Weijian Mao

Simultaneous inversion of velocity structures and hypocentral locations: application to the Friuli seismic area NE Italy

A layeredP- andS-wave velocity model is obtained for the Friuli seismic area using the arrival time data ofP- andS-waves from local earthquakes. A damped least-squares method is applied in the inversion.The data used are 994P-wave arrival times for 177 events which have epicenters in the region covered by the Friuli seismic network operated by Osservatorio Geofisico sperimentale (OGS) di Trieste, which are jointly inverted for the earthquake hypocenters andP-wave velocity model. TheS-wave velocity model is estimated on the basis of 978S-wave arrival times and the hypocenters obtained from theP-wave arrival time inversion. We also applied an approach thatP- andS-wave arrival time data are jointly used in the inversion (Roecker, 1982). The results show thatS-wave velocity structures obtained from the two methods are quite consistent, butP-wave velocity structures have obvious differences. This is apparent becauseP-waves are more sensitive to the hypocentral location thanS-waves, and the reading errors ofS-wave arrival times, which are much larger than those ofP-waves, bring large location errors in the joint inversion ofP- andS-wave arrival time. The synthetic data tests indicated that when the reading errors ofS-wave arrivals are larger than four times that ofP-wave arrivals, the method proposed in this paper seems more valid thanP- andS-wave data joint inversion. Most of the relocated events occurred in the depth range between 7 and 11 km, just above the biggest jump in velocity. This jump might be related to the detachment line hypothesized byCarulli et al. (1982). From the invertedP- andS-wave velocities, we obtain an average value 1.82 forVp/Vs in the first 16 km depth.

Rapid multi-wave-type ray tracing in complex 2-D and 3-D isotropic media

We describe a method for seismic ray tracing in complex 2-D and 3-D heterogeneous isotropic media. Both the interface geometry and the horizontal velocity field are parameterized by using nonuniformly spaced cubic B‐spline nodes. In particular, we present a modified cubic B‐spline method for modeling discontinuities. This model parameterization scheme facilitates tomographic inversion of traveltimes and can represent any realistic geological structure that is continuously varying with embedded discontinuities. Many wave types, such as transmitted, reflected, refracted, mode‐converted, diffracted, and turning waves, are desirable for complex geological models. We select rays of various wave types by choice of initial paths and refine them by applying Fermats minimum time principle. Since the raypath is piecewise linear between interfaces, we solve a system of linearized equations by iteration to produce the actual raypath between source and receiver. The method is fast and unifies the ray‐tracing procedur...

Depth imaging examples and methodology in the Gulf of Mexico

Advances in seismic imaging over the past several years have revolutionized interpretation of geologic structures in complex areas. Nowhere has the impact of this technology been greater than the Gulf of Mexico, where the ability to interpret structures in subsalt areas has led to very large oil discoveries. Interestingly, although many techniques used in imaging these complex areas are new, the basis for many may be found in the classic methods of time imaging, many of which are still used in large-scale production depth imaging. Inherent in these techniques has been the assumption of a locally flat-layered earth consistent with hyperbolic moveout, which although incorrect for complex areas such as the subsalt imaging in the Gulf of Mexico, carries with it a robustness and determinism. Gradually, depth-imaging techniques are evolving to overcome the limitations of a local flat-layer earth assumption but at the cost of this determinism. For a true depth model, velocities, densities, and other parameters must be determined in a spatially varying way, so there is an explosion in the number of parameters to be determined. A consistent earth model from the depth-imaging perspective relies on measurement redundancy—i.e., reflections from the subsurface appear on traces from numerous source-receiver pairs in the acquisition geometry. The imaging process is then done in a way that produces not one but many images, each created using energy that has traveled through different parts of the earth. Consistency requires that these images agree. Hence, difficulties have shifted from the imaging algorithms themselves, as with the local flat-layer assumption in time imaging, to those associated with the data, their redundancy, and the uncertainty in determining a consistent model. In this article we examine a number of examples of depth imaging in the Gulf of Mexico. In the process we chronicle depth-imaging methods as they …

Transmission-reflection tomography: Application to reverse VSP data

A multiphase tomographic algorithm is presented that allows 2-D and 3-D slowness (inverse of velocity) and variable reflector depth to be reconstructed simultaneously from both transmission and reflection traveltimes. We analyze the ambiguity in the determination of velocity and depth in transmission and reflection data and realize that depth perturbation is more sensitive to reflection traveltime anomalies than slowness perturbation, whereas the reverse is true of transmission traveltime anomalies. Because of the constraints on velocity and depth provided by the different wave types, this algorithm reduces the ambiguity substantially between velocity and depth prevalent in reflection tomography and also avoids the undetermined problem in transmission tomography. The linearized inversion was undertaken iteratively by decoupling velocity parameters from reflector depths. A rapid 2-D and 3-D ray‐tracing algorithm is used to compute transmission and reflection traveltimes and partial derivatives with respect...

Three-Operator Proximal Splitting Scheme for 3-D Seismic Data Reconstruction

The proximal splitting algorithm, which reduces complex convex optimization problems into a series of smaller subproblems and spreads the projection operator onto a convex set into the proximity operator of a convex function, has recently been introduced in the area of signal processing. Following the splitting framework, we propose a novel three-operator proximal splitting (TOPS) algorithm for 3-D seismic data reconstruction with both singular value decomposition (SVD)-based low-rank constraint and curvelet-domain sparsity constraint. Compared with the well-known forward–backward splitting (FBS) method, our proposed TOPS algorithm can be flexibly employed to recover a signal satisfying double convex constraints simultaneously, such as low-rank constraint and sparsity constraint used in this letter. We have used both synthetic and field data examples to demonstrate the superior performance of the TOPS method over traditional SVD-based low-rank method and curvelet-domain sparsity method based on the FBS framework.

Simultaneous determination of time delays and stacking weights in seismic array beamforming

An algorithm for the estimation of time delays and weights in an arbitrary-single or three-component seismic array is developed by the use of a linearized waveform inversion technique. This algorithm differs from conventional crosscorrelation methods in its ability to simultaneously obtain time delays and weights by minimizing residuals of all possible waveform fittings, and by its robustness in the presence of high random noise levels and local geological scattering. There are N stations in an array, and for each station, a beam is formed by a weighted linear combination of the remaining (N - 1) seismic traces. The time delays and weights are model parameters to be found by minimizing the sum of N objective functions. Two optimization algorithms for solving the least-squares problem, singular-value decomposition and conjugate gradient, are compared, and the conjugate gradient method is found to be satisfactory and faster for large arrays. The algorithm was tested using synthetic array data with high noise, real data from shots in a borehole to a linear array on land, and Ms 6.7 earthquake data recorded with a broadband three-component array. The success with synthetic and real data shows the algorithm to be useful for seismic data stacking, residual static corrections, and phase picking when the data quality is poor.

Regional And High-resolution 3D Pore-pressure Prediction In Deep-water Offshore West Africa

Using both a regional and a high-resolution (HR), automated 3D velocity analysis method and the appropriate rock models, we predict a regressive pore-pressure system in a deep-water basin, offshore West Africa. The onset of overpressure takes place at the seafloor. The pressure gradient increases slowly but almost continuously, then rapidly to a maximum value, and then gradually reverses back to a lower value. The pressure profile follows certain geologic time horizons and structures very closely. Radial canyons on the seafloor significantly affect the porepressure profile. The high-resolution study provides velocity and pore pressure in more detail than the regional study.

Automated Interval Velocity Inversion

Automated velocity picking combined with a vertical velocity update provides an effective tool for automated interval velocity inversion. Interval velocities are reconstructed by minimizing the differences between picked stacking velocities and calculated RMS velocities. Median smoothing operators are used to control the resolution of the geological structure. This results in a gridded velocity model which can be directly used for depth migration. A key feature of this technique is that no horizon picking is required. The output consists of a fully gridded velocity model which in turn can be fed iteratively to a subsequent depth migration. The use of migrated CMP gathers not only makes the vertical update the appropriate inversion tool but it also reduces stacking conflicts, thereby making the picking of stacking velocities more accurate.

Fast P wave propagation in subducted Pacific lithosphere : refraction from the plate

P waves traveling from events in the Tonga-Kermadec seismic zone to stations in New Zealand are very fast with highly emergent, dispersed waveforms. Ray tracing has shown the waves to travel close to the subducted Pacific plate throughout their length, and synthetic seismogram calculations have shown the dispersion requires a very thin (8–12 km) fast layer. Previous work has been based on data from analogue records and one digital, single-component short-period instrument; no polarization analysis was possible, and measurements of dispersion were limited by the bandwidth. From January 1991 to August 1992 we deployed nine broad band, three-component seismometers in good sites for observing these arrivals; the data are augmented by three-component, short-period digital records from new stations of the New Zealand National Network. In this study we analyze 1191 broad-band and 2076 short period seismograms from 71 events for polarization of the initial P wave. The polarization directions are found to be up to 30° off the great circle path and consistently steep (20° from vertical). They are too steep to be explained by standard ray paths or refraction from a fast horizontal layer. We invert the polarization directions for a tilted interface beneath the array and use arrival times to control the depth to the interface, which is found to lie close to the top of the subducted plate inferred from the seismicity. We conclude that these precursive, emergent P waves have traveled through a fast layer close to the top of the subducted plate and refract upward to the station. A second arrival, with lower dominant frequency near 1 Hz and normal travel time, is occasionally seen on both broad band and short-period stations. Its polarization direction is similarly steep but difficult to measure; the evidence suggests that it also travels within the plate with similar ray path to the precursor.

Evidence for variations of mechanical properties in the Friuli seismic area

Abstract Tidal strains of the earth were extracted from three horizontal strainmeter records (1979–1986) in the Friuli seismic area by the “filter method”. The areal strain factor, ignoring the tidal loading effects, shows that its time variation is significant: their amplitudes in 1986 are about 50% of those in 1979. The modifications of mechanical properties, estimated in terms of the local shear and bulk modulus variations, were obtained considering the envelope of the tidal strain signals. The seismic wave velocity determined by the simultaneous inversion of the arrival time data of the local seismometric network displayed comparable changes. A major change both in the seismic velocities and the elastic parameters started in March 1982, which was about 11 months before an earthquake of magnitude 4.1, the largest event from 1979 to 1986, which occurred within the seismic network on Feb. 10, 1983.