DEBUBBLING: A GENERALIZED LINEAR INVERSE APPROACH*

On seismograms recorded at sea bubble pulse oscillations can present a serious problem to an interpreter. We propose a new approach, based on generalized linear inverse theory, to the solution of the debubbling problem. Under the usual assumption that a seismogram can be modelled as the convolution of the earth's impulse response and a source wavelet we show that estimation of either the wavelet or the impulse response can be formulated as a generalized linear inverse problem. This parametric approach involves solution of a system of equations by minimizing the error vector (ΔX = X^obs– X^cal) in a least squares sense. One of the most significant results is that the method enables us to control the accuracy of the solution so that it is consistent with the observational errors and/or known noise levels. The complete debubbling procedure can be described in four steps: (1) apply minimum entropy deconvolution to the observed data to obtain a deconvolved spike trace, a first approximation to the earth's response function; (2) use this trace and the observed data as input for the generalized linear inverse procedure to compute an estimated basic bubble pulse wavelet; (3) use the results of steps 1 and 2 to construct the compound source signature consisting of the primary pulse plus appropriate bubble oscillations; and (4) use the compound source signature and the observed data as input for the generalized linear inverse method to determine the estimated earth impulse response—a debubbled, deconvolved seismogram. We illustrate the applicability of the new approach with a set of synthetic seismic traces and with a set of field seismograms. A disadvantage of the procedure is that it is computationally expensive. Thus it may be more appropriate to apply the technique in cases where standard analysis techniques do not give acceptable results. In such cases the inherent advantages of the method may be exploited to provide better quality seismograms.     

An Approximation to Sparse-Spike Reflectivity Using the Gold Deconvolution Method

Wiener deconvolution is generally used to improve resolution of the seismic sections, although it has several important assumptions. I propose a new method named Gold deconvolution to obtain Earth’s sparse-spike reflectivity series. The method uses a recursive approach and requires the source waveform to be known, which is termed as Deterministic Gold deconvolution. In the case of the unknown wavelet, it is estimated from seismic data and the process is then termed as Statistical Gold deconvolution. In addition to the minimum phase, Gold deconvolution method also works for zero and mixed phase wavelets even on the noisy seismic data. The proposed method makes no assumption on the phase of the input wavelet, however, it needs the following assumptions to produce satisfactory results: (1) source waveform is known, if not, it should be estimated from seismic data, (2) source wavelet is stationary at least within a specified time gate, (3) input seismic data is zero offset and does not contain multiples, and (4) Earth consists of sparse spike reflectivity series. When applied in small time and space windows, the Gold deconvolution algorithm overcomes nonstationarity of the input wavelet. The algorithm uses several thousands of iterations, and generally a higher number of iterations produces better results. Since the wavelet is extracted from the seismogram itself for the Statistical Gold deconvolution case, the Gold deconvolution algorithm should be applied via constant-length windows both in time and space directions to overcome the nonstationarity of the wavelet in the input seismograms. The method can be extended into a two-dimensional case to obtain time-and-space dependent reflectivity, although I use one-dimensional Gold deconvolution in a trace-by-trace basis. The method is effective in areas where small-scale bright spots exist and it can also be used to locate thin reservoirs. Since the method produces better results for the Deterministic Gold deconvolution case, it can be used for the deterministic deconvolution of the data sets with known source waveforms such as land Vibroseis records and marine CHIRP systems.     

A cloud-based synthetic seismogram generator implemented using Windows Azure

Synthetic seismograms generated by solving the seismic wave equation using numerical methods are being widely used in seismology. For fully three-dimensional seismic structure models, the generation of these synthetic seismograms may require large amount of computing resources. Conventional high-performance computer clusters may not provide a cost-effective solution to this type of applications. The newly emerging cloud-computing platform provides an alternative solution. In this paper, we describe our implementation of a synthetic seismogram generator based on the reciprocity principle using the Windows Azure cloud application framework. Our preliminary experiment shows that our cloud-based synthetic seismogram generator provides a cost-effective and numerically efficient approach for computing synthetic seismograms based on the reciprocity principle.     

WAVELET DECONVOLUTION USING A SOURCE SCALING LAW*

We present a new method for the extraction and removal of the source wavelet from the reflection seismogram. In contrast to all other methods currently in use, this one does not demand that there be any mathematically convenient relationship between the phase spectrum of the source wavelet and the phase spectrum of the earth impulse response. Instead, it requires a fundamental change in the field technique such that two different seismograms are now generated from each source-receiver pair: the source and receiver locations stay the same, but the source used to generate one seismogram is a scaled version of the source used to generate the other. A scaling law provides the relationship between the two source signatures and permits the earth impulse response to be extracted from the seismograms without any of the usual assumptions about phase. We derive the scaling law for point sources in an homogeneous isotropic medium. Next, we describe a method for the solution of the set of three simultaneous equations and test it rigorously using a variety of synthetic data and two types of synthetic source waveform: damped sine waves and non-minimum-phase air gun waveforms. Finally we demonstrate that this method is stable in the presence of noise.     

STABILIZATION OF NORMAL-INCIDENCE SEISMOGRAM INVERSION REMOVING THE NOISE-INDUCED BIAS*

A main problem in computing reflection coefficients from seismograms is the instability of the inversion procedure due to noise. This problem is attacked for two well-known inversion schemes for normal-incidence reflection seismograms. The crustal model consists of a stack of elastic, laterally homogeneous layers between two elastic half-spaces. The first method, which directly computes the reflection coefficients from the seismogram is called “Dynamic Deconvolution”. The second method, here called “Inversion Filtering”, is a two-stage procedure. The first stage is the construction of a causal filter by factorization of the spectral function via Levinson-recursion. Filtering the seismogram is the second stage. The filtered seismogram is a good approximation for the reflection coefficients sequence (unless the coefficients are too large). In the non-linear terms of dynamic deconvolution and Levinson-recursion the noise could play havoc with the computation. In order to stabilize the algorithms, the bias of these terms is estimated and removed. Additionally incorporated is a statistical test for the reflection coefficients in dynamic deconvolution and the partial correlation coefficients in Levinson-recursion, which are set to zero if they are not significantly different from noise. The result of stabilization is demonstrated on synthetic seismograms. For unit spike source pulse and white noise, dynamic deconvolution outperforms inversion filtering due to its exact nature and lesser computational burden. On the other hand, especially in the more realistic bandlimited case, inversion filtering has the great advantage that the second stage acts linearly on the seismogram, which allows the calculation of the effect of the inversion procedure on the wavelet shape and the noise spectrum.     

ON THE POSSIBILITY OF SEISMIC EXPLORATION USING SURFACE TORQUE SOURCE AND RELATED TOPICS*

In this study we derive expressions for particle displacement or particle velocity anywhere inside a stratified earth and at its surface due to horizontal torque source located in the top layer. Equivalently, invoking Green's function reciprocity theorem, the solution applies also to the case of a surface or subsurface source when the resulting displacement or velocity is measured within the top layer. In order to evaluate the closed-form analytical solution economically and accurately it is advisable to introduce inelastic attenuation. Causal inelastic attenuation also lends the necessary realism to the computed seismic trace. To provide proof that the analytical solution is indeed correct and applicable to the multilayer case, a thick uniform overburden was assumed to consist of many thin layers. The correctness of the computed particle velocity response can be very simply verified by inspection. The computed response can also serve as a check on other less accurate methods of producing synthetic seismograms, such as the techniques of finite differences, finite elements, and various sophisticated ray-tracing techniques. It is not difficult to construct horizontal surface torque source. It appears that such source is well suited for seismic exploration in areas with a high-velocity surface layer. A realistic source function is analyzed in detail and normalized displacement response evaluated at different incidence angles in the near and the far fields. In an effort to distinguish the features of an SH torque seismogram from a pressure seismogram two models with identical layerings and layer parameters have been set up. As expected the torque seismogram is very different from the compressional seismogram. One desirable feature of a torque seismogram is the fast decay of multiples. Exact synthetic seismograms have many uses; some of them, such as the study of complex interference phenomena, phase change at wide angle reflection, channeling effects, dispersion (geometrical and material), absolute gain, and inelastic attenuation, can be carried out accurately and effortlessly. They can also be used to improve basic processing techniques such as deconvolution and velocity analysis. The numerical evaluation of the analytical solution of the wave equation as described in this paper has a long history. Most of the work leading to this paper was carried out by one of us (M. J. K.) in the years 1957 to 1968 at the Geophysical Research Corporation. However, the full testing of the various computer codes was carried out only very recently at the Phillips Petroleum Company.     

关于“反射法”计算综合地震图的实施方案

本文针对反射法计算综合地震图中的运算速度和存储安排等问题,提出一种有效的计算实施方案。文中附有三种模型的体波综合地震图计算实例。     

LEVINSON INVERSION OF EARTHQUAKE GEOMETRY SH-TRANSMISSION SEISMOGRAMS IN THE PRESENCE OF NOISE*

The Kunetz-Claerbout equation for the acoustic transmission problem in a layered medium in its original form establishes the relation between the transmission and the reflec tion response for P-waves in an horizontally layered medium and with vertical incidence. It states that the reflection seismogram due to an impulsive source at the surface, is one side of the autocorrelation of the seismogram due to an impulsive source at depth and a surface receiver. By adapting Claerbout's formulation to the transmission of SH-waves, the Kunetz-Claerbout equation also holds for reflection and transmission coefficients dependent on the incident angle. Thus, earthquake geometry SH-transmission seismograms can be used to caculate corresponding pseudoreflection seismograms which, in turn, can be inverted for the impedance structure using the Levinson algorithm. If the average incidence angle is known, a geometrical correction on the resulting impedance model can improve the resolution of layer thicknesses. In contrast to the inversion of reflection seismograms, the Levinson algorithm is shown to yield stable results for the inversion of transmission seismograms even in the presence of additive noise. This noise stabilization is inherent to the Kunetz-Claerbout equation. Results of inverted SH-wave microearthquake seismograms from the Swabian Jura, SW Germany, seismic zone obtained at recording site Hausen im Tal have been compared with sonic-log data from nearby exploration drilling at Trochtelfingen. The agreement of the main structural elements is fair to a depth of several hundred metres.     

关于“反射法”计算综合地震图的实施方案

本文针对反射法计算综合地震图中的运算速度和存储安排等问题,提出一种有效的计算实施方案。文中附有三种模型的体波综合地震图计算实例。     

Determining the focal mechanisms and depths of relatively small earthquakes using a few stations by full‐waveform modelling

Determining the focal mechanism of earthquakes helps us to better define faults and understand the stress regime. This technique can be helpful in the oil and gas industry where it can be applied to microseismic events. The objective of this paper is to find double couple focal mechanisms, excluding scalar seismic moments, and the depths of small earthquakes using data from relatively few local stations. This objective is met by generating three‐component synthetic seismograms to match the observed normalized velocity seismograms. We first calculate Green's functions given an initial estimate of the earthquake's hypocentre, the locations of the seismic recording stations and a 1D velocity model of the region for a series of depths. Then, we calculate the moment tensor for different combinations of strikes, dips and rakes for each depth. These moment tensors are combined with the Green's functions and then convolved with a source time function to produce synthetic seismograms. We use a grid search to find the synthetic seismogram with the largest objective function that best fits all three components of the observed velocity seismogram. These parameters define the focal mechanism solution of an earthquake. We tested the method using three earthquakes in Southern California with moment magnitudes of 5.0, 5.1 and 4.4 using the frequency range 0.1–2.0 Hz. The source mechanisms of the events were determined independently using data from a multitude of stations. Our results obtained, from as few as three stations, generally match those obtained by the Southern California Earthquake Data Center. The main advantage of this method is that we use relatively high‐frequency full‐waveforms, including those from short‐period instruments, which makes it possible to find the focal mechanism and depth of earthquakes using as few as three stations when the velocity structure is known.     

Teleseismic receiver function using stacking and smoothing of multi seismic-records at a single station

Receiver functions (RFs) obtained using teleseismic wave records at a seismic station and synthetic seismograms indicate that RF with a single teleseismic wave record is related to the selection of record section and to the calculating parameters of the RF. The scatter noise contained in the seismogram also affects the quality of RF. A new method for calculating receiver function, stacking and smoothing multi-seismic records in a single station, is presented in this paper. The RF results using some records and some synthetic seismograms with different noises indicate prominent mantle discontinuity and thus prove that the method is effective and satisfied.     

Focus-of-attention techniques in the automatic interpretation of seismograms

The focus-of-attention techniques implemented in SNA2, a knowledge-based system for seismogram interpretation, are presented. They consist of data compression of the input digital records, scanning of the compressed traces to detect candidate seismograms and extraction of seismogram features. A criterion is given to rate the clarity of seismograms; the clarity defines the order in which the system will consider them to build up the interpretation. The proposed techniques are simple and fast; they allow quick rejection of noise and focussing the attention of the system on the portions of traces containing relevant information.     

The optimum source－time function for generating finite－difference synthetic seismograms

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Interstation surface wave attenuation by autoregressive deconvolution

A new technique for calculating interstation Green's functions and attenuation coefficients for seismic surface waves is presented.The interstation Green's function is evaluated from the autocorrelation functions of the seismograms, which are obtained from a maximum entropy process.Since a data-invariant time window is not used, the evaluated Green's functions gives reliable information on both the amplitude and the phase spectra of the system.This new technique is compared with other methods by applying them to both synthetic and real data from a path in the Canadian shield.     

SEISMOGRAM SYNTHESIS AND RECOMPRESSION OF DISPERSIVE IN-SEAM SEISMIC MULTIMODE DATA USING A NORMAL-MODE SUPERPOSITION APPROACH

In spite of a geometrical rotation into radial and transverse parts, two- or three-component in-seam seismic data used for underground fault detection often suffer from the problem of overmoding ‘noise’. Special recompression filters are required to remove this multimode dispersion so that conventional reflection seismic data processing methods, e.g. CMP stacking techniques, can be applied afterwards. A normal-mode superposition approach is used to design such multimode recompression filters. Based on the determination of the Green's function in the far-field, the normal-mode superposition approach is usually used for the computation of synthetic single- and multi-mode (transmission) seismograms for vertically layered media. From the filter theory's point of view these Green's functions can be considered as dispersion filters which are convolved with a source wavelet to produce the synthetic seismograms. Thus, the design of multimode recompression filters can be reduced to a determination of the inverse of the Green's function. Two methods are introduced to derive these inverse filters. The first operates in the frequency domain and is based on the amplitude and phase spectrum of the Green's function. The second starts with the Green's function in the time domain and calculates two-sided recursive filters. To test the performance of the normal-mode superposition approach for in-seam seismic problems, it is first compared and applied to synthetic finite-difference seismograms of the Love-type which include a complete solution of the wave equation. It becomes obvious that in the case of one and two superposing normal modes, the synthetic Love seam-wave seismograms based on the normal-mode superposition approach agree exactly with the finite-difference data if the travel distance exceeds two dominant wavelengths. Similarly, the application of the one- and two-mode recompression filters to the finite-difference data results in an almost perfect reconstruction of the source wavelet already two dominant wavelengths away from the source. Subsequently, based on the dispersion analysis of an in-seam seismic transmission survey, the normal-mode superposition approach is used both to compute one- and multi-mode synthetic seismograms and to apply one- and multimode recompression filters to the field data. The comparison of the one- and two-mode synthetic seismograms with the in-seam seismic transmission data reveals that arrival times, duration and shape of the wavegroups and their relative excitation strengths could well be modelled by the normal-mode superposition approach. The one-mode recompressions of the transmission seismograms result in non-dispersive wavelets whose temporal resolution and signal-to-noise ratio could clearly be improved. The simultaneous two-mode recompressions of the underground transmission data show that, probably due to band-limitation, the dispersion characteristics of the single modes could not be evaluated sufficiently accurately from the field data in the high-frequency range. Additional techniques which overcome the problem of band-limitation by modelling all of the enclosed single-mode dispersion characteristics up to the Nyquist frequency will be mandatory for future multimode applications.     

Inversion of seismograms to determine simultaneously the moment tensor components and source time function for a point source buried in a horizontally layered medium

Summary A method of determining simultaneously the moment tensor and source time function in the point source approximation is presented. For trial values of the moment tensor components and of the source time function, parametrized by the sum of overlapping triangles delayed in time, theoretical seismograms can be synthetized and compared with the recorded ones. The iterative procedure determines the adjustment of source parameters until a good correlation of both synthetic and observed records is reached. The Green functions in a horizontally stratified medium are constructed with the use of a modal summation method.The limits of applicability of the algorithm are illustrated by the inversion of four synthetic seismograms constructed for two horizontally stratified models of the structure in Friuli area, Italy. The records constructed for the same structural model as for which the Green functions were computed can be inverted even in the high-frequency range. In the opposite case, when the records and Green functions used corresponded to different structural models, a good correlation of the input records with the final synthetics was obtained for low - pass filtered data only.Additional tests performed with input seismograms contaminated with random noise yielded good resolution of the moment tensor and the duration of the source time function even for a high noise to signal ratio.     

A NONITERATIVE PROCEDURE FOR INVERTING PLANE-WAVE REFLECTION DATA AT SEVERAL ANGLES OF INCIDENCE USING THE RICCATI EQUATION*

Various exact methods of inverting the complete waveform of vertical seismic reflection data to produce acoustic impedance profiles have been suggested. These inverse methods generally remain valid for nonvertical, plane-wave data, provided total reflection does not occur. Thus, in principle, the “seismogram” at each ray parameter in a slant stack can be interpreted separately. Rather than invert each plane-wave seismogram separately, they can all be interpreted simultaneously and an “average” model thus obtained. Inversion for both the velocity and the density also becomes possible when two or more plane-wave seismograms are simultaneously inverted. The theory for a noniterative inversion method, based on the time-domain Riccati equation, is discussed. Numerical examples of inversions using this technique on synthetic data demonstrate its numerical stability and the advantage of simultaneous inversion of several seismograms to reduce the effect of noise in the data and increase the stability of the inversion process.     

Seismogram Analysis of Earthquake C060394F,South Java: S-wave Velocity Structure

The S wave velocity structure between the hypocenter of C060394F earthquake,South Java and a series of observatory stations located in Australia and South-East Asia have been investigated through seismogram analysis in the time domain and the three Cartesian components.The synthetic seismogram is constructed from the PREMAN global earth model.Seismogram comparison between the measured and synthetic seismograms shows large discrepancies.A correction to the S wave velocity structure is needed to solve these d...     

分时窗提取地震子波及在合成地震记录中的应用

提出了利用地震和测井资料精确提取井旁地震子波的分时窗提取地震子波方法，将此方法用于合成地震记录的制作，提高了合成地震记录与地震剖面的吻合度和分辨率，文中详细介绍了该方法的具体实现步骤，并给出了模型处理分析和实例分析。     

An approach of refraction seismology for processing and modeling of local earthquake seismogram sections of virtual sources at multiple depths in seismogenic regions—application to Koyna-Warna region,India, for upper crustal P and S velocity structure

We present an approach based on controlled source seismology (CSS) methods, especially developed for processing and modeling of the local earthquake seismograms. Record sections of the local earthquake seismograms generated for multiple source depths illuminate the upper crustal velocity structure in the region. Extensive travel times and synthetic seismograms modeling of the observed record sections reveal the P and S velocity structure in the region. The strength of this approach essentially lies with the possibility of validating the upper crustal velocity models inferred in various subregions of the seismogenic region. A redundant and significantly large number of virtual source local earthquake seismogram sections, gathered for multiple source depths and varying source mechanisms in each of the subregions, validate the same set of P and S velocity models in that region. Further, those models are found to generate the synthetic seismograms consistent with the observed sections. The proposed approach effectively utilizes a reliable dataset from a great volume of well-located local earthquake recordings of a state-of-the-art digital seismograph network. Such a dataset of local earthquake seismograms in the Koyna-Warna active earthquake zone is used here to demonstrate this approach and obtained subregion-specific models of upper crustal P and S velocity structure in the epicentral region. The results indicate that the technique presented here is efficient for processing and modeling the local earthquake seismograms and deriving upper crustal velocity models in the seismogenic regions.