Joint viscoacoustic waveform inversion with the separated upgoing and downgoing wavefields in zero-offset vertical seismic profile data

The attenuation of seismic waves propagating in reservoirs can be obtained accurately from the data analysis of vertical seismic profile in terms of the quality-factor Q. The common methods usually use the downgoing wavefields in vertical seismic profile data. However, the downgoing wavefields consist of more than 90% energy of the spectrum of the vertical seismic profile data, making it difficult to estimate the viscoacoustic parameters accurately. Thus, a joint viscoacoustic waveform inversion of velocity and quality-factor is proposed based on the multi-objective functions and analysis of the difference between the results inverted from the separated upgoing and downgoing wavefields. A simple separating step is accomplished by the reflectivity method to obtain the individual wavefields in vertical seismic profile data, and then a joint inversion is carried out to make full use of the information of the individual wavefields and improve the convergence of viscoacoustic full-waveform inversion. The sensitivity analysis of the different wavefields to the velocity and quality-factor shows that the upgoing and downgoing wavefields contribute differently to the viscoacoustic parameters. A numerical example validates our method can improve the accuracy of viscoacoustic parameters compared with the direct inversion using full wavefield and the separate inversion using upgoing or downgoing wavefield. The application on real field data indicates our method can recover a reliable viscoacoustic model, which helps reservoir appraisal.     

IMPROVEMENTS IN THE OBSERVATION OF SHEAR WAVES*

The observation of shear waves is finding more interest in seismic exploration, especially for the determination of additional lithologic parameters, e.g. V^p/V^s. We demonstrate the observation of converted waves in routine seismic work by means of horizontal geophones. Field technique and data processing permit acquisition and interpretation of converted waves in connection with routine seismic measurements. A special interpretation of the recorded converted waves results in the shear wave velocity and the V^p/V^s relation.     

Elastic parameters of rocks from well logging in near surface sediments

Acoustic full waveforms recorded in wells are the simplest way to get the velocity of P, S, and Stoneley waves in situ. Processing and interpretation of acoustic full waveforms in hard formations does not generate problems with identification packets of waves and calculation of their slowness and arrivals, and determination of the elastic parameter of rocks. But in shallow intervals of wells, in soft formations, some difficulties arise with proper evaluation of the S-wave velocity due to the lack of refracted S wave in case when its velocity is lower than the velocity of mud. Dynamic approach to selection of a proper value of semblance to determine the proper slowness and arrival is presented. Correlation between the results obtained from the proposed approach and the theoretical modeling is a measure of the correctness of the method.     

An insightful parametrization for the flatlander's interpretation of time‐lapsed seismic data

An approximation is developed that allows mapped 4D seismic amplitudes and time‐shifts to be related directly to the weighted linear sum of pore pressure and saturation changes. The weights in this relation are identified as key groups of parameters from a petroelastic model and include the reservoir porosity. This dependence on groups of parameters explains the inherent non‐uniqueness of this problem experienced by previous researchers. The proposed relation is of use in 4D seismic data feasibility studies and inversion and interpretation of the 4D seismic response in terms of pore pressure and water saturation changes. A further result is drawn from analysis of data from the North Sea and West Africa, which reveals that the relative interplay between the effects of pore pressure and saturation changes on the seismic data can be simplified to the control of a single, spatially variant parameter C_S/C_P. Combining these results with those from published literature, we find that C_S/C_P = 8 appears to be a generality across a range of clastic reservoirs with a similar mean porosity. Using this C_S/C_P value, an in situ seismic‐scale constraint for the rock stress sensitivity component of the petroelastic model is constructed considering this component carries the largest uncertainty.     

Microseismic Event Detection Kalman Filter: Derivation of the Noise Covariance Matrix and Automated First Break Determination for Accurate Source Location Estimation

Since 1972, Weir-Jones Engineering Consultants (WJEC) has been involved in the development and installation of microseismic monitoring systems for the mining, heavy construction and oil/gas industries. To be of practical value in an industrial environment, microseismic monitoring systems must produce information which is both reliable and timely. The most critical parameters obtained from a microseismic monitoring system are the real-time location and magnitude of the seismic events. Location and magnitude are derived using source location algorithms that typically utilize forward modeling and iterative optimal estimation techniques to determine the location of the global minimum of a predefined cost function in a three-dimensional solution space. Generally, this cost function is defined as the RMS difference between measured seismic time series information and synthetic measurements generated by assuming a velocity structure for the area under investigation (forward modeling). The seismic data typically used in the source location algorithm includes P- and S-wave arrival times, and raypath angles of incidence obtained from P-wave hodogram analysis and P-wave first break identification. In order to obtain accurate and timely source location estimates it is of paramount importance that the extraction of accurate P-wave and S-wave information from the recorded time series be automated—in this way consistent data can be made available with minimal delay. WJEC has invested considerable resources in the development of real-time digital filters to optimize extraction, and this paper outlines some of the enhancements made to existing Kalman Filter designs to facilitate the automation of P-wave first break identification.     

Anisotropic 4D seismic response inferred from ultrasonic laboratory measurements: A direct comparison with the isotropic response

Pore-pressure depletion causes changes in the triaxial stress state. Pore-pressure depletion in a flat reservoir, for example, can be reasonably approximated as uniaxial compaction, in which the horizontal effective stress change is smaller than the vertical effective stress. Furthermore, the stress sensitivity of velocities can be angle-dependent. Therefore, time-lapse changes in reservoir elastic anisotropy are expected as a consequence of production, which can complicate the interpretation of the 4D seismic response. The anisotropic 4D seismic response caused by pore-pressure depletion was investigated using existing core velocity measurements. To make a direct comparison between the anisotropic 4D seismic response and the isotropic response based only on vertical velocities, pseudoisotropic elastic properties were utilized, and the two responses were compared in terms of a dynamic rock physics template. A comparison of the dynamic rock physics templates indicates that time-lapse changes in reservoir elastic anisotropy have a noticeable impact on the interpretation of 4D seismic data. Changes in anisotropy as a result of pore-pressure depletion cause a time-lapse amplitude variation with offset response as if there is a reduction in V_P/V_S (i.e., pseudoisotropic V_P/V_S decreases), although the vertical V_P/V_S increases. The impact of time-lapse changes in anisotropy on the amplitude variation with offset gradient was also investigated, and the time-lapse anisotropy was found to enhance changes in the amplitude variation with offset gradient for a given case.     

Application of Analytical Modeling to the Far-field Investigation of Tsunami and Oceanic Rayleigh Waves from the 1998 Papua New Guinea Earthquake

We analyze far-field Rayleigh and tsunami waves generated by the 1998 Papua New Guinea (PNG) earthquake. Using the normal mode theory and Thomson-Haskell matrix formalism we calculate synthetic mareograms of oceanic surface waves excited by finite-dimensional line source and propagated in a flat, multilayered oceanic structure. Assuming that the source of destructive sea waves was the main shock of the PNG event and based on the expression for seismic wave displacement in the far-field zone, we compute the energy of the seismic and tsunami waves and the E_z /E_ts ratio. The results of our modeling are generally consistent with those obtained empirically for events with magnitude 7. Also, treating the results of a submarine slide as a single solitary wave and using the theoretical arguments of Striem and Miloh (1976) we estimate the energy of the tsunami induced by a landslide. The difference between the energy of the seismic tsunami and of the aseismic one is about one order of magnitude.The results of our theoretical modeling show that surface sea waves in the far-field zone account well for seismic origin, although additional tsunami energy from a landslide source could be required to explain the local massive tsunami in the Sissano Lagoon.     

Correlation Between Local Slip Rate and Local High-frequency Seismic Radiation in an Earthquake Fault

For any earthquake, the slipping fault and the source of high-frequency seismic waves, by and large, coincide. On a more local scale, however, the areas of high seismic slip rate and of increased high-frequency radiation output (seismic luminosity) need not match. To study in some detail how slip rate and seismic luminosity are interrelated, a systematic study is performed that uses 251 records of teleseismic P waves from 23 intermediate-depth earthquakes of magnitude 6.8 and above. From a broadband trace we extract two time histories: (1) displacement and (2) 0.5–2.5 Hz band-passed and squared velocity, or ``HF power', and calculate correlation coefficient, ρ between the two. To reduce the bias related to formation of P coda, a special procedure is applied to data. We estimated the average value ρ = 0.52 (range of event averages 0.35 to 0.65) for the correlation coefficient between the radiated time histories for displacement and ``HF power', which is considerably below the ``ideal' value of unity. We argue that the same or even lower value characterizes the degree of slip rate - seismic luminosity correlation at the fault. Two factors may contribute to the revealed decorrelation: (1) random fluctuations of observed HF power (inevitable for a signal with a limited bandwidth), and (2) the genuine mismatch of slip rate and mean luminosity. We show that these factors, acting separately, would result in the ρ values equal to, correspondingly, 0.72 and 0.80. We also show that genuine decorrelation is statistically significant. We conclude that the observed values of ρ indicate genuine differences between the distributions of the slip rate and the seismic luminosity over the fault area. These results provide important constraints both for the accurate wide-band simulation of strong ground motion and for theoretical dynamic source models.     

Coda waves: A review

The analysis and interpretation of coda waves have received increasing attention since the early seventies. In the past few years interest in this subject has spread worldwide, and the study of high-frequency seismic coda waves has become a very important seismological topic. As a conclusion of the studies accomplished in this time, coda waves are considered the result of scattering processes caused by heterogeneities acting on seismic waves.P andS waves play a particularly important role in this interaction. The process introduces an attenuation which, added to the intrinsic absorption, gives the observed apparent attenuation. Therefore, coda waves constitute a thumbprint left by the heterogeneities on the seismograms. Coda waves offer decisive information about the mechanism of how scattering and attenuation take place. This review describes coda waves in detail, and summarizes the work done in this subject to 1986. The relation between coda waves and attenuation in the context of research on seismic scattering problems is stressed. Particular attention has been given to the application of coda waves to estimate source and medium parameters. The state-of-the-art of the temporal variations of coda wave shape, and the possible use of these variations as an earthquake precursor also are presented. Care has been taken to introduce the statistical models used to deal with the heterogeneities responsible for scattering.     

Simultaneous determination of the source mechanism and the seismic wave energy

Summary It is necessary to know the source mechanism for the determination of the seismic energy of seismic waves from the seismogram recorded at one station. For sparse data (selected events of the 1985/86 Western-Bohemia earthquake swarm) the source mechanisms cannot be determined fromP-wave first motions. Therefore, a new method of determining the source mechanism simultaneously with the energy calculated from observations at two stations has been developed. The method is described and tested. Advantages, disadvantages and the stability of the method are discussed.     

Source parameters of the 2004 Kaliningrad earthquakes

An analysis of source parameters of the two unexpected earthquakes from the Kaliningrad (Russia) area is presented. The earthquakes occurred on 21 September 2004 at 11:05:01 and 13:32:31 UT, respectively. The first event was located at the latitude φ = 54.924°N and the longitude λ = 20.120°E, with a depth h = 16 km, and the second event at φ = 54.876°N, λ = 20.120°E and h = 20 km. Magnitudes Mw of the two events were very similar: 5.1 and 5.2. The magnitude values reported by various international data centers have been meaningfully different. The reason is the presence of high-frequency components in Z velocity component of the S wavefield. They were observed along the direction defined by two stations, BLEU in Sweden and SUW in Poland, located in opposite sides of the source. Along the direction perpendicular to it, the effects are relatively very small. The high-frequency waves are understood to mean components in the 6–8 Hz band for event 1 and 2-4 Hz for event 2. The effects in question are also clearly visible on displacement spectrograms. The magnitude values calculated at such stations from S-wave amplitudes or from seismic spectra are clearly overestimated and are close to 6. Therefore, we made a careful selection of channels in order to determine the spectral parameters and, on this basis, the source parameters. The size of the source is relatively small, of about 2 km. The closest seismic station is at 100 source radii from the source. One can clearly see the effect of the TT zone which markedly reduces the seismic moment value for seismic stations laying on the opposite sides of the source. Both events have very similar spatial distributions of the source parameters: magnitude, seismic moment and radius.     

ComprehensiveanalysesofseismicsourcelayerinXingtaiandTangshanseismicregionsandtheconditionsofmediaab

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Stratigraphic filtering of seismic waves: The influence of mode conversion multiples onP-wave andS-wave phase and attenuation

We demonstrate how multiples, generated at the interfaces of plane parallel beds, modify the propagation characteristics of an originally coherent seismic wave. For waves propagating at an angle to the bedding plane we find that theSV andP-waves couple so that neither is a pure mode. TheSH-wave, while modified in its propagation characteristics by multiples, remains a pure mode. The coupling ofSV-multiples into the quasi-P-mode appears weaker than the coupling ofP-wave multiples into the quasi-SV mode; at least this is so for the two simple cases of (a) density fluctuations only and (b) correlatedV _p andV _s fluctuations which conserve Poisson's ratio.We also find that the coupling is sensitive to both the angle of propagation and frequency. In addition there is a cut-off angle forP-wave multiples influencing the quasi-SV mode. Propagation angles larger than the cut-off permit theP-multiples to modify the phase of the quasi-SV mode, but not its effective attenuation. No such cut-off effect is found for SV-multiples influencing the quasi-P mode, whose angle-dependent and frequency-dependent phase distortion and effective attenuation are influenced both byP-wave multiples andSV-multiples.In view of the mathematical complexity of the expressions describing the phase, and effective attenuation of modes when allowance is made forP-andS-wave multiples, we strongly advocate numerical coding of the major mathematical formulae. By so doing a systematic study can be undertaken of the frequency and offset dependence of seismic waves as a function of seismic source input and power spectral behavior of the fluctuations in density and elastic constants of beds. It is our opinion that the full mathematical expressions are too involved to permit an analytic, systematic investigation to be given of the phase and attenuation of seismic waves with any degree of sophistication or generality.     

Borehole study of compressional and shear attenuation of basalt flows penetrated by the Brugdan and William wells on the Faroes shelf

We investigated the seismic attenuation of compressional (P‐) and converted shear (S‐) waves through stacked basalt flows using short‐offset vertical seismic profile (VSP) recordings from the Brugdan (6104/21–1) and William (6005/13–1A) wells in the Faroe‐Shetland Trough. The seismic quality factors (Q) were evaluated with the classical spectral ratio method and a root‐mean‐square time‐domain amplitude technique. We found the latter method showed more robust results when analysing signals within the basalt sequence. For the Brugdan well we calculated effective Q estimates of 22–26 and 13–17 for P‐ and S‐waves, respectively, and 25–33 for P‐waves in the William well. An effective Q_S/Q_P ratio of 0.50–0.77 was found from a depth interval in the basalt flow sequence where we expect fully saturated rocks. P‐wave quality factor estimates are consistent with results from other VSP experiments in the North Atlantic Margin, while the S‐wave quality factor is one of the first estimates from a stacked basalt formation using VSP data. Synthetic modelling demonstrates that seismic attenuation for P‐ and S‐waves in the stacked basalt flow sequence is mainly caused by one‐dimensional scattering, while intrinsic absorption is small.     

Regional Seismic Wavefield Computation on a 3-D Heterogeneous Earth Model by Means of Coupled Traveling Wave Synthesis

-- I present a new algorithm for calculating seismic wave propagation through a three-dimensional heterogeneous medium using the framework of mode coupling theory originally developed to perform very low frequency (f < ~0.01т.05 Hz) seismic wavefield computation. It is a Greens function approach for multiple scattering within a defined volume and employs a truncated traveling wave basis set using the locked mode approximation. Interactions between incident and scattered wavefields are prescribed by mode coupling theory and account for the coupling among surface waves, body waves, and evanescent waves. The described algorithm is, in principle, applicable to global and regional wave propagation problems, but I focus on higher frequency (typically f S ~0.25 Hz) applications at regional and local distances where the locked mode approximation is best utilized and which involve wavefields strongly shaped by propagation through a highly heterogeneous crust. Synthetic examples are shown for P-SV-wave propagation through a semi-ellipsoidal basin and SH-wave propagation through a fault zone.     

Body-wave Attenuation in the Region of Garda, Italy

We analyzed the spectral amplitude decay with hypocentral distance of P and S waves generated by 76 small magnitude earthquakes (M_L 0.9–3.8) located in the Garda region, Central-Eastern Alps, Italy. These events were recorded by 18 stations with velocity sensors, in a distance range between 8 and 120 km. We calculated nonparametric attenuation functions (NAF) and estimated the quality factor Q of both body waves at 17 different frequencies between 2 and 25 Hz. Assuming a homogeneous model we found that the Q frequency dependence of P and S can be approximated with the functions Q _P = 65 f ^0.9 and Q _S = 160 f ^0.6 , respectively. At 2 Hz the Q _S /Q _P ratio reaches the highest value of 2.8. At higher frequencies Q _S /Q _P varies between 0.7 and 1.7, suggesting that for this frequency band scattering may be an important attenuation mechanism in the region of Garda. To explore the variation of Q in depth, we estimated Q at short (r ≤ 30 km) and intermediate (35–90 km) distance paths. We found that in the shallow crust P waves attenuate more than S (1.3 < Q _S /Q _P < 2.5). Moreover, P waves traveling along paths in the lower crust (depths approximately greater than 30 km) attenuate more than S waves. To quantify the observed variability of Q in depth we considered a three-layer model and inverted the NAF to estimate Q in each layer. We found that in the crust Q increases with depth. However, in the upper mantle (~40–50 km depth) Q decreases and in particular the high frequency Q _S (f > 9 Hz) has values similar to those estimated for the shallow layer of the crust.     

The regional characteristics of seismic activity in China

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Seismoelectric and electroseismic responses to a point source in a marine stratified model

We investigate the seismoelectric/electroseismic wavefields excited by a point source in an air/seawater/three-layered porous medium configuration containing a hydrocarbon layer. The results show that if an explosive source for excitation is used, receivers at seafloor can record the coseismic electromagnetic fields accompanying the P, S, fluid acoustic waves and the interface responses converted from the acoustic waves at seafloor interface and from the seismic waves at the interfaces beneath the seafloor. Employing a vertical electric dipole source shows that, with the exception of the interface responses converted from electromagnetic waves at seafloor, the interface responses converted from transmitted electromagnetic waves at the interfaces beneath the seafloor can also be identified. Given that the strength of the explosive source is within excitation capability of industry air guns, the generated interface responses from the hydrocarbon layer can be detected by current electromagnetic sensors considering the low ambient noise at the seafloor. Our results demonstrate the feasibility of the seismoelectric method applied to marine hydrocarbon exploration. Electroseismic modelling results suggest that it is not practical to employ this method to prospect marine hydrocarbon layer due to the weak interface response signal, unless a much larger current is injected into seafloor.     

Three-dimensional elastic wave scattering and diffraction due to a rigid cylinder embedded in an elastic medium by a point source

The formal solutions of displacement field to the problem of elastic wave scattering and diffraction due to an infinitely long rigid cylinder embedded in an infinite elastic medium by an impulsive point source have been obtained in the integral form. The integrals for the reflected and the diffracted waves both in the shadow zone and in the illuminated zone are evaluated asymptotically for the early time motion by the Reisdue-Cagniard method and the Saddle-point-Cagniard method.Numerical results of the diffractedP, S andPS waves at a fixed circum-distance from the surface of the rigid cylinder show noticeably that (1) the energy partition for the diffractedS wave is small in comparison with that for the diffractedP wave, (2) the wave form of the diffractedS wave is broader and more diffused than that of the diffractedP wave, (3) the direction of the radial motions of the diffractedP andS waves varies as a function of the observational point, and (4) the energy partition for the diffractedP wave is much smaller than that for the direct or the reflectedP waves.This paper has been presented at the 46th Annual International Meeting of Society of Exploration Geophysicists in Houston, Texas, Oct. 28, 1976.