio and higher frequency data than surface seismic techniques. The operational environments for borehole seismic instruments are however much more demanding than for surface seismic instruments making both the instruments and the installation much more expensive. To address the critical site characterization and monitoring needs for CCUS programs, US Department of Energy (DOE) funded Paulsson, Inc. in 2010 to develop a fiber optic based ultra-large bandwidth clamped borehole seismic vector array capable of deploying up to one thousand 3C sensor pods suitable for deployment into high temperature and high pressure boreholes. Tests of the fiber optic seismic vector sensors developed on the DOE funding have shown that the new borehole seismic sensor technology is capable of generating outstanding high vector fidelity data with extremely large bandwidth: 0.01 – 6,000 Hz. Field tests have shown that the system can record events at magnitudes much smaller than M-2.6 at frequencies up to 2,000 Hz. The sensors have also proved to be about 100 times more sensitive than the regular coil geophones that are used in borehole seismic systems today. The fiber optic seismic sensors have furthermore been qualified to operate at temperatures over 300 °C (572 °F). Simultaneously with the fiber optic based seismic 3C vector sensors we are using the lead-in fiber to acquire Distributed Acoustic Sensor (DAS) data from the surface to the bottom the vector array. While the DAS data is of much lower quality than the vector sensor data it provides a 1 m spatial sampling of the downgoing wavefield which will be used to build the high resolution velocity model which is an essential component in high resolution imaging and monitoring.

Shot-profile true amplitude crosscorrelation imaging condition

The U/D imaging condition for shot profile migration can be used to estimate the angle dependent reflection coefficient, but is difficult to implement numerically because of the spectral division involved. Most techniques for stabilizing the division require a damping factor which might be difficult to estimate and which also introduces bias into the final result. A stable result can be achieved by approximating the imaging condition with a crosscorrelation of the up- and downgoing wavefields at zero time lag, but this will lead to incorrect amplitude-versus-angle (AVA) behavior of the estimated reflection coefficient. We use a simple model for wave propagation of primary reflections in the wavenumber frequency domain and invert the model with respect to the reflection coefficient. By using the properties of wavefield extrapolators it can then be shown that the reflection coefficients can be estimated by crosscorrelation of the upgoing wavefield and a downgoing wavefield where the initial wavefield is the inverse of the wavefield generated by a point source. The new imaging condition gives the correct AVA behavior for horizontal reflectors. For dipping reflectors it is shown that a postmigration correction factor can be used to recover the correct angle behavior of the reflection coefficient. The new imaging condition is numerically stable, does not involve damping factors, is simple to implement numerically, and is a simple modification of the classical crosscorrelation imaging condition. Numerical examples confirm the correct AVA behavior of the new imaging condition.

Imaging 3D Sea Surfaces from 3D Dual-Sensor Towed Streamer Data

3D realistic sea surface imaging from 3D dual-sensor towed streamer data is presented. The technique is based on separating data acquired by collocated dual-sensors into up-going and down-going wavefields. Subsequently, these wavefields are extrapolated upwards in order to image the sea surface. This approach has previously been demonstrated using 2D data examples. Here, the focus is on 3D data. Controlled 3D data based on the Kirchhoff-Helmholtz algorithm is generated, and the 3D sea surface imaging technique is applied. For coarsely spaced streamers from 3D field data, the technique is applied streamerwise (i.e., 2D wavefield separation, extrapolation, and imaging). In the latter case, the resulting sea surface profiles corresponding to each time frame are interpolated to demonstrate that the main sea surface characteristics are preserved, and artefacts due to 2D processing of 3D data are mainly limited to areas corresponding to large angles of incidence. Time-varying sea surfaces from two different 3D field data are imaged. The data examples were acquired under different weather conditions. The imaged sea surfaces show realistic wave heights, and their spectra suggest plausible speeds and directions.

Deconvolution-type imaging condition effects on shot-profile migration amplitudes

Amplitude preservation in Pre-Stack Depth Migration (PSDM) processes that use wavefield extrapolation must be ensured – first, in the operators used to continue the wavefield in time or depth, and second, in the imaging condition used to estimate the reflectivity function. In the later point, the conventional correlation-type imaging condition must be replaced by a deconvolution-type imaging condition. Migration performed in common-shot profile domain obtains the final migrated image as the superposition of images resulting of migrate each shot separately. The amplitude obtained in a point of the migrated image corresponds to the sum of the reflectivities for each shot which has illuminated such point, along the angles determined by the velocity model and the positions of the source and the receiver. The deeper the reflector, the lower the amplitude of the illumination field will be. As result, the correlation-type imaging condition produces images with an unbalanced amplitude decrease with depth. A deconvolution-type imaging condition scales the amplitudes through a correlation, using the weighting function dependent on the spectral density or the illumination of the downgoing wave field. In this article, two possible scaling functions have been used in the case of a single shot. In the case of data with multiple shots, five scaling possibilities are presented with the spectral density or the illumination function. The results of applying these imaging conditions to synthetic data with multiple shots show that the values of the amplitude in the migrated images are influenced by the coverage of the common midpoint, compensating this effect only in one of the imaging conditions described. Numerical experiments with synthetic data generated using Seismic Unix and the Sigsbee2a data are presented, highlighting that in velocity fields with strong vertical and lateral velocity variations, the balance of the amplitudes of the deep reflectors relative to the shallow reflectors is strongly influenced by the imaging condition applied.

Attenuation of free-surface multiples by up/down deconvolution for marine towed-streamer data

Free-surface-related multiples in marine seismic data are commonly attenuated using adaptive subtraction of the predicted multiple energy. An alternative method, based on deconvolution of the upgoing wavefield by the downgoing wavefield, was previously applied to ocean-bottom data. We apply the deconvolution method to towed-streamer data acquired in an over/under configuration. We also use direct arrival deconvolution that results in source wavelet designature only, as a benchmark to verify the full multiple deconvolution result. Detailed synthetic data analysis, including sensitivity tests, explains each data processing step and its effects on the final result. We then apply this verified preprocessing sequence to field data from the Kristin area of the North Sea, with a focus on the direct arrival prediction using the near-field hydrophone method. Prestack evaluation of the results shows that the method applied to the field data provides designature, source-side deghosting, and attenuation of multiples. We show comparable stacked results from our method and from 2D iterative surface-related multiple elimination. The workflow has the benefit that it does not require an adaptive subtraction step or iterative application. However, an accurate direct arrival prediction is essential for the successful application of the method. This prediction is obtained using near-field hydrophone measurements that can be recorded with some commercial acquisition systems.

Deconvolution imaging conditions and cross-talk suppression

Deconvolution imaging conditions offer improved resolution over standard, crosscorrelation-based imaging conditions. Additionally, these imaging conditions produce a result more directly related to a reflection coefficient than do crosscorrelation-based imaging conditions. In simple analytical cases, deconvolution imaging conditions also offer the possibility of eliminating crosstalk (i.e., energy in the image due to reflected energy arriving at a location at the same time as incident energy that did not cause the reflected energy) when the full up- and down-going wavefields are used. This means that in such cases, surface-related multiples can be eliminated from the image, or that multiple shots could potentially be fired simultaneously without degrading the image. However, this cross-talk-suppression property is not observed in most situations. We show that this is due to a number of issues: the correct order of deconvolution must be used, stabilization causes imperfect deconvolution, finite apertures lead to some of the signal being lost, and an assumption of horizontal stratification is often not being met. Further, imperfect knowledge of the incident and reflected field due to such factors as anisotropy, poorly estimated velocity fields, and measurement noise can also lead to imperfect deconvolution. Thus, deconvolution imaging conditions should not be counted on to completely eliminate crosstalk from images.

Imaging the sea surface using a dual-sensor towed streamer

Sea-surface profile and reflection coefficient estimates are vital input parameters to various seismic data processing applications. The common assumption of a flat sea surface when processing seismic data can lead to misinterpretations and mislocations of events. A new method of imaging the sea surface from decomposed wavefields has been developed. Wavefield separation is applied to the data acquired by a towed dual-sensor streamer containing collocated pressure and vertical particle velocity sensors to obtain upgoing and downgoing wavefields of the related sensors. Time-gated upgoing and downgoing wavefields corresponding to a given sensor are then extrapolated to the sea surface where an imaging condition is applied so that the time-invariant shape of the sea surface can be recovered. By sliding the data time-window, the temporal changes of the sea surface can be correspondingly estimated. Ray tracing and finite-difference methods were used to generate different controlled data sets used in this feasibility study to demonstrate the imaging principle and to test the image accuracy. The method was also tested on a first field data example of a marginal weather line from the North Sea.

On data-independent multicomponent interpolators and the use of priors for optimal reconstruction and 3D up/down separation of pressure wavefields

In marine acquisition, the interference between the upgoing and downgoing wavefields introduces a receiver ghost which reduces the effective bandwidth of the seismic wavefield. A two-component streamer provides means for removing the receiver ghost by measuring pressure and vertical particle velocity. However, due to nonuniform and relatively sparse sampling in the crossline direction, the seismic data are usually severely aliased in the crossline direction and the deghosting may not be feasible in a true 3D sense. A true multicomponent streamer measures all components of the particle motion wavefield in addition to the pressure wavefield. This enables solving the 3D deghosting and crossline reconstruction problems simultaneously, without making assumptions on the wavefield or the subsurface. We havedeveloped two data-independent algorithms suited for multicomponent acquisition. The first algorithm reconstructs the total pressure wavefield in the crossline direction by using the pressure and the crossline component of particle motion simultaneously. The second algorithm reconstructs the upgoing pressure wavefield by using the pressure, the crossline, and the vertical components of particle motion simultaneously. Both algorithms are optimal in the minimum-mean-squares-error sense and are ideally suited for a small number of irregularly spaced samples, as is common in towed marine acquisition. We find that by using the spectrum of the wavefield as a priori information, these algorithms have the potential to overcome higher-order aliasing than what is predicted by multichannel sampling theorems. Such a priori information can be extracted from an unaliased portion of the seismic data in novel and robust manners.

A new stabilized least-squares imaging condition

The classical deconvolution imaging condition consists of dividing the upgoing wave field by the downgoing wave field and summing over all frequencies and sources. The least-squares imaging condition consists of summing the cross-correlation of the upgoing and downgoing wave fields over all frequencies and sources, and dividing the result by the total energy of the downgoing wave field. This procedure is more stable than using the classical imaging condition, but it still requires stabilization in zones where the energy of the downgoing wave field is small. To stabilize the least-squares imaging condition, the energy of the downgoing wave field is replaced by its average value computed in a horizontal plane in poorly illuminated regions. Applications to the Marmousi and Sigsbee2A data sets show that the stabilized least-squares imaging condition produces better images than the least-squares and cross-correlation imaging conditions.

A comparison of imaging conditions for wave-equation shot-profile migration

The application of a deconvolution imaging condition in wave-equation shot-profile migration is important to provide illumination compensation and amplitude recovery. Particularly if the aim is to successfully recover a measure of the medium reflectivity, an imaging condition that destroys amplitudes is unacceptable. We study a set of imaging conditions with illumination compensation. The imaging conditions are evaluated by the quality of the output amplitudes and artifacts produced. In numerical experiments using a vertically inhomogeneous velocity model, the best of all imaging conditions we tested is the one that divides the crosscorrelation of upgoing and downgoing wavefields by the autocorrelation of the downgoing wavefield, also known as the illumination map. In an application to Marmousi data, unconditional division by autocorrelation turned out to be unstable. Effective stabilization was achieved by smoothing the illumination map.

Plane wave shot PSDM and controlled illumination techniques

The Pre-Stack Depth Migration (PSDM) method based on wavefield continuation is the most reliable method for imaging complex structure in the subsurface, although there are large computational costs and poorly adaptive geometry. Plane wave shot migration is another method to perform exact wave equation prestack imaging with high computational efficiency and without the migration aperture problem. Moreover, wavefield energy can be compensated at the target zone by controlled illumination. In this paper, plane wave shot PSDM was implemented by the control of the plane down-going wavefield and selection of number and range of the raypaths in order to optimize the imaging effect. In addition, controlled illumination techniques are applied to enhance the imaging precision of interesting areas at different depths. Numerical calculation indicates that plane wave shot imaging is a rapid and efficient method with less computational cost and easy parallel computation compared to the single-square-root operator imaging for common shot gathers and doublesquare-root operator imaging for common midpoint gathers.

Smoothing imaging condition for shot-profile migration

Amplitudes in shot-profile migration can be improved if the imaging condition incorporates a division (deconvolution in the time domain) of the upgoing wavefield by the downgoing wavefield. This division can be enhanced by introducing an optimal Wiener filter which assumes that the noise present in the data has a white spectrum. This assumption requires a damping parameter, related to the signal-to-noise ratio, often chosen by trial and error. In practice, the damping parameter replaces the small values of the spectrum of the downgoing wavefield and avoids division by zero. The migration results can be quite sensitive to the damping parameter, and in most applications, the upgoing and downgoing wavefields are simply multiplied. Alternatively, the division can be made stable by filling the small values of thespectrum with an average of the neighboring points. This averaging is obtained by running a smoothing operator on the spectrum of the downgoing wavefield. This operation called the smoothing imaging condition. Our results show that where the spectrum of the downgoing wavefield is high, the imaging condition with damping and smoothing yields similar results, thus correcting for illumination effects. Where the spectrum is low, the smoothing imaging condition tends to be more robust to the noise level present in the data, thus giving better images than the imaging condition with damping. In addition, our experiments indicate that the parameterization of the smoothing imaging condition, i.e., choice of window size for the smoothing operator, is easy and repeatable from one data set to another, making it a valuable addition to our imaging toolbox.

Multipathing and spectral modulation of the downgoing wavefield in a complex crust: an example from the KTB (Germany) borehole

VSP data collected in the KTB (Germany) borehole to a depth of 8.5 km in 1999 show a surprising spectral modulation of the downgoing wavefield. After filtering the data with the singular value decomposition technique it was found that below about 6.2 km there are two depth intervals where the modulation can be explained in terms of a basic wavelet plus two weighted and delayed copies of that wavelet, with the delay for each wavelet remaining almost constant in each interval. The boundary between the two intervals is at about 7.25 km depth and above and below this depth the delay for the second wavelet is almost the same, while the delay for the third wavelet is significantly different. Neither the modulation nor its depth variation are source related and cannot be explained in terms of multiple reflections in a subhorizontal low-velocity layer. On the other hand, finite difference synthetic data show that subvertical layering (which is prevalent in the borehole area) provides a mechanism that can explain the observations. This mechanism has analogies with the generation of the standard refracted (i.e. head) waves. When a plane wave front propagates perpendicular to the boundaries of a vertical low-velocity layer surrounded by two vertical high-velocity layers, refracted wave fronts are generated in the low-velocity layer, which in turn generate secondary wave fronts in the high-velocity layers. These wave fronts trail the primary wave fronts by a constant delay whose magnitude has a simple dependence on the thickness of the low-velocity layer and the velocities involved. This process creates multipath arrivals that in geological settings with steeply inclined and faulted layers may appear and disappear rather abruptly, which may contribute to a scattered appearance of the wavefield.

Prestack depth migration of primary and surface-related multiple reflections: Part II — Identification and removal of residual multiples

Depth imaging using primary and multiple reflections (DIPMR), as described in Part I of this study, allows subsurface information carried by multiple reflections to be utilized. In the presence of strong lateral heterogeneity, however, the migration results may be distorted by artifacts originating from reflections associated with layers above the imaging plane that are commonly referred to as crosstalk. We present an image enhancement procedure that allows such artifacts to be effectively suppressed by predicting the initial crosstalk in a second migration phase. This second migration uses reflections imaged at shallower depth levels and requires knowledge of the total and primary downgoing wavefield at the receiver level. The predicted crosstalk image it-self may assist the interpretational effort by indicating areas where artifacts may result in incorrect identification of geologic structures or may cause local distortions of amplitude informa-tion. Furthermore, a clean depth image can be obtained by adap-tively subtracting the predicted crosstalk-related noise from the original image. The proposed method is an extension of the DIPMR procedure outlined in Part I of this study. However, it is also applicable to seismic data imaged by using conventional mi gration techniques that are based exclusively on primary reflec-tions. In the latter case, the enhancement procedure allows the ef-fects of imperfect multiple removal during preprocessing to be revealed in the migrated sections. When applied to synthetic data simulated for a complex salt model, the proposed enhancement procedure proved to be valid and effective.

Separation of up-going and down-going wave fields of vertical cable data

The vertical cable method for acquiring and processing pre-stack 3-D marine seismic data is based on the technology developed by the US Navy for antisubmarine warfare. In order to achieve the maximum utilization of vertical cable field data, a new separation method of the up-going and down-going wave fields of the vertical cable data processing was developed in this paper, which is different from the separation of the down-going and up-going wave fields of normal VSP data processing. In tests with synthetic modeling data and actual field data, this newly developed method performs well and is also computationally simpler without pre-assumption conditions.

Asymptotic error analysis of constant‐velocity viscoacoustic migration

The deterioration of prestack migration images caused by an erroneous velocity or dissipation model can be represented by a space‐variant filter. We have derived an approximate expression of this spatial filter for the case of a plane horizontal reflector between two homogeneous half‐spaces, using analytical expressions for the Green’s functions and a stationary phase approximation of the Kirchhoff integral. We have used complex, frequency‐dependent velocities to represent a general homogeneous viscoacoustic medium. Hence, the filter can describe the effects of errors in phase velocity and absorption on the image of the reflector for different situations. A pure phase velocity error deforms the reflector, affects the value of the recovered reflectivity, and creates a spurious amplitude versus offset (AVO) effect. Neglecting dissipation destroys the phase of the image, decreases the resolution, and causes an underestimation of the reflectivity. To have a true‐amplitude, good‐resolution migration with Claerbout’s crosscorrelation imaging principle, the forward extrapolation of the downgoing wavefield should be done with the complex conjugate of the velocity in the viscoacoustic medium, and the backward extrapolation of the upgoing wavefield should be done with the complex velocity. In both cases, this amplifies the wavefields to compensate for the effects of attenuation on wave propagation.

Separation of upgoing and downgoing wavefields using the boundary element method

Summary The boundary element method has been applied for decomposing seafloor measurements into upgoing and downgoing waves. Two complementary solutions in the forms of a linear matrix system and a multiple multipole expansion are obtained without any assumptions about the subsurface. If the elastic parameters below the seafloor are known, these solutions are explicit. They do not require any knowledge of the source signature. Basic components—such as Green’s function computation—can be replaced by alternative acoustic or elastic solutions. Results are useful for deghosting, free-surface multiple attenuation and P/S splitting of ocean-bottom cable data.