Seismic Ray Research Articles

Oceanic mantle reflections in deep seismic profiles offshore Sumatra are faults or fakes

In the late 90’s, some faults identified within oceanic crust were demonstrated to be artifacts arising from out-of-plane scattering along linear sediment-buried fault scarps. Symmetrical mantle reflections observed southwest northern Sumatra on seismic reflection profiles have been identified as faults cutting through the upper mantle down to unprecedented depths reaching ~45 km. Seawater being conveyed along sub-vertical re-activated fracture zones (FZs) to the upper mantle, the mantle portions of FZs are serpentinized and act as mirrors for seismic rays. We suggest that the mantle features are not faults but artifacts resulting from out-of-plane reflections on these mirrors. Two perpendicular seismic profiles crossing the same FZ display two dipping features down to 30 km, which cannot be explained as faults from recent tectonic and structural constraints but merely as out-of-plane reflections on this FZ. This result confirms that most of mantle reflections observed southwest northern Sumatra are fakes rather than faults.

On conformally flat fourth root (α,β)-metrics

The theory of 4-th root metrics plays an important role in Biology, General Relativity and Seismic Ray Theory. Using the Shen's sy-separating trick, we prove that every conformally flat weakly Einstein 4-th root (α,β)-metric on a manifold M of dimension n≥3 is either a Riemannian metric or a locally Minkowski metric. Then, we show that every conformally flat 4-th root (α,β)-metric of almost vanishing Ξ-curvature on a manifold M of dimension n≥3 reduces to a Riemannian metric or a locally Minkowski metric.

Constraint nip-tomographic inversion of strong sparse seismic data

This work is a result of specific numerical experiments motivated by real cases of processing strong sparse seismic data, as an application of techniques based on the common-reflection-surface (CRS) stack technology aiming at estimating a smooth velocity depth distribution. The paper is primarily limited to numerical tests with a depth velocity model that attends closely the paraxial theory validated by the seismic ray hypotheses. A complete modeling of a seismic survey was performed, and the common-shot sections were submitted to random muting of traces, to noise addition, and afterwards followed by reconstruction of the section by trace interpolation. The interpolation was controlled by the 2D spectral non-aliasing condition, where the t − x spectral amplitude content was limited to the two main Fourier quadrants f − k. It was admitted that most information was based on primary compressional (P) wave content; therefore, multiples and the P − S conversion were considered as noise. The trace interpolation used the stack attributes of the original gather (conventional stack) with sparse data to construct supergather sections (for the supergather stack). The velocity distribution in depth uses the principle of interpreting the inversion data as normal incidence point (NPI) information. The applied inversion algorithm is NIP-tomographic, classified as curve fitting, non-linear, multi-parametric, that uses the wave front kinematic and dynamic CRS attributes as data-driven constraints to estimate a consistent depth velocity distribution. As a general conclusion, we emphasized also interpolation, inclusive of sparse data, as a step for spectral analysis, consequently in filtering, stacking, and tomography to obtain a velocity distribution for further use in the estimation for velocity distribution, imaging, geological interpretation and sedimentary basin modeling.

A simple inversion algorithm to estimate a linearly increasing velocity model for microseismic monitoring

Microseismic monitoring is used to optimise shale gas production or enhanced geothermal stimulation. The technical tools for microseismic monitoring, which is a passive seismic method, are similar to those used in earthquake detection, but differ in that the target area is much smaller than areas affected by earthquakes. Therefore, it is important to use an accurate velocity model. However, such models require conducting an additional survey, which can be both expensive and time-consuming. Many microseismic monitoring studies have used an approximated velocity model constructed from well logging data to reduce these additional costs. In this study, we used a simple approximated model in which velocity increases linearly with depth and creates an accurate velocity model, eliminating the need for an additional survey. We analytically derived formulas for seismic ray traveltime and inverted the velocity gradient using the Gauss–Newton method. Using a numerical example, we verified that the proposed algorithm accurately describes the long-wavelength trend of the true velocity model in a negligibly short time. We performed a Monte Carlo simulation to evaluate the effects of traveltime picking errors. The simulation results indicated that the proposed algorithm provides a reasonable solution under the probable uncertainty of traveltime picking. Finally, we verified that our algorithm was not sensitive to the initial velocity gradient through inversion tests using various initial values. Thus, the numerical example and analysis confirm that the proposed algorithm is efficient and robust.

Anisotropic Crosshole+VSP Traveltime Tomography Through Triangular Cell Model with a Normalized Jacobian Matrix and Multistage Inversion Strategy

To overcome the difficulty in forward and inversion problem in complex geological model, including undulated topography and irregular subsurface interface, we in this paper realize a multistage triangular shortest-path method for multi-phase seismic ray tracing and combine a nonlinear inversion solver (damped minimum norm and constrained least squares problem solved by a conjugated gradient method) to simultaneously invert four elastic parameters (or four Thomsen parameters) in anisotropic media using combined direct and reflected arrival times. For trading-off between different parameter updating, we normalize the sensitivity functions (traveltimes derivatives with respect to different elastic (or Thomsen) parameter changes) to balance four updated elastic (or Thomsen) parameters in simultaneous inversion process, due to the magnitude and pattern of partial derivatives more sensitive to different phase slowness angles. In addition, in order to solve the multi-solution problems of qSV-wave inversion, a strategy of multistage inversion is proposed. For testing the efficiency and correctness of proposed inversion method, we use the picked traveltimes in synthetic seismograms as the observed traveltimes in the inversion. The results show that both inverted images by taking the picked traveltimes in synthetic seismograms as the observed data and by taking predicted traveltimes using ray tracing method as observed data have a similar imaging pictures, which verify the efficiency and correctness of the proposed inversion method. Furthermore, the inverted results by normalized kernel functions are better than that of inversion without applying the normalized kernel functions for both qP and qSV data, and the results of the multistage inversion are better than that of the simultaneous inversion without multistage inversion applied in qSV-wave inversion. In addition, both elastic and Thomsen parameter inversions for the same anisotropic model indicate that there are no big differences between the two inverted results even though the sensitivity kernels related to the Thomsen parameters have relatively large values.

Relationship Between Geological Structures and Velocity Anomalies in Two-Dimensional Tomography with First-Arrival Seismic Travel Time (FAST): A New Recognization

Two-dimensional (2D) tomography with first-arrival seismic travel time (FAST) is widely and effectively used to detect geological anomalies. For detecting small geostructures in a coalbed, 2D seismic tomography with FAST depends primarily on the seismic wave velocity. The seismic velocity tomography of a coalbed, sources and receivers are placed in the coal seam, differs from the cross-hole seismic tomography on the ground. The response of the seismic wave velocity anomaly to common geostructures, like the response of a high-velocity anomaly to a normal fault, has been comprehensively summarized. However, the interpretation of the response has not been fully discussed. Therefore, in this paper, a numerical simulation is used to corroborate the relationship. A special three-layer coalbed model was constructed and used to investigate the relationship between geostructures and velocity anomalies in coalbeds using seismic ray tracing technology. The results indicated that the thickness and inclinations of the coalbed, the size and position of abnormal geological bodies are the key factors for 2D tomography with FAST on the coal mining face. The morphology of the roof and floor strata determines the path that the seismic wave travels. Finally, the roof and floor strata are other important factors affecting the velocity anomaly.

A three-dimensional oblique incidence method based on stress time-history functions of seismic body waves

This paper presents a three-dimensional oblique incidence method based on stress time-history functions of seismic body waves. This method realizes the three-dimensional oblique incidence of a single body wave phase or superposed multiple phases, which considers the earthquake action in the analysis of the slope seismic response. To implement this method, first, the spatial relationship between slope and incident seismic wave rays is described, and the direction of incident seismic waves is defined with two parameters: the azimuth angle $$\alpha$$, which reflects the azimuth of epicenter; and the incident angle $$\theta$$, which is a concentrated expression of the hypocentral depth and epicentral distance. Second, at the bottom boundary of the slope numerical model, the vibration starting time of each node excited by an oblique incident seismic wave is calculated. By considering vibration time sequence, the successive disturbance of rock and soil medium at the bottom of the slope is achieved. Then the stress time-history functions of six body wave phases are derived. Numerical simulation results of the x demonstrate the effectiveness, applicability and necessity of the proposed method.

Calculation of slowness vectors from ray directions for qP-, qSV-, and qSH-waves in tilted transversely isotropic media

Kinematic ray tracing is an effective way to simulate the seismic wave propagation in isotropic and anisotropic media. It is essential to know the ray velocity when tracing seismic rays. But in anisotropic media, the ray velocity is a function of the direction of the slowness vector instead of the ray direction and it often deviates from the phase velocity. In this case, it causes a critical problem for ray tracing, which is how to calculate the ray velocity from a known ray direction. If we could calculate the phase slowness vector from ray directions, the ray velocity could be computed. We have evaluated a previous method in the first place. Then, we developed two new methods to solve two existing problems of the previous method: (1) It leads to complex and multiple solutions of the slowness vector and (2) it mixes up the qP- and qSV-wave modes. Our first method solves the two problems by applying eigenvalues to separate the wave modes and decrease the two unknowns ([Formula: see text] and [Formula: see text]) to only one unknown in two equations. Our second method is based on the general relationship between the slowness and ray-velocity vectors and shows that only one unknown is involved in one equation for tilted transversely isotropic (TTI) media. After obtaining the slowness vector, the ray velocity can be computed easily. A 2D model is designed to test the feasibility of the new methods. Using the results for the model, we found that the presented approaches were applicable for ray tracing in TTI media.

Inversion of velocity parameters in multilayered elliptical anisotropy medium - synthetic data example

In the medium composed of parallel sedimentary layers, model of elliptic anisotropy is often better approximation of real conditions than simple layers with constant velocity. In such model a velocity is described with 3 parameters: a, b (responsible for vertical velocity and its gradient) and χ - elliptic anisotropy coefficient, describing changes of velocity with direction of wave propagation. In this case, seismic rays are no longer straight lines but elliptic-shaped curves. In this contribution we present a tool for inversion of velocity parameters in multilayered medium considering model of elliptic anisotropy. Input data contains measured traveltimes of direct wave between all sources and receivers. The depth of boundaries and existence of elliptic anisotropy in specific layers are not subject of inversion. In order to obtain each synthetic traveltime, necessary for the target function, ray tracing must be carried out using Fermat’s principle directly. The optimization in both parameters inversion and ray tracing is local and performed with Simplex algorithm from GSL library. The tests of the tool was conducted on the synthetic data with various types of start model containing one or more layers with or without elliptic anisotropy.

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameterization in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in transversely homogeneous elliptically anisotropic media. Seismic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in elliptically anisotropic media with an irregular surface.

A comparative analysis of two-dimensional multi-valued ray tracing techniques

Seismic wavefront self-intersection (or multi-valued seismic rays) is a natural phenomenon when a seismic wave propagates through a complex medium, which is commonly ignored in most previous studies. The later arrivals not only contain useful information regarding low velocity anomalous zones and/or irregular reflecting interfaces, but also have the potential to improve the ray coverage in subsequent seismic imaging. Due to the relative immaturity of this field of research, it is instructive to compare different algorithms and therefore develop more advanced, efficient, and practical schemes for tracing multi-valued arrivals between the source and the receivers when the medium is heterogeneous and incorporates irregular or curved interfaces. For these reasons, we first modify the so-called reduced phase space method, in which a continuous wavefront mapping method is implemented for efficient and accurate consideration, and then compare it with two newly developed grid-based algorithms for tracing multi-valued direct arrivals in heterogeneous media and multi-valued reflected arrivals when undulating interfaces are present. The results show that the modified reduced phase space method is a potent and useful algorithm for tracking both multi-valued direct and reflected arrivals. The first-order “raylet” method is simple in principle but is unable to trace all possible later arrivals. Under such circumstances, the extremal solution method is a good choice to trace the multi-valued reflected arrivals; it is comparable to the modified reduced phase space method in practical application.

Four families of projectively flat Finsler metrics with $$\mathbf{K}=1$$ K = 1 and their non-Riemannian curvature properties

For the first time, Bryant introduced a locally projectively flat non-Riemannian Finsler metric with flag curvature $$\mathbf{K}=1$$ on $${\mathbb {S}}^2$$ . In this paper, we construct four new non-Riemannian families of projectively flat Finsler metrics with flag curvature $$\mathbf{K}=1$$ . These metrics belong to the class of generalized 4-th root metrics. The class of generalized 4-th root metrics is an extension of the class of 4-th root metrics which has close relations with General Relativity and Seismic Ray Theory. In this class, we characterize Finsler metrics of isotropic flag curvature. We find the necessary and sufficient condition under which a metric in this class be weakly Einstein. In this class, we characterize Finsler metrics of isotropic S-curvature and almost vanishing $$\Xi $$ -curvature. Finally, we find the necessary and sufficient condition under which a Finsler metric in this class has vanishing projective Ricci curvature.

Global propagation of seismic body waves and correlation

We discuss the nature of retrieved body waves at teleseismic distances from correlation of records in two separate bands T<10 s and T>30 s. The short period correlations indicate the presence of deep phases that appear as correct reconstructions of actual phases. We present an example of application to the reflectivity of the core-mantle boundary region. Careful tests show the reliability of the images produced with ambient noise records. On the opposite, we analyze long period records and show that the correlations are dominated by strong coherent phases (with time close to actual ScS or P'P'df) that are the signatures of high quality factor normal modes. By using array analysis and spectral analysis, we identify the dominant constituents. We then make use of geometrical quantization to derive the ballistic reverberations of rays that contributes to the emergence of signals at times close to body wave arrivals. Our study indicates that the signals measured in the long period correlations have a physical significance, but their interpretation as station to station seismic ray is nontrivial.

Three-dimensional Seismic Velocity Structure beneath Unzen Volcano, Kyushu, Japan Inferred by Tomography from Experimental Explosion Data

Seismic travel time inversion is widely used to estimate the velocity structure within a target area. For a given velocity structure a suitable ray tracer is needed to calculate the ray path and travel time between points. The velocity structure of volcanic areas varies considerably. Any seismic ray tracer used in volcanic areas should therefore be robust to velocity variation. A seismic ray tracer developed by the author to be effective with strongly varying velocity fields is used to calculate the travel time in an inversion scheme, and is shown to work well in volcanic regions (Nishi, 2001). The present paper gives the results of this travel time inversion method applied to data obtained from experimental explosions in Unzen volcano, Kyushu Japan. Seismic velocity in the center of the volcanic edifice is in general higher than peripheral area, as was already known from an analysis of the travel time by the refraction method (Explosion Seismic Research Group of Unzen Volcano and Shimizu, 1997). In detail, however seismic velocity structure in this region is laterally heterogeneous. Among the high velocity zone, some low velocity zones and also still higher velocity zone are found. Low velocity zone beneath the Fugendake peak (near to the lava dome generated in the 1991-1995 activity) is seemed to be related to the pressure source beneath the Fugendake peak estimated from leveling survey.

P47 火山地域用 3 次元地震波線追跡法 (Fermat) による Shell 型マグマ溜りモデルの検討

P47 火山地域用 3 次元地震波線追跡法 (Fermat) による Shell 型マグマ溜りモデルの検討

The nature of precursor waves from distant earthquakes

It is shown that, in accordance with the data used when determining velocity distribution in the Earth’s core [14], so called “precursor” earthquakes cannot be produced by wave scattering to lower mantle inhomogeneities, because seismic rays linking the earthquake sources and seismic stations are located in different inner zones of the Earth and travel at different azimuths, producing a stable wave pattern on aggregate. Thus, the present work considers the fundamental problem regarding what precursor earthquakes are. Solution of this problem will guide ideas about the structure of the Earth’s core.

Method to find the Minimum 1D Linear Gradient Model for Seismic Tomography

The changes in the state of a geophysical medium before a strong earthquake can be found by studying of 3D seismic velocity images constructed for consecutive time windows. A preliminary step is to see changes with time in a minimum 1D model. In this paper we develop a method that finds the parameters of the minimum linear gradient model by applying a twodimensional Taylor series of the observed data for the seismic ray and by performing least-square minimization for all seismic rays. This allows us to obtain the mean value of the discrete observed variable, close to zero value.

Seismic evidence for flow in the hydrated mantle wedge of the Ryukyu subduction zone.

It is widely accepted that water-rich serpentinite domains are commonly present in the mantle above shallow subducting slabs and play key roles in controlling the geochemical cycling and physical properties of subduction zones. Thermal and petrological models show the dominant serpentine mineral is antigorite. However, there is no good consensus on the amount, distribution and alignment of this mineral. Seismic velocities are commonly used to identify antigorite-rich domains, but antigorite is highly-anisotropic and depending on the seismic ray path, its properties can be very difficult to distinguish from non-hydrated olivine-rich mantle. Here, we utilize this anisotropy and show how an analysis of seismic anisotropy that incorporates measured ray path geometries in the Ryukyu arc can constrain the distribution, orientation and amount of antigorite. We find more than 54% of the wedge must consist of antigorite and the alignment must change from vertically aligned to parallel to the slab. This orientation change suggests convective flow in the hydrated forearc mantle. Shear wave splitting analysis in other subduction zones indicates large-scale serpentinization and forearc mantle convection are likely to be more widespread than generally recognized. The view that the forearc mantle of cold subduction zones is dry needs to be reassessed.

Wadati method as a simple tool to study seismically active fault zones: a case study from the West-Bohemia/Vogtland region, central Europe

The ratio of P- to S-wave velocities, VP/VS, is an important parameter characterizing rock composition and fluid saturation. We have studied properties of the ratio in the West-Bohemian seismically active region, using data from the earthquake swarm which occurred here in 2008. The earthquake swarm was well recorded by 23 seismic stations from epicentral distances less than 25 km. We selected a subset of 158 events with local magnitudes between 1.5 and 3.8. Applying the Wadati method to the measured arrival times of P and S waves, we arrived at an average value of VP/VS =1.68 ± 0.01. This differs a little from the value of VP/VS = 1.70, which is routinely used for earthquake locations in the region at present. Moreover, it was recognized that the points in the Wadati graphs for some stations were systematically deviated from the mean straight lines. In particular, the stations with the largest positive deviations (above the mean straight lines) are situated close to the Marianske Lazně Fault and to some intensive mofettes. Further analyses revealed reduced P- and S-wave velocities along the seismic rays toward these anomalous stations. In our opinion, the seismic waves arriving at the anomalous stations probably propagated along a fault or another zone of weakness. In this way, our results support the hypothesis that the Marianske Lazně Fault is a deep-seated fault continuing down to the seismically active zone of local earthquakes. From a general point of view, this study demonstrates that even some narrow structural anomalies in the crust, such as fault zones, can be recognized by the simple Wadati method if data from a dense seismic network are available.

Seismic network configuration by reduction of seismic source location errors

This article discusses the possibilities of improving the locations of seismic emission sources induced during underground mining works. The application of three-component seismic sensors made it possible to identify the location of sources using the propagation times of seismic waves and the directions of seismic rays. The article is a case study of Rudna, the largest underground Polish copper mine, and presents location methods that use times or/and directions of seismic wave propagation. For both methods, a discussion of location errors is also presented. The presented considerations are illustrated with a synthetic example that imitates the typical data recorded in Polish copper mines. A real example of source location for both the discussed methods of source location and error assessment is presented. The distributions of the location errors are presented for the two discussed methods for a sample panel of the Rudna mine. The best location for the three-component sensor that minimizes average location errors in the mining panels is presented. In the discussion, special attention is devoted to accurately determining the depth of seismic sources.