PS Waves Research Articles

Research on multi-wave joint elastic modulus inversion based on improved quantum particle swarm optimization

Young's modulus and Poisson's ratio are crucial parameters for reservoir characterization and rock brittleness evaluation. Conventional methods often rely on indirect computation or approximations of the Zoeppritz equations to estimate Young's modulus, which can introduce cumulative errors and reduce the accuracy of inversion results. To address these issues, this paper introduces the analytical solution of the Zoeppritz equation into the inversion process. The equation is re-derived and expressed in terms of Young's modulus, Poisson's ratio, and density. Within the Bayesian framework, we construct an objective function for the joint inversion of PP and PS waves. Traditional gradient-based algorithms often suffer from low precision and the computational complexity. In this study, we address limitations of conventional approaches related to low precision and complicated code by using Circle chaotic mapping, Lévy flights, and Gaussian mutation to optimize the quantum particle swarm optimization (QPSO), named improved quantum particle swarm optimization (IQPSO). The IQPSO demonstrates superior global optimization capabilities. We test the proposed inversion method with both synthetic and field data. The test results demonstrate the proposed method's feasibility and effectiveness, indicating an improvement in inversion accuracy over traditional methods.

Joint PP and PS AVA inversion using an acceleration algorithm and a multi-trace strategy

Abstract Exploration utilizing converted wave (PS) technology has garnered considerable interest in recent years owing to its ability to provide distinct insights into subsurface properties compared to compressional waves (PP). PS wave is particularly advantageous for accurately determining S-wave velocity (${V}_S$) and bulk density ($\rho $), whereas PP wave is better suited for assessing P-wave velocity (${V}_P$). Thus, theoretically, joint PP and PS AVA inversion can yield precise results for ${V}_P$, ${V}_S$, and $\rho $. However, a critical step before joint inversion is PP and PS registration, which is prone to causing lateral discontinuity in the inversion outcomes. To mitigate this issue, we present a simultaneous multi-trace joint inversion method. The method can improve the lateral consistency of inversion results by imposing lateral continuity constraints on the elastic parameters being inverted. Nevertheless, this simultaneous multi-trace inversion method inherently increases computational burden. To enhance algorithmic efficiency without sacrificing inversion precision, we implement an acceleration strategy. Synthetic and real data examples demonstrate that the proposed method offers remarkable performance in enhancing computational efficiency and lateral continuity compared to the conventional methods.

Value of PS Waves for 3D and 4D AVO Inversion

Value of PS Waves for 3D and 4D AVO Inversion

Prediction of tight sandstone reservoirs by multiwave joint prestack inversion technology: A case study of the Qiulin area in the Sichuan Basin

The Shaximiao (SXM) Formation of the Middle Triassic in the central Sichuan Basin is a river-lake sedimentary system with an average burial depth of 2800 m. The channel sand bodies of the SXM Formation in the Qiulin area are developed with large lateral variation and high- and medium-porosity sand. This leads to great differences in the seismic response and difficulty in predicting the sand bodies and reservoirs using P-wave data. We carry out well-log analysis for different types of sand bodies. The no. 8 sand body of high porosity can be effectively identified using P-wave impedance (PI). Whereas for the no. 7 sand body of relatively lower porosity (mainly due to the higher shale content in the no. 7 sand compared with the no. 8 sand), sandstone and mudstone can be distinguished using S-wave impedance (SI), and reservoirs can be recognized by the P- to S-wave velocity ratio ([Formula: see text]/[Formula: see text]). Based on the PP wave and the P-to-S converted wave (PS wave) (after matching) angle-stacked data, a prestack inversion of multicomponent data is performed. Multiwave joint inversion results (SI and [Formula: see text]/[Formula: see text]) have better accuracy and stronger stability than the PP-wave inversion in practical application. In addition, the PI of the joint inversion more clearly describes the distribution and boundaries of the channel sand and better matches the prediction and drilling data in sand 8. The SI of the joint inversion can identify subtle sand bodies (weak PI contrast) that are difficult to be detected by PP-wave inversion. The distribution of the reservoir predicted by the [Formula: see text]/[Formula: see text] of the joint inversion is clearer (the no. 7 sand body) and better than that by the PP-wave inversion. This study demonstrates the advantage of the multiwave joint inversion technology in tight sand identification.

A translithospheric magmatic system revealed beneath Changbaishan volcano

Abstract Changbaishan volcano (CBV), located on the border between China and North Korea, has undergone violent eruptions since the Oligocene, making it one of the most captivating and explosive volcanoes on Earth. However, the lack of precise characterization regarding the magmatic system makes it difficult to decipher its eruption risk and mechanism, despite its significant size and past devastating effects. In this study, we employed newly developed teleseismic receiver function techniques, including Ps and Sp waves, to construct a lithospheric structure model beneath the CBV region. The results show a thick crust (~37 km) and a weak, thin lithosphere under the CBV, with a low-amplitude width of 80 km at the Moho depth and 200 km at the depth of the lithosphere-asthenosphere boundary. These features depict the seismological response of a translithospheric magmatic system beneath the CBV, where hot upwelling material rises through the lithospheric mantle, underplates at the base of the crust, and forms the magma chamber(s) at shallow depth. Such magmatic system features can be taken as a unifying paradigm for large volcanic regions worldwide.

QS‐wave decoupling equation for wavefield separation in transversely isotropic media

AbstractConsidering the anisotropy of the earth media is helpful in reducing the depth error between seismic and drilling and providing reliable imaging data for seismic interpretation and inversion. Transversely isotropic media with a vertical axis of symmetry are the most common type of anisotropic media and have been under constant study. The separation of the P‐ and S‐wavefields, which affects the accuracy of elastic wave imaging and the inversion in transversely isotropic media with a vertical axis of symmetry, is a hot research topic. Among the commonly used wavefield decoupling methods, the S‐wave is typically obtained by subtracting the P‐wave from the total wavefield. However, this kind of wavefield decoupling method often leads to severe P‐wave crosstalk in the separated S‐wavefield; thus, it needs further development. In this paper, the principle that the divergence of the S‐wave is zero is employed to solve the unresolved S‐wave elastic parameters of the S‐wave stiffness matrix by utilizing the modified zero‐order pseudo‐Helmholtz decomposition operator. The obtained S‐wave elastic parameters are employed to construct the qS‐wave stress and facilitate the derivation of the relationship between the qS‐wave particle velocity and the qS‐wave stress. Furthermore, a qS‐wave decoupling first‐order velocity–stress equation, which matches the qP‐wave decoupling first‐order velocity–stress equation, is derived. By jointly using the decoupling equations of qS‐ and qP‐wave, the separation of the P‐ and S‐wavefields in transversely isotropic media with a vertical axis of symmetry is realized. The efficiency of the proposed method is demonstrated via numerical tests conducted to assess the wavefield separation. Moreover, a complex model is employed to perform elastic reverse‐time migration, resulting in the acquisition of accurate imaging results for PP, PS, SP, and SS waves, without the presence of significant artefacts. The correctness of the qS‐wave decoupling equation in transversely isotropic media with a vertical axis of symmetry is confirmed by the comparative tests using decoupling methods in isotropic media.

Imaging faults and fractures with the difference of fast and slow shear-wave splitting reflectivity, Δγ(S): 3D/9C survey in Midland Basin, West Texas, and 3D/3C survey in Washakie Basin, Wyoming

One of the most important applications of shear-wave (S-wave) seismic exploration has been in reservoir fracture characterization. While many advancements have been made over the past 30 years to compute and correct for the long-wavelength kinematics of S-wave splitting (SWS) (fast S-wave polarization directions and slow S-wave time delays), practically no progress has been made in imaging the short-wavelength reflectivity of fractures directly with Δγ(S). This property is the contrast in the SWS anisotropy parameter, γ(S), and represents the reflection amplitude at vertical incidence for changes in fracture density and orientation across an interface. In this article, we examine the Lupin nine-component survey in Midland Basin, Texas, for the technical reliability of imaging fractures in depth with converted P to S waves (PS waves) guided by pure-mode horizontal shear waves and vertical shear waves. Final Δγ(S) amplitude maps for each mode show sensitivity to fractures, faults, and the maximum horizontal stress direction. These maps are computed from the difference between fast and slow S-wave stacks (after SWS analysis and correction) and P-wave amplitude variation with offset gradient stacks. The S-wave difference maps identify an east–west lineament, possibly a strike-slip fault or fracture corridor, that is not observed by P-wave depth slices. Pure-mode S waves and PS waves are orders of magnitude more sensitive to Δγ(S) than P waves. We also review the development of Δγ(S) and find that it has been relatively unexploited by the exploration industry. In addition, we demonstrate that Δγ(S) can be obtained directly from the objective function of the transverse energy to correct for SWS, and show a four-component Alford rotation example from a previous PS-wave survey in the Washakie Basin, Wyoming.

Early Results of Modelling Subsurface Study in Lake Toba, North Sumatra Using Receiver Function

The island of Sumatra was dominated by tectonic interaction between the Indo-Australian plate subducting beneath the Eurasian plate. Lake Toba is one of the results of the collision and had a large eruption several tens of thousands of years ago. The goal of this study was to use the receiver function approach to calculate the depth variation of the Moho layer and identify the presence of a low-velocity zone (LVZ) under Lake Toba, and then compare the results of the deconvolution method. To process data on receiver functions around Lake Toba, 31 data stations from the Lake Toba (LT) project have been chosen, with data sources coming from Geofon (Germany). Water level (frequency domain deconvolution) and iterative time-domain deconvolution are the receiver function methods employed. According to the findings, the depth of the Moho layer varies between 27.5 and 36.95 kilometres, and it thickens to the northeast of Lake Toba. The average depth of Moho is roughly 31.05 km, and the Vp/Vs ratio obtained is around 1.86 on average. The presence of a low-velocity zone was then detected at a depth of 15 km to 25 km in the A-A′ section leading from northwest to southeast on the east side of Lake Toba, and at a depth of 8 km to 22 km in the B-B′ section leading from southwest to northeast across Lake Toba, as indicated by low amplitude. The Investigator Fracture Zone (IFZ) beneath Lake Toba was identified as a magma reservoir and source of volcanic activity. The iterative time-domain deconvolution approach was then used to illustrate the result of the best receiver function in this investigation, which revealed that the arrival time of the Ps wave was more spiky than the result of the water level.

Structure of the Gonghe Sedimentary Basin in the northeastern Tibetan Plateau: evidence from teleseismicPwaves recorded by a dense seismic array

SUMMARYThe Gonghe Basin in the northeast Tibetan Plateau presents significant potential for hot dry rock (HDR) geothermal resources. A 1990 Mw 6.4 earthquake in the basin furthers the need for an improved understanding of its sedimentary structure. In this study, we utilize data from a dense seismic array of 88 short-period seismometers deployed at an interstation spacing of approximately 3 km to scrutinize the sedimentary structure of the Gonghe Basin. By analysing teleseismic P waveforms, we identify P-to-S converted waves (Ps wave) originating from the sedimentary basement. We then determine the delay time between the Ps waves and the direct P waves (P wave) through waveform cross-correlation. By integrating this delay time with empirical velocity structure models, HDR borehole data and results from teleseismic receiver function analysis, we derive a sediment thickness model of the Gonghe Basin for the Qabqa geothermal area. Our findings reveal a gradual increase in sediment thickness from around 500 m in the east to approximately 3000 m in the west, which is consistent with other geophysical surveys and borehole data. The thick sediments in the basin could potentially serve as an excellent thermal storage cover for HDR. The strong ground motion simulation using our sediment thickness model shows that thick sediments can amplify seismic waves, increasing the risk of seismic hazards. Moreover, our study indicates that the clear Ps waves can be effectively extracted to construct a dependable sediment thickness model using teleseismic P waves recorded by a short-period dense seismic array.

PS reflection moveout in a homogeneous anisotropic layer of arbitrary symmetry and tilt

Use of unconverted reflected PP waves leads to moveout formulae, which relate the moveout to only a limited number of parameters specifying anisotropy. Use of converted reflected PS waves extends the number of parameters to, generally, a complete set of twenty-one parameters. It leads, on the other hand, to more complicated formulae and phenomena unknown from studies of unconverted PP waves. In anisotropic media one has to deal with the existence of two S waves and their singularities, acoustic approximation cannot be used. We present and test approximate formulae for the reflection moveout of PS waves converted at a horizontal reflector underlying a homogeneous layer of arbitrary anisotropy symmetry and orientation. For their derivation, we use the combination of weak-anisotropy approximation and A-parameters specifying anisotropy. The complete set of twenty-one A-parameters represents an alternative to twenty-one independent elements of the stiffness tensor. In addition to the moveout formulae for separate PS1 and PS2 waves, we also present moveout formula for a P to common S wave whose traveltimes represent an average of traveltimes of PS1 and PS2 waves. Use of the P to common S wave reflection leads to several simplifications. Presented tests indicate that for most offsets and models with P-wave anisotropy up-to to 26% and S-wave anisotropy over 25%, the relative traveltime errors do not exceed 2.5%.

Converted PS-wave imaging based on offset vector tiles

Stacking using offset vector tiles (OVTs) is a technique used to simultaneously retain the offset and azimuth information in a wide-azimuth seismic survey by building minimal data sets of underground homogeneous illumination. Currently, derived from the assumption that reflection points and common midpoints are in the same lateral location because the raypath is symmetric, PP-wave OVT processing has been widely applied to seismic imaging and offset and/or azimuth analysis. However, it is difficult to directly apply the PP-wave OVT gathering method to the PS wave because the PS-wave raypath is asymmetric and the conversion point varies with depth. To solve this problem, we have developed an improved PS-wave OVT imaging technique based on the precise conversion point calculation and the equivalent converted-wave hypothesis, in which the PS-wave OVT gather with homogeneous illumination can be obtained in a manner similar to the PP wave. Moreover, to further improve the imaging quality, an azimuthal anisotropic normal moveout is applied to correct the traveltime difference. With tests of synthetic and field data, it can be concluded that our method represents a new and feasible solution for PS-wave OVT gathering.

Deep carbonate reservoir and gas prediction based on multicomponent seismic amplitude attributes — A case study

Multicomponent seismic exploration provides more valuable information for the prediction of underground structures, lithology, fluids, and fractures. Most studies on lithology estimation and fluid description using PP- and PS-wave seismic data mainly focus on relatively shallow targets with high porosity. Focusing on deep carbonate (dolomite) reservoirs with low porosity (generally less than 5%), we first analyze the characteristics of the seismic response difference between PP and PS waves, and then we combine logging data and seismic forward modeling to implement the identification of fluids using the amplitude difference between PP and PS waves. Data sets are acquired over grain beach dolomite reservoirs in the Cambrian Longwangmiao Formation, the central Sichuan Basin, Western China. The reservoirs are filled with different types of fluids (e.g., gas, water, bitumen, etc.). Based on comparisons between seismic responses of PP and PS waves, we observe that, at the location of the gas-bearing layer, PP-wave amplitude exhibits strong peaks and PS-wave amplitude finds relatively weak peaks, which is different from that obtained for the water-saturated layer. However, at the location of bitumen-filled reservoirs, PP- and PS-wave amplitudes exhibit strong peaks, and the reflection amplitude of PP waves is stronger than that of PS waves. Therefore, the amplitude difference of PP and PS waves provides valuable information and feasibility for fluid identification. We verify that the maximum peak amplitude attribute of PS waves may better characterize the distribution of porous dolomite reservoirs than that of PP waves, and using the attribute of maximum peak amplitude difference between PP and PS waves, we may distinguish gas-bearing and water-saturated layers. Comparing with actual drilling results, we conclude that our PP/PS interpretation technique is feasible for fluid identification in deep carbonate reservoirs.

Microearthquake location and uncertainty analysis using a Kirchhoff wavefront imaging method: A comparison with traveltime inversion and full wavefield imaging methods

The uncertainty and resolution of microearthquake location are an important topic for reservoir characterization and early warning of induced earthquakes. Many independent studies have either improved certain source location methods or applied a certain method to a data set without perhaps studying the full limitations compared with other methods. We have developed a P- and PS-wavefront imaging (WI) method to estimate the source origin time sequentially, which overcomes the unknown variable of source origin time in Kirchhoff-type imaging and helps to reduce the location uncertainties originating from the source origin time. We develop a 3D synthetic example by finite-difference modeling the realistic elastic 3C data using the SEG advanced modeling (SEAM) 4D earth model, and jointly compare the reservoir and basement microearthquake source location uncertainties based on traveltime inversion (TI), WI, and full wavefield imaging (FWIMG) methods. For each method, we also investigate the source location uncertainties between the P- and PS-wave results. Our results indicate that, using P waves and typical surface receiver arrays, TI has larger depth location uncertainties and cannot separately resolve the reservoir and basement events, whereas WI has larger horizontal uncertainties; FWIMG has the smallest horizontal location uncertainty, its depth uncertainty is similar to the WI method, and it is much smaller than the TI. Using PS waves can significantly reduce the location uncertainty compared with using only P waves for the three methods, and the full wavefield method has the smallest location uncertainty. The WI method has a moderate computation cost between TI and full wavefield methods. Data noise and velocity scaling errors change the source location uncertainties based on different imaging methods.

Reflection and transmission coefficients of spherical waves at an interface separating two dissimilar viscoelastic solids

SUMMARY Spherical wave reflection and transmission (R/T) coefficients at an interface are not only of theoretical significance but also play an important role in the amplitude variation with offset (AVO) analysis of wide-angle reflection seismic data and cross-borehole surveys. For sources close to the interface the resulting wavefields cannot be adequately described in terms of a single incident plane wave. Rather, the spherical waves must be viewed as the superposition of an infinite number of plane waves. Moreover, the R/T coefficients for each individual plane wave in viscoelastic media have proven to be more complicated than expected due to the difficulty in selecting the correct vertical slowness. In such attenuating media the R/T coefficients cannot be properly determined by simply replacing the real elastic parameters with their complex viscoelastic counterparts. In this study, the reflection and transmission coefficients of spherical waves at a plane interface separating two dissimilar viscoelastic solids are rigorously investigated. The difficulty in selecting the vertical slowness is shown to be circumvented if the spherical wavefields are calculated from the plane wavefields using the Sommerfeld integral appropriate for the dissipative materials. However, some resulting phase curves of the complex spherical wave R/T coefficients tend to be of opposite sign to the corresponding phase curves of plane waves due to non-uniqueness of the latter for post-critical wave incidence. In this contribution we propose a new definition of spherical wave R/T coefficients for viscoelastic media which differs from the conventional one. Its advantages are that it is not explicitly expressed as a function of the R/T angles, it is valid for both P and S waves, yet it is consistent with the existing definitions of spherical wave R/T coefficients but is more robust. By way of examples we compute both spherical wave reflection coefficients (SWRC) and spherical wave transmission coefficients (SWTC) for two different viscoelastic models. Unlike plane waves, both the SWRC and the SWTC of converted PS waves are found to be non-zero at vertical incidence and may be drastically affected by the existence of longitudinal PS waves which are confirmed by full waveform calculations for the converted PS waves.

Moho Complexity in Southern California Revealed by Local PmP and Teleseismic Ps Waves

AbstractThe Moho discontinuity plays an important role in crustal growth and evolution. In this study, we delineate the Moho geometry in southern California by jointly using local Moho‐reflected waves PmP and teleseismic Moho‐converted waves Ps. To well constrain the Moho geometry, we have developed a two‐stage process to pick PmP waves and have created a reliable PmP travel time data set with a total of 10,192 picks. We have also extracted 38,648 high‐quality P‐wave receiver functions (RFs). The Moho depth is initially estimated via the common conversion point (CCP) stacking of RFs and then refined by inverting the PmP travel time data in a community velocity model (CVM‐H, version 15.1.1). The newly built Moho geometry is generally consistent with the California Moho Model version 1.0 (CMM‐1.0), that is, a shallow Moho beneath the Salton Trough (23 km), a uniformly shallow Moho beneath the Mojave Desert and the Basin and Range (<29 km), and a sliver of deep Moho under the western Peninsular Ranges, the eastern Transverse Ranges, and the western Sierra Nevada (>34 km). However, our Moho model reveals some new features different from the CMM–1.0, such as a deep Moho (∼34 km) beneath the northern end of the central and western Transverse Ranges, consistent with the observation of deep seismicities due to a thick brittle crust there. We also find a gradual transition from the lower crust to the uppermost mantle beneath the western Peninsular Ranges, leading to the rareness of pickable PmP waves as well as weak Moho‐converted signals there.

Regional seismic velocity changes following the 2019 Mw 7.1 Ridgecrest, California earthquake from autocorrelations and P/S converted waves

SUMMARY We examine regional transient changes of seismic velocities generated by the 2019 Mw 7.1 Ridgecrest earthquake in California, using autocorrelations of moving time windows in continuous waveforms recorded at regional stations. We focus on traveltime differences in a prominent phase generated by an interface around 2 km depth, associated with transmitted Pp waves and converted Ps waves from the ongoing microseismicity. Synthetic tests demonstrate the feasibility of the method for monitoring seismic velocity changes. Taking advantage of the numerous aftershocks in the early period following the main shock, we obtain a temporal resolution of velocity changes up to 20 min in the early post-main-shock period. The results reveal regional coseismic velocity drops in the top 1–3 km with an average value of ∼2 per cent over distances up to 100 km from the Ridgecrest event. These average velocity drops are likely dominated by larger changes in the shallow materials and are followed by rapid recoveries on timescales of days. Around the north end of the Ridgecrest rupture and the nearby Coso geothermal region, the observed coseismic velocity drops are up to ∼8 per cent. The method allows monitoring temporal changes of seismic velocities with high temporal resolution, fast computation and precise spatial mapping of changes. The results suggest that significant temporal changes of seismic velocities of shallow materials are commonly generated on a regional scale by large events.

Application of multi-wave and multi-component seismic data in the description on shallow-buried unconsolidated sand bodies: Example of block J of the Orinoco heavy oil belt in Venezuela

The use of multi-wave and multi-component seismic information for reservoir prediction and characterization has been a popular research direction. The study area is located in the Orinoco heavy oil belt in Venezuela. The reservoir is a braided river delta plain deposit and the sandstone is shallowly buried and unconsolidated. Thereby, it is difficult to predict and characterize the type of reservoir effectively with seismic data of conventional P-waves. Based on multi-wave and multi-component seismic acquisition data, the study has conducted petrophysical analysis and seismic horizon calibration with converted wave (PS). Vertically, superimposed sand bodies were identified with PP wave because the PP wave has higher vertical resolution than that of PS wave. Laterally, sectional morphology and plane distribution scale of sand bodies were delineated by using the higher lateral resolution of PS wave. By combining the characteristics of PP wave and PS wave, five models for intersection and sand body superposition were summarized and the architecture units of sand bodies were divided. The seismic attribute (RMS amlpitude) boundary characteristics and continuity of the high amplitude region described by PS wave are more evident to obtain plane distribution of channel bars and braided channels. Three different seismic inversion results of seismic impedance, density and sand thickness from three different methods were compared. The average accuracy of sand body prediction with the method of PP-PS wave combined pre-stack inversion reached approximately 85% which is greater than that of the PP wave post-stack inversion and PP-PS combined post-stack inversion, with accuracy of 64% and 66% respectively. The research results showed that in the study area, the combination of multi-wave and multi-component seismic reflection information can effectively identify and predict multi-stage superimposed sand bodies with clearer vertical superposition and more accurate lateral boundary. Due to the inherent non-uniqueness of seismic information on predicting reservoir distribution, the resolution of seismic data and the difficulty of identification of the highly superimposed shallow-buried unconsolidated sandbodies, reservoir prediction uncertainty still exists. In particular, the interpretation on the sedimentary microfacies distribution and sand-body scale may only be one of the relatively reliable interpretation schemes.

The analysis on PS wave reflection coefficient in equivalent porous fractured media

Combining the equivalent fractured media with Thomsen fractured media theory, the anisotropic parameters expressed in compliance are obtained. The new PS wave reflection coefficient formula presented in matrix porosity, fluid type, and fracture density were established. Numerical simulations show that the PS wave reflection coefficient in water-saturated fracture media is more sensitive to the fracture density than that in gas-saturated media; the difference between the reflection coefficients in the gas-saturated and water-saturated state greatly increases when the matrix porosity of fractured media exceeds 0.01. It shows that fracture density and matrix porosity can be used as good fluid indicators in fractured reservoir.

Первые результаты оценки глубины поверхности Мохо методом обменных Ps-волн для Азербайджанской части Большого Кавказа

The methodology of the converted waves, or as it is commonly called, the "Receiver function" method, is well known and is widely used throughout the world to study the deep structure of the Earth up to 800 km. The method is based on the registration and interpretation of converted Ps waves. These studies were carried out as part of the International Seismotomo-graphic Laboratory using a software package developed at the University of Missouri (USA). One of the best regions for studying the early stages of mountain building is the Greater Caucasus, where most of the volcanism and mountain building appears to be 5 million years. Of particular interest is the immersion zone of the Kura Basin beneath the Greater Caucasus, the so-called subduction zone, which has not been sufficiently studied to date. To this end, we began our studies of the depth of the Moho border with this region. Thus, for the first time on the basis of the analysis of the wave characteristics of distant earthquakes recorded at seismic and telemetric stations of the RSSC, within the framework of the international project "Transect", the depths of the Moho border for the Azerbaijan part of the Greater Caucasus were refined by the method of exchange reflected Ps waves ("Receiver function"). Seismo-grams of the selected earthquakes were processed using the Seismic Analysis Code (SAC) software package under the MacOs operating system. The study examined seismological data recorded by a network of telemetry stations (N=20) for 2009-2019. In total, 2428 earth-quakes recorded at an epicenter distance of 35 to 90 degrees were analyzed. At the first stage, frequency filtering was carried out in order to eliminate oscillations that were too high, containing the effects of random scattering on inhomogeneities, and too low frequencies that re-duce the resolution. The working range of the periods ranged from two to 10 seconds. Next, two-dimensional and three-dimensional rotation of the axes was carried out. The summation of all traces was carried out with time shifts relative to some reference epicentral distance, which is assumed to be 60 degrees. On the summarized Q-tracks of the receiving functions, the Moho boundary with a delay time of 4.0 sec is clearly distinguished. Thus, a map of iso-lines of the depths of the Moho surface was constructed and depths were determined for the territory of the Guba-Gusar region 48-50 km, the Zagatala-Balakan region 46-47 km, the Shamakhi-Ismayilli region 48-52 km. As it was said earlier, the first definitions of the depth of the surface of Moho in Azerbaijan were made based on the data from the state earthquake and the gravitational model of the Earth's crust. R.M. Gadzhiev in 1965 and E.Sh. Shikhalibeyli in 1996 built such models. The data obtained are consistent with the available data, but discrepancies have been received. Compared with the map constructed according to the GSZ-KMPV and gravimetric data by R.M. Gadzhiev (1965), the difference in the thickness of the earth's crust was from one to 15 km. Compared with the map constructed according to the FGP and gravimetric data by E.Sh Shikhalibeyli (1996), the difference in the thickness of the earth's crust varied from one to 10 km.

Triplications for the converted wave in transversely isotropic media with a tilted symmetry axis

ABSTRACTIn seismic data processing, serious problems could be caused by the existence of triplication and need to be treated properly for tomography and other inversion methods. The triplication in transversely isotropic medium with a vertical symmetry axis has been well studied and concluded that the triplicated traveltime only occurs for S wave and there is no triplication for P and converted PS waves since the P wave convexity slowness always compensates the S wave slowness concavity. Compared with the vertical symmetry axis model, the research of the triplication in transversely isotropic medium with a tilted symmetry axis is still keeping blank. In order to analyse the triplication for the converted wave in the tilted symmetry axis model, we examine the traveltime of the triplication from the curvature of averaged P and S wave slowness. Three models are defined and tested in the numerical examples to illustrate the behaviour of the tilted symmetry axis model for the triplicated traveltime with the change of the rotation angle. Since the orientation of an interface is related to the orientation of the symmetry axis, the triplicated traveltime is encountered for the converted wave in the tilted symmetry axis model assuming interfaces to be planar and horizontal. The triplicated region is influenced by the place and level of the concave curvature of the P and S wave slowness.