Source-receiver Azimuth Research Articles

SKHASH: A Python Package for Computing Earthquake Focal Mechanisms

Abstract We introduce a Python package for computing focal mechanism solutions. This algorithm, which we refer to as SKHASH, is largely based on the HASH algorithm originally written in Fortran over 20 yr ago. HASH innovated the use of suites of solutions, spanning the expected errors in polarities and takeoff angles, to estimate focal mechanism uncertainty. SKHASH benefits from new features with flexible input formats and allows users to take advantage of recent advances in constraining focal mechanisms for small magnitude or poorly recorded earthquakes. The 3D locations of earthquakes and the velocity models used are varied when finding acceptable solutions. As a result, source–receiver azimuths are reflective of errors from the earthquake locations and velocity models, in addition to the takeoff angles. Users can consider weighted P-wave first-motion polarities derived from traditional or machine-learning picks, cross-correlation consensus, and/or imputation techniques using SKHASH. Focal mechanism solutions can also be further constrained using traditional, machine learning, and/or cross-correlation consensus S/P amplitude ratios. With improved reporting of individual and collective P polarity and S/P amplitude misfits, users can better evaluate the success of the solutions and the quality of the measurements. The reporting also makes it easier to identify potential issues with metadata, including incorrectly reported station polarity reversals. In addition, by leveraging vectorized operations, taking advantage of an efficient backend Python C Application Programming Interface, and the use of a parallel environment, the Python SKHASH routine may compute mechanisms quicker than the HASH routine.

Comparison of Single-Well Microseismic Focal Mechanism Inversions with Different Source Models

ABSTRACT Through downhole monitoring, the focal mechanisms of microearthquakes can be quantitatively determined, thus providing valuable information for characterizing the fracturing process and the in situ stress status. The double-couple (DC) and moment tensor (MT) source models are commonly used to study microearthquakes. However, the DC model fails to include non-DC mechanisms, and MT inversion from single-well data is still challenging. One possible way to address this is using the shear–tensile general dislocation (GD) source model. We provide a detailed comparison of the DC, GD, and MT models, and introduce the differences in their modeling and inversion theories. These three models are described by four, five, and six parameters, and correspond to a single point, a straight line, and the entire space in the Hudson source-type plots, respectively. Both the DC and GD models yield nonlinear inversions, whereas the MT inversion is linear. Synthetic tests set up from a field single-well monitoring case are performed to study the resolvability of the DC, GD, and MT models in single-well focal mechanism inversions. The results indicate that the inversion error increases from DC→GD→MT for a single-well acquisition system, and the GD and DC inversions are both stable, whereas the MT inversion deviates from the inputs in cases with a perfectly vertical receiver array, 5% model velocity perturbations, 10 m horizontal source location errors, or 40% noise levels. We also find that the focal mechanism inversion mainly depends on the horizontal source–receiver azimuth coverage, and that the nonvertical well direction is helpful for constraining single-well inversions. According to our study, focal mechanism inversions based on the GD model can obtain reliable solutions from near-vertical single-well data, which will help improve non-DC earthquake studies.

Migration of reflector orientation attributes in deep seismic profiles: evidence for decoupling of the Yilgarn Craton lower crust

Abstract. Interpretation of deep seismic data is challenging due to the lack of direct geological constraints from drilling and the more limited amount of data available from 2-D profiles in comparison to hydrocarbon exploration surveys. Thus other constraints that can be derived from the seismic data themselves can be of great value. Though the origin of most deep seismic reflections remains ambiguous, an association between seismic reflections and crustal strain, e.g. shear zones, underlies many interpretations. Estimates of the 3-D orientation of reflectors may help associate specific reflections, or regions of the crust, with geological structures mapped at the surface whose orientation and tectonic history are known. In the case of crooked 2-D onshore seismic lines, the orientation of reflections can be estimated when the range of azimuths in a common midpoint gather is greater than approximately 20∘, but integration of these local orientation attributes into an interpretation of migrated seismic data requires that they also be migrated. Here we present a simple approach to the 2-D migration of these orientation attributes that utilizes the apparent dip in reflections on the unmigrated stack and maps reflector strike, for example, to a short linear segment depending on its original position and a migration velocity. This interpretation approach has been applied to a seismic line shot across the Younami Terrane of the Australian Yilgarn Craton and indicates that the lower crust behaved differently from the overlying middle crust as the newly assembled crust collapsed during the Late Archean. Some structures related to approximately east-directed shortening are preserved in the middle crust, but the lower crust is characterized by reflectors that suggest N-NNE-oriented ductile flow. Deployment of off-line receivers during seismic acquisition allows the recording of a larger range of source-receiver azimuths and should produce more reliable future estimates of these reflector attributes.

A probabilistic model for ghost delay time estimation based on recording geometry

ABSTRACTIn order to deconvolve the ghost response from marine seismic data, an estimate of the ghost operator is required. Typically, this estimate is made using a model of in‐plane propagation, i.e., the ray path at the receiver falls in the vertical plane defined by the source and receiver locations. Unfortunately, this model breaks down when the source is in a crossline position relative to the receiver spread. In this situation, in‐plane signals can only exist in a small region of the signal cone.In this paper, we use Bayes' theory to model the posterior probability distribution functions for the vertical component of the ray vector given the known source–receiver azimuth and the measured inline component of the ray vector. This provides a model for the ghost delay time based on the acquisition geometry and the dip of the wave in the plane of the streamer. The model is fairly robust with regard to the prior assumptions and controlled by a single parameter that is related to the likelihood of in‐plane propagation.The expected values of the resulting distributions are consistent with the deterministic in‐plane model when in‐plane likelihood is high but valid everywhere in the signal cone. Relaxing the in‐plane likelihood to a reasonable degree radically simplifies the shape of the expected‐value surface, lending itself for use in deghosting algorithms. The model can also be extended to other plane‐wave processing problems such as interpolation.

Stress-induced seismic azimuthal anisotropy, sand-shale content, and depth trends offshore North West Australia

Seismic azimuthal anisotropy is apparent when P-wave velocities vary with source-receiver azimuth and downward-propagating S-waves split into two quasi-S-waves, polarized in orthogonal directions. Not accounting for these effects can degrade seismic image quality and result in erroneous amplitude analysis and geologic interpretations. There are currently no physical models available to describe how azimuthal anisotropy induced by differential horizontal stress varies with sand-shale lithology and depth; we develop a model that does so, in unconsolidated sand-shale sequences offshore North West Australia. Our method naturally introduces two new concepts: “critical anisotropy” and “anisotropic depth limit.” Critical anisotropy is the maximum amount of azimuthal anisotropy expected to be observed at the shallowest sediment burial depth, where the confining pressure and sediment compaction are minimal. The anisotropic depth limit is the maximum depth where the stress-induced azimuthal anisotropy is expected to be observable, where the increasing effects of confining pressure, compaction, and cementation make the sediments insensitive to differential horizontal stress. We test our model on borehole log data acquired in the Stybarrow Field, offshore North West Australia, where significant differential horizontal stress and azimuthal anisotropy are present. We determine our model parameters by performing regressions using dipole shear log velocities, gamma-ray shale volume logs, and depth trend data. We perform a blind test using the model parameters derived from one well to accurately predict the azimuthal anisotropy values at two other wells in an adjacent area. We use our anisotropy predictions to improve the well-tie match of the modeled angle-dependent reflectivity amplitudes to the 3D seismic amplitude variation with offset data observed at the well locations. Future applications of our method may allow the possibility to estimate the sand-shale content over a wide exploration area using anisotropic parameters derived from surface 3D seismic data.

Continuous estimation of 3-D reflector orientations along 2-D deep seismic reflection profiles

Interpretation of 2-D deep seismic reflection data can be limited by the recording of out-of-plane reflections that cannot be readily distinguished from those originating beneath a seismic line. Here I present a method analogous to semblance velocity analysis that utilizes varying source-receiver azimuths to derive continuous estimates of 3-D reflector orientations along onshore 2-D reflection profiles. For each zero-offset time within a common depth point supergather, the semblance is calculated along 3-D travel time curves, and the dip and strike of the most coherent reflection is determined. Relative errors in these angles are derived from the range of travel time curves that have semblance values greater than a specified fraction, for example 90%, of the maximum. The method is illustrated using a section from line 10GA-YU1 from the Youanmi terrane of the Yilgarn craton in Australia in which the original field data have been replaced with synthetic in-line and cross-line reflections. Reflector orientations are generally well recovered where the range of available source-receiver azimuths is greater than 20o, but the method fails at lower ranges where the seismic line is almost linear, and this behavior is also observed in analysis of the field data. Nevertheless when using a realistic 1-D velocity function the orientation of upper crustal shear zones can be readily determined, and on unmigrated sections subhorizontal sills can be distinguished on the basis of their geometry from the mid-crustal reflectivity. In future surveys, reflector orientations can be determined along the near-linear sections of a seismic profile by deploying additional receivers, perhaps as cross-line recording spreads, to supplement the limited range of azimuths available from the in-line acquisition. The method can in principle be extended to marine reflection surveys, and more complex sub-surface velocity models.

Categorization of seismic sources by auditory display: A blind test

Recordings of the Earth's surface oscillation as a function of time (seismograms) can be sonified by compressing time so that most of the signal's frequency spectrum falls in the audible range. The pattern-recognition capabilities of the human auditory system can then be applied to the auditory analysis of seismic data. In this experiment, we sonify a set of seismograms associated with a magnitude-5.6 Oklahoma earthquake recorded at 17 broadband stations within a radius of ~300km from the epicenter, and a group of volunteers listen to our sonified seismic data set via headphones. Most of the subjects have never heard a sonified seismogram before. Given the lack of studies on this subject, we prefer to make no preliminary hypotheses on the criteria employed by the listeners: we follow the free categorization approach, asking listeners to simply group sounds that they perceive as similar. We find that listeners tend to group together sonified seismograms sharing one or more underlying physical parameters, including source-receiver distance, source-receiver azimuth, and, possibly, crustal structure between source and receiver and/or at the receiver. This suggests that, if trained to do so, human listeners can recognize subtle features in sonified seismic signals. It remains to be determined whether auditory analysis can complement or lead to improvements upon the standard visual and computational approaches in specific tasks of geophysical interest. HighlightsSeismic data is sonified.The resulting sounds are presented to subjects in a listening task.Subjects are sensitive to some geophysical features.

Experimental study of the influence of fluids on seismic azimuthal anisotropy

Abstract Seismic characterization of subsurface fractures has important applications and implications to reservoir characterization. Recent studies have shown that characterization of azimuthal anisotropy can help delineate orientation and intensity of fractures, as well as indicate the fluid content of their embedded cracks. To explore the influence of fluids on seismic response in a transversely isotropic medium, an experimental study using vertically aligned and preconditioned polycarbonate material embedded in isotropic resin was conducted. Part of the theoretical motivation for this experimental study was the Hudson and Thomsen theories of the elastic response of penny-shaped cracks. Our composite model was designed to simulate a single set of aligned vertical cracks (HTI symmetry) filled with fluids. In a series of ultrasonic transmission and reflection experiments, the model was initially filled with air (a natural gas proxy) and then liquids (distilled water and glycerin as brine and oil proxies, respectively) were gradually injected into the composite material to simulate different rates of fluid saturation. Porosity in our assembled cracked media was about 2.5% and crack density was estimated to be 3.5%. Our results show changes in ultrasonic compressional and shear-wave velocities in alternate directions as a function of different saturating fluids. We also detected changes in delay between fast and slow split shear-waves with different saturating fluids. The NMO velocity measured from the ultrasonic reflection response, showed not only changes in velocity values on saturation, but also a difference in the trend of NMO velocities as a function of source–receiver azimuth. Anisotropic parameters also varied with different levels of saturation. Our experiments indicate that the anisotropic parameter e is reduced by 30% on full saturation with water (brine proxy) and 50% with glycerin (oil proxy). The anisotropic parameter γ increased by 50% from a gas-to-brine saturated medium and 60% from a gas-to-oil saturated medium. We conclude that the most significant changes in anisotropic and stiffness properties occur when gas is substituted for distilled water or glycerin. These changes are much smaller when brine is substituted for oil or vice versa .

Assessing the scalar moment of moderate earthquake and the effect of lateral heterogeneity on normal modes—An example from the 2013/04/20 Lushan earthquake, Sichuan, China

Medium-frequency normal modes in the frequency range of 2.0–6.0mHz excited by moderate earthquakes (6.0<Mw<7.0) are weak seismic signals and seldom concerned in academic study. We show that the validity of predicted M0 (scalar seismic moment) for a complex moderate earthquake can be effectively assessed by a systematic comparison of observed and synthetic medium-frequency spheroidal modes, and the effect of lateral heterogeneity on normal-mode amplitudes can also be well assessed in the comparison. For a complex moderate earthquake, the differences between predicted M0 derived from different inversion methods are significant, in some cases as large as factors of 1.56–3.18. In this study we focus on the Lushan earthquake, a moderate thrust event on 20 April 2013 in the Western Sichuan, China. Five reported M0 for the earthquake differ significantly from 0.4×1019 to 1.06×1019Nm, up to about 2.5 times difference. To assess the validity of reported M0, we compare observed with synthetic modes corresponding to five centroid moment tensor solutions at 17 stations, which located within epicental distances of 5–30° and distributed in a wide range of source-receiver azimuths. Synthetic modes corresponding to moment tensor solutions derived from long-period waveforms show good agreement to observations. However, synthetics corresponding to moment tensor solutions derived from body waves display significant deviations of amplitudes from observations. We show underestimate of M0 is the main cause for such a large deviation. Another important result obtained from the comparison is that lateral heterogeneity has very little effects on the amplitudes of spherical modes at frequencies below 6.0mHz. This observational result is inconsistent with previous theoretical result of lateral structure perturbations to normal modes.

Azimuth-preserved local angle-domain prestack time migration in isotropic, vertical transversely isotropic and azimuthally anisotropic media

Conventional prestack migration does not preserve local directional information of the seismic waves at the image points. New attempts such as sectored migration of azimuth-limited or common-offset-vector data only concern source-receiver azimuth and offset on the surface, which can be poor representation of subsurface wavepath direction. Moreover, they could result in inaccurate imaging because they do not account for the energy propagation between azimuths or offset-vectors. In the past decade, local angle-domain seismic imaging has been highly advocated to avoid migration artifacts and to improve velocity estimation in complex media. Considering prestack time migration (PSTM) is still widely used in seismic imaging and seismic data preconditioning for amplitude variations with offset or incident-angle (AVO/AVA) analysis, fracture detection, and reservoir characterization, we present an azimuth-preserved local angle-domain Kirchhoff PSTM approach for such purposes. We apply a seismic imaging condition in 3D local angle domain and use extended superposition of impulse responses retaining subsurface angular attributes, which are evaluated through the incident and scattering phase slowness vectors using classical-diffraction moveout equations in isotropic, vertical transversely isotropic (VTI) and azimuthally anisotropic media. Two-dimensional synthetic examples demonstrate what the migrated results look like in local angle domain. A wide-azimuth synthetic example with horizontal transversely isotropy (HTI) proves the necessity of azimuthal migration for reliable imaging and azimuthal analysis when azimuthal anisotropy exists in the overburden. Real data examples show the advantages of imaging in subsurface angle domain for properly focusing and revealing azimuth- and angle-dependent variations of residual moveout and migrated amplitudes.

Introduction to this special section: Practical applications of anisotropy

The use of seismic anisotropy is a topic that has evolved dramatically in the last 25 years in the oil and gas industry. Even though physicists who study waves and vibrations in solids have taught us that elastic properties of rocks should be described by a complex set of functions and parameters, many years of seismic data processing were conducted assuming that the velocities in the subsurface rocks were isotropic, and that the shear modulus was zero (that the rocks could be treated as “a liquid”). “Isotropic” means that the value measured (e.g., velocity) is the same in all directions (whether you consider angles of incidence or source-receiver azimuths) for a rock volume of interest.

3D Kirchhoff prestack time migration in average illumination-azimuth and incident-angle domain for isotropic and vertical transversely isotropic media

Conventional offset domain prestack migration tends to bring ambiguity and migration artifacts because it smears energy from different angles at the image point. To avoid this, prestack depth migration implementations in angle domain have been investigated in the past decades. As an efficient imaging tool, angle domain Kirchhoff prestack time migration is still useful and was proposed recently. However, existing algorithms cannot handle ray bending and anisotropy correctly. Practically, azimuth analysis for fractured reservoirs should be carried out after migration for most geological settings. Unfortunately, the existing migration algorithm implicitly involves some kind of binning to source-receiver azimuth, which may not be the real wave-pathazimuth, especially for side-scattering or out-of-plane waves. In this paper, we present an algorithm for 3D Kirchhoff prestack time migration in average illumination azimuth and incident angle domain, which matches true wave path naturally and more accurately. To handle ray bending and vertical transversely isotropy, we propose several approaches to estimate two-way traveltime and the corresponding angular attributes through extended offset-to-angle mapping. Based upon these approaches, our 3D prestack time migration can provide high-quality common-image gathers for amplitude variation with incident angle and/or amplitude variation with offset and azimuth analyses, even in media with slight to moderate lateral heterogeneity. The 2D and 3D synthetic examples prove the validity of our methods.

Multi-azimuth processing and its applications to wide-azimuth OBC seismic data offshore Abu Dhabi

Wide-azimuth ocean bottom cable (OBC) seismic data have several advantages for imaging, such as high fold, long offsets, and a wide range of source-receiver azimuths. However, conventional wide-azimuth processing has some drawbacks because the full range of advantages is not exploited. In conventional wide-azimuth processing, azimuthal variations are usually ignored, whereas multi-azimuth processing treats each source-receiver azimuth individually. We performed a pilot multi-azimuth processing trial on wide-azimuth OBC seismic data offshore Abu Dhabi, United Arab Emirates to evaluate its benefits compared to conventional wide-azimuth processing, and discuss its applications for fault imaging and fracture characterization. We show that: (a) multi-azimuth processing achieves significantly higher signal-to-noise ratio, and effectively corrects the distortions in the subsurface image resulting from azimuthal variations; (b) mono-azimuth processing enhances imaging of existing subtle faults; and (c) azimuthal variations extracted from mono-azimuth processed data provide indications about fracture orientation, relative fracture intensity, and their spatial distributions. The results should encourage us to apply multi-azimuth processing to wide-azimuth OBC seismic data to improve focusing quality, image subtle faults, and gain insights into fracture characteristics.

Rich azimuth marine seismic, a cost effective approach to better subsalt images

There are many areas of complex velocity structure, such as subsalt areas in the Gulf of Mexico, where improvements in depth imaging and noise removal have given better images. However, with several subsalt discoveries, we found some areas where these images are inadequate for cost effective appraisal and development. There have been many cases (some published, for example, O’Connell et al., 1993) where a new seismic survey in a different orientation improves the image in some areas of complex structure, while the image in other areas is better on the original data. These examples suggested that source-receiver azimuth was an important part of the equation. In the spring of 2006, we acquired a rich azimuth survey over our Shenzi discovery (centered on Green Canyon block 653) that took substantially less effort (cost) than we originally imagined. We have presented results at both EAGE and SEG meetings (Howard et al., 2006). This paper documents for a larger audience the studies that led to the decision to conduct the survey and some of those results.

Prestack and poststack migration of crooked-line seismic reflection data: A case study from the South Portuguese Zone fold belt, southwestern Iberia

Crooked-line 2D seismic reflection survey geometries violate underlying assumptions of 2D imaging routines, affecting our ability to resolve the subsurface reliably. We compare three crooked-line imaging schemes involving prestack and poststack time migration using the 2D IBERSEIS deep seismic reflection profile running over the South Portuguese Zone thrust-and-fold belt to obtain crisp high-resolution images of the shallow crust. The crust is characterized by a complex subsurface geometry with conflicting dips of up to [Formula: see text]. In summary, the three schemes are (1) normal-moveout (NMO) corrections, dip-moveout (DMO) corrections, common-midpoint (CMP) stacking, CMP projection, and poststack time migration; (2) NMO corrections, DMO corrections, CMP projection, zero-offset time migration of the common-offset gathers, and CMP stacking; (3) CMP projection, prestack time migration in the common-offset domain, and CMP stacking. An essential element of all three schemes is a CMP projection routine, projecting the CMPs first binned along individual segments for preprocessing onto one straight line, which is parallel to the general dip direction of the subsurface structures. After CMP projection, the data satisfy the straight-line assumption of 2D imaging routines more closely. We observe that the prestack time-migration scheme yields comparable or more coherent synthetic and field-data images than the other two DMO-based schemes along the parts of the profile where the acquisition overall follows a straight line. However, the schemes involving DMO corrections are less plagued by migration artifacts than the prestack time-migration scheme along profile parts where the acquisition line is crooked. In particular, prominent migration artifacts on the prestack migrated synthetic data can be related to significant variations in source-receiver azimuths for which 2D prestack migration cannot account. Thus, the processing scheme including DMO corrections, CMP projection, and zero-offset migration of common-offset gathers offers a reliable and effective alternative to prestack migration for crooked-line 2D seismic reflection processing.

Polarization rotation upon reflection of direct shear waves in purely isotropic media

Summary We show that the polarizations of reflected shear waves from a fixed polarization source vary quite dramatically with offset and source-receiver azimuth in a purely isotropic medium. We also demonstrate that a critical factor in the polarization of these waves is the zero crossing on the incident angle axis of the SV-SV and SH-SH shear wave reflection response, as found by analysis of the full Zoeppritz equations. The zero crossings for SV-SV and SH-SH reflections are controlled primarily by the contrast in shear velocity and density. We numerically modeled the Zoeppritz equations for seismic reflectivity and show a remarkably wide range of variation in the polarity of the reflected shear wave for a single source polarization. We formulated a two term correction to account for these variations, and the resulting corrected polarization show a significant improvement over the original observations at angles of incidence used in normal 3D surveys.

Efficient 3D wave-equation migration using virtual planar sources

Full-volume seismic imaging is essential for a sound interpretation of structurally complex geologies. Prestack depth imaging is the most appropriate tool for such imaging, but it requires a precise and often complex velocity model. In such situations, 3D Kirchhoff prestack depth migration can be quite expensive. On the other hand, a wavefield approach, although generally tremendously expensive, is not affected by the complexity of the velocity model. We propose an affordable 3-D wavefield prestack depth-migration technique. It is designed for marine surveys for which the source-receiver azimuth is approximately constant. The technique applies a plane-wave migration algorithm to time-shifted data — quite a surprising approach when we realize that marine surveys do not allow the synthesis of genuine plane-wave data. Additionally, the imaging principle has to be modified to give results consistent with shot-record migration. Our technique also produces image gathers that allow an update of the velocity model by means of migration velocity analysis. Results from synthetics and conventional marine data demonstrate the effectiveness of the method.

A strategy for optimal marine 4D acquisition

Repeating source-receiver azimuths can be an important aspect of 4D acquisition. Seismic repeatability will decrease with an increase of source-receiver azimuth differences between base and monitor surveys. This paper discusses a marine acquisition strategy with respect to the optimal preservation of source-receiver azimuths in the presence of feathering. We show that repeating shot positions is favorable for azimuth preservation in 4D acquisition in combination with overlap configurations (additional outer streamers). With a dense streamer separation, source-receiver azimuths can be repeated very accurately by using this strategy. In a base survey, overlap configurations allow the vessel to follow the survey?s pre-plot sail lines with significantly reduced crossline deviations. A well-conditioned base survey simplifies and optimizes the repetition of vessel/source positions in a future monitor survey.

3D description and inversion of reflection moveout of PS-waves in anisotropic media

Common-midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t2(x2) conventionally used for pure modes. Here, we present concise parametric expressions for both common-midpoint (CMP) and common-conversion-point (CCP) gathers of PS-waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi-azimuth) CMP gathers without time-consuming two-point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P-wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P- and S-waves (VP0 and VS0) and the Thomsen parameters e and δ can be found from surface data alone by combining P-wave moveout with the traveltimes of the converted PS(PSV)-wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P- and PS-waves from both a horizontal and a dipping interface. At the first stage of the velocity-analysis procedure, we build an initial anisotropic model by applying a layer-stripping algorithm to CMP moveout of P- and PS-waves. To overcome the distorting influence of conversion-point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (VP0, VS0, e and δ) using reflections from a single mildly dipping interface. In this case, the P-wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS-wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P-waves, as well as processing (e.g. transformation to zero offset) of converted waves.

Influence of Data Irregularities on 3d Common Offset Migration

In 3D seismics offset is a vector characterized by the source-receiver distance and azimuth. Due to irregularities in the acquisition (for instance streamer feathering in marine acquisition) common offset data are not available and, in turn, 3D common offset migration does not make sense any longer. We then introduce the concept of migration by offset class: it is a straightforward extension of common offset migration in which we migrate all traces that belong to a given offset class, namely all traces with offset close to a given one. The result of such a migration depends of course on how the offset class is constructed or, in other words, on what is meant with close . The aim of this paper is to investigate by means of a 3D numerical study how to design offset classes so as to obtain migrated images that can be interpreted without trouble (such an interpretation is a key element for a successful migration velocity analysis). We have to find a trade-off between two extremes:- a too loose offset class that would mix heterogeneous offsets (in particular mixing substantially different azimuths can be dangerous); - a too narrow offset class that would result in sparse seismic traces with, in turn, an inadequate coverage of the reflector. The regularity, within an offset class, of the offset variation as well as the one of the distribution of midpoints are parameters that can have a drastic influence on the quality of the migrated image. It is shown that migration by offset class appears as a robust procedure all the more than the offset varies slowly with the midpoint coordinate within an offset class. Besides, the smaller the mean offset norm, the lower is the contamination of the image due to the mixing of azimuths within an offset class.