Seismic Imaging Methods Research Articles

P Wave Tomography Beneath Greenland and Surrounding Regions: 2. Lower Mantle

AbstractWe study the 3‐D P wave velocity (Vp) structure of the whole mantle beneath Greenland and surrounding regions using the latest P wave arrival time data. We use a new method of global seismic tomography by setting 3‐D grid nodes densely in the study volume to enhance the resolution. We invert ~5.6 million arrival times of P, pP, and PP waves from 16,257 earthquakes extracted from the ISC‐EHB catalog, which were recorded at 12,549 seismic stations in the world. Our results reveal a hot plume rising from the core‐mantle boundary beneath central Greenland, which is called the Greenland plume. This plume has the main conduit and two branches in the lower mantle, and the main conduit rises to the mantle transition zone (MTZ) beneath eastern Greenland, so it is distinguishable from the Iceland plume that appears to rise from a midmantle depth (~1,500 km) beneath Iceland. The Iceland plume itself is a powerful plume, but it may also be fed by hot mantle materials from three joints with other plumes: a branch of the Greenland plume at ~1,500 km depth, a plume beneath Western Europe at ~1,000 km depth, and the main conduit of the Greenland plume at the MTZ, leading to many active volcanoes in Iceland. We deem that the main conduit of the Greenland plume mixes with the Iceland plume incompletely and splits mainly into the Jan Mayen and Svalbard plumes in the upper mantle, which supply magma to the Jan Mayen hotspot and a geothermal area in western Svalbard, respectively.

P Wave Tomography Beneath Greenland and Surrounding Regions: 1. Crust and Upper Mantle

AbstractWe study the 3‐D P wave velocity (Vp) structure of the crust and upper mantle beneath Greenland and surrounding regions using the latest P wave arrival time data. The Greenland Ice Sheet Monitoring Network (GLISN), initiated in 2009, is an international project for seismic observation in these regions using 34 stations. We use a regional seismic tomography method to simultaneously invert P wave arrival times of local earthquakes and P wave relative traveltime residuals of teleseismic events. These data are extracted from the ISC‐EHB catalog; however, for the teleseismic data, we picked new arrival times from seismograms using a cross‐correlation method. Our tomographic results clearly reveal the Iceland plume, the Jan Mayen plume, and a newly discovered “Svalbard plume,” which merge together in the mantle transition zone. A high‐Vp body exists beneath the Greenland Sea, which might act as an obstacle against the rising Svalbard plume. Furthermore, our results reveal a remarkable low‐Vp anomaly elongated in the NW‐SE direction at depths ≤250 km beneath central Greenland, which is connected with the Iceland and Jan Mayen hotspots. Although previous studies have suggested a similar feature, our result is the first to show the low‐Vp zone existing at all depths in the Greenland lithosphere, and its spatial distribution coincides with a high heat flux region. These characteristics indicate that the low‐Vp zone reflects residual heat from the Iceland plume when the Greenland lithosphere passed over this plume at ~80–20 Ma. Our results also indicate the possible existence of residual heat from the Jan Mayen plume.

Separation and imaging of seismic diffractions using a localized rank-reduction method with adaptively selected ranks

Seismic diffractions are weak seismic events hidden within the more dominant reflection events in a seismic profile. Separating diffraction energy from the poststack seismic profiles can help infer the subsurface discontinuities that generate the diffraction events. The separated seismic diffractions can be migrated with a traditional seismic imaging method or a specifically designed migration method to highlight the diffractors, that is, the diffraction image. Traditional diffraction separation methods based on the underlying plane-wave assumption are limited by either the inaccurate slope estimation or the plane-wave assumption of the plane-wave destruction filter and thus will cause reflection leakage into the separated diffraction profile. The leaked reflection energy will deteriorate the resolution of the subsequent diffraction imaging result. We have adopted a new diffraction separation method based on a localized rank-reduction (LRR) method. The LRR method assumes the reflection events to be locally low-rank and the diffraction energy can be separated by a rank-reduction operation. Compared to the global rank-reduction method, the LRR method is more constrained in selecting the rank and is free of separation artifacts. We use a carefully designed synthetic example to demonstrate that the LRR method can help separate the diffraction energy from a poststack seismic profile with kinematically and dynamically accurate performance.

Velocity model estimation of karstic fault reservoirs using full-waveform inversion accelerated on graphics processing unit

The karstic fault reservoir is a type of hydrocarbon-enriched carbonate reservoir. It is a combination of small-scale caves, vugs, and fractures developing near deep-seated faults, which makes it difficult to delineate using traditional seismic imaging methods. Recent research on geologic characteristics of paleokarst reservoirs facilitates hydrocarbon exploration and exploitation in western China. To interpret karstic fault systems and reservoirs, the seismic image is an effective tool. A high-quality velocity model is essential for high-resolution migration. These seismic results contain crucial information to interpret reservoirs. Full-waveform inversion (FWI) is a powerful method to obtain high-precision velocity models because it makes use of the kinematic and dynamic information in the seismic full wavefield. To image such complicated and irregular fractured-cavity reservoirs accurately, we have applied a multiscale FWI method accelerated on graphics processing unit devices to fault-controlled paleokarst reservoir models. According to the model test results, FWI shows high performance in delineating the boundaries of fault-controlled karstic reservoirs. The proposed method also has the potential to characterize inner structures. Based on the high-precision velocity model provided by FWI, the seismic image obtained by reverse time migration is also improved. These seismic results will show the location, width, and shape of the fault-karst structure, which gives detailed information for fault-controlled paleokarst reservoir interpretation.

High-Resolution Anisotropic Prestack Kirchhoff Dynamic Focused Beam Migration

Kirchhoff beam migration is a kind of ray-based seismic imaging method boasting the advantages of both high efficiency and high accuracy. In this paper, anisotropic ray tracing will be applied to extend it to an anisotropic seismic imaging method. However, two problems exist in this method for imaging calculation: Firstly, the conventional local plane wave decomposition method has a low computational precision; secondly, the original beam propagator diverges quickly when the propagation distance increases. These two problems can both increase imaging noise, and finally reduce the resolution of the final imaging results. In this paper, the high-resolution anisotropic Kirchhoff dynamic focused beam migration is proposed to solve these two problems. Local plane wave decomposition method considered from the perspective of inversion is employed to obtain higher-quality slant stack data and dynamic focused beam propagator is adopted to control the divergence of beams. Both the anisotropic layer model and Hess model are adopted to test the imaging ability of the new method.

Seismic Imaging Method for Medical Ultrasound Systems

Medical ultrasound usually implements ray-based imaging algorithms, in which the most severe limitation involves the implicit assumption of constant-velocity media. When there are tissues with different velocities---typical for the human body---, the image of the underlying targets is strongly degraded in placement and resolution, due to $p\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}e$ $a\phantom{\rule{0}{0ex}}b\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n$. To address this problem, the authors look to concepts developed in the context of seismic prospecting, relying upon an undulatory description of the physical process. Laboratory assessment of this imaging strategy, even in the presence of an aberrant layer, reveals remarkable spatial resolution and highly accurate target placement.

Adjoint-based inversion for porosity in shallow reservoirs using pseudo-transient solvers for non-linear hydro-mechanical processes

Porous flow is of major importance in the shallow subsurface, since it directly impacts on reservoir-scale processes such as waste fluid sequestration or oil and gas exploration. Coupled and non-linear hydro-mechanical processes describe the motion of a low-viscous fluid interacting with a higher viscous porous rock matrix. This two-phase flow may trigger the initiation of solitary waves of porosity, further developing into vertical high-porosity pipes or chimneys. These preferred fluid escape features may lead to localised and fast vertical flow pathways potentially problematic in the case of for instance CO2 sequestration. Constraining the porosity and the non-linearly related permeability distribution in such environments is a major challenge. Although seismic imaging methods accurately localise the high-porosity chimneys in the inverted wave-speed field, the conversion to porosity is not straightforward. We develop an inversion framework to reconstruct the unknown porosity field using relevant observable quantities such as subsurface fluid fluxes. We introduce the adjoint framework for the two-phase flow equations, which allows for efficient calculations of the pointwise gradients of the flow solution with respect to the porosity. We then use the gradients in a gradient descent method to invert for the pointwise porosity. We solve the forward and the adjoint equations using an iterative matrix-free pseudo-transient approach with the finite difference method. The proposed parallel solving procedure executes optimally on the latest many-core hardware accelerators such as GPUs. Numerical results show that an inversion for porosity is challenging if data is sparse since the porosity is very locally sensitive to the fluid flux. We introduce the concepts of sensitivity kernels as employed in seismology for the set of two-phase equations and suggest this approach as a standard for future studies.

3D Crustal Structure and Seismicity Characteristics of Changning–Xingwen Area in the Southwestern Sichuan Basin, China

ABSTRACTUsing seismic data recorded on permanent and temporary stations around the Changning area in the Sichuan basin, the high-resolution 3D crustal VP, VS, VP/VS models and earthquake locations in the Changning–Xingwen area are obtained using the VP/VS model consistency-constrained double-difference seismic tomography method. The results show that crustal structures in the source area of the 2019 Ms 6.0 Changning earthquake have significant variations, especially in the depth of 0–7 km. Seismic activity in the Shuanghe and Yutan anticline areas before the Ms 6.0 Changning earthquake outlined several northeast-trending stripes, implying pre-existing small-scale faults that are perpendicular to the major northwest-striking faults in the Changning–Shuanghe anticline system. We found that the Ms 6.0 Changning earthquake broke through these pre-existing small-scale faults and extended from the Shuanghe to the Yutan anticlines. Both the rupture process and aftershock activity were influenced by the pre-existing small-scale faults. Most earthquakes within the Changning area are located in a slant zone that gradually deepens from the Shuanghe anticline on the east to the Yutan anticline on the west with the maximum depth from 5 to 10 km, which are associated with obvious high-VS and low-VP/VS features. The relocated seismic clusters in the Luochang–Jianwu syncline area have different strikes and dips, which are mainly located at the edge of low-velocity anomaly bodies and correspond to the low-VP/VS area.

Velocity structure of the upper crust and its correlation with earthquake swarms activity in Laizhou Bay and its adjacent areas, China

This study used the double-difference seismic tomography method to obtain the upper crustal velocity structure in Laizhou Bay and its adjacent areas (LBAA). We found that the horizontal and vertical distributions of the earthquakes after relocation in earthquake swarms are more concentrative than that before relocation. The lateral heterogeneity of crustal velocity structure near the surface in the LBAA is weak, and the low-velocity sedimentary caprocks are developed in most areas except for the Jiaobei uplift. The velocity structure in 5–25 km depth range is highly heterogeneity, which is closely related to different tectonic units. The local uplift tectonic units in Jiyang depression show high-velocity anomalies and should have deep crustal media properties. The high-velocity anomalies under the crust of Tancheng–Lujiang fault zone and the northern Laizhou Bay indicate the properties of upwelling mantle material media. Earthquake swarms activity in the study area are mainly concentrated in the high-velocity interlayer of the upper crust and its periphery. Compared with the relatively stable high-velocity body at the bottom crust, the location of high-velocity interlayer in the study area is more prone to earthquakes under the combined action of gravity and tectonic stress.

Inferring rheology and geometry of subsurface structures by adjoint-based inversion of principal stress directions

SUMMARY Imaging subsurface structures, such as salt domes, magma reservoirs or subducting plates, is a major challenge in geophysics. Seismic imaging methods are, so far, the most precise methods to open a window into the Earth. However, the methods may not yield the exact depth or size of the imaged feature and may become distorted by phenomena such as seismic anisotropy, fluid flow, or compositional variations. A useful complementary method is therefore to simulate the mechanical behaviour of rocks on large timescales, and compare model predictions with observations. Recent studies have used the (non-linear) Stokes equations and geometries from seismic studies in combination with an adjoint-based approach to invert for rheological parameters that are consistent with surface observations such as GPS velocities. Nevertheless, it would be useful to use other surface observations, such as principal stress directions, as constraints as well. Here, we derive the adjoint formulation for the case that principal stress directions are used as observables with respect to rheological parameters. Both an algebraic and a discretized derivation of the adjoint equations are described. This thus enables the usage of two data fields - surface velocities and stress directions - as a misfit for the inversion. We test the performance of the inversion for principal stress directions on simplified 3-D test cases. Finally, we demonstrate how the adjoint approach can be used to compute 3-D geodynamic sensitivity kernels, which highlight the areas in the model domain that have the largest impact on the misfit value of a particular point. This provides a simple, yet powerful, way to visualize which parts of the model domain are of key importance if changing rheological constants.

OpenMP Implementation of a Novel Potential-Field-Data Source-Growth-Based Inversion Approach for 3D Salt Imaging in Deepwater Gulf of Mexico

Potential-field-data imaging of complex geological features in deepwater salt-tectonic regions in the Gulf of Mexico remains an open active research field. There is still a lack of resolution in seismic imaging methods below and in the surroundings of allochthonous salt bodies. In this work, we present a novel three-dimensional potential-field-data simultaneous inversion method for imaging of salt features. This new approach incorporates a growth algorithm for source estimation, which progressively recovers geological structures by exploring a constrained parameter space; restrictions are posed from a priori geological knowledge of the study area. The algorithm is tested with synthetic data corresponding to a real complex salt-tectonic geological setting commonly found in exploration areas of deepwater Gulf of Mexico. Due to the huge amount of data involved in three-dimensional inversion of potential field data, the use of parallel computing techniques becomes mandatory. In this sense, to alleviate computational burden, an easy to implement parallelization strategy for the inversion scheme through OpenMP directives is presented. The methodology was applied to invert and integrate gravity, magnetic and full tensor gradient data of the study area.

The MAGIC Experiment: A Combined Seismic and Magnetotelluric Deployment to Investigate the Structure, Dynamics, and Evolution of the Central Appalachians

Abstract The eastern margin of North America has undergone multiple episodes of orogenesis and rifting, yielding the surface geology and topography visible today. It is poorly known how the crust and mantle lithosphere have responded to these tectonic forces, and how geologic units preserved at the surface related to deeper structures. The eastern North American margin has undergone significant postrift evolution since the breakup of Pangea, as evidenced by the presence of young (Eocene) volcanic rocks in western Virginia and eastern West Virginia and by the apparently recent rejuvenation of Appalachian topography. The drivers of this postrift evolution, and the precise mechanisms through which relatively recent processes have modified the structure of the margin, remain poorly understood. The Mid-Atlantic Geophysical Integrative Collaboration (MAGIC) experiment, part of the EarthScope USArray Flexible Array, consisted of collocated, dense, linear arrays of broadband seismic and magnetotelluric (MT) stations (25–28 instruments of each type) across the central Appalachian Mountains, through the U.S. states of Virginia, West Virginia, and Ohio. The goals of the MAGIC deployment were to characterize the seismic and electrical conductivity structure of the crust and upper mantle beneath the central Appalachians using natural-source seismic and MT imaging methods. The MAGIC stations operated between 2013 and 2016, and the data are publicly available via the Incorporated Research Institutions for Seismology Data Management Center.

On the impact of alternative seismic time imaging methods on subsurface fault mapping in the northernmost Molasse Basin, Switzerland

The identification and characterization of tectonic faults in the subsurface represent key aspects of geologic exploration activities across the world. We have evaluated the impact of alternative seismic time imaging methods on initial subsurface fault mapping in three dimensions in the form of a case study situated in the most external foreland of the European Central Alps (the northernmost Molasse Basin). Four different seismic amplitude volumes of one and the same 3D seismic data set, differing in imaging technologies and parameterizations applied, were considered for the interpretation of a fault zone dissecting a Mesozoic sedimentary sequence that is characterized by a pronounced mechanical stratigraphy and has witnessed a multiphase tectonic evolution. For this purpose, we interpreted each seismic amplitude volume separately. In addition, we computed a series of seismic attributes individually for each volume. Comparison of the different data interpretations revealed consistent results concerning the mapping of the seismic marker horizons and main fault segments. Deviations concern the apparent degree of vertical and lateral fault zone segmentation and the occurrence of small-scale fault strands that may be regarded as important fault kinematic indicators. The compilation of all fault interpretations in map form allows the critical assessment of the robustness of the initial seismic fault mapping, highlighting well-constrained from poorly defined fault zone elements. We conclude that the consideration of multiple seismic processing products for subsurface fault mapping is advisable to evaluate general imaging uncertainties and potentially guide the development of fault zone model variants to tackle previously discussed aspects of conceptual interpretation uncertainties.

A scalable online algorithm for passive seismic tomography in underground mines

Understanding and monitoring the seismic responses of rock masses to massive mining are crucial for safety and economic viability of ever larger and deeper underground operations. Seismic monitoring can be used to detect stress variations and hazardous instabilities, but its effectiveness requires accurate estimations of the nonhomogeneous propagation velocity of microseismic waves. While predetermined velocity models are not accurate enough and might bias hypocenter localization, using active-source seismic tomography methods to estimate the velocity field provides limited spatial coverage. Thus, passive seismic tomography using first-arrival traveltimes of mining-induced microseisms (of unknown hypocenters) constitutes a promising tool. However, available methods solving this high-dimensional statistical inverse problem do not scale well with the data set size and cannot easily refine or update estimations with new data. We have developed a novel passive seismic tomography method able to dynamically learn the nonhomogeneous velocity field from a streaming of noisy first-arrival times, online (in real time) or from catalogs. We have developed a new Bayesian approach that avoids linearizing the forward problem and allows for general 3D velocity models. This is combined with the use of the stochastic gradient descent (SGD) method, which underlies much of the recent progress in machine learning and provides increasing accuracy at a cost scaling linearly with the data set size. Moreover, we introduce an adaptive variant of SGD based on raypath density, which significantly improves the speed of the algorithm, and we implement a parallel version of our method enabling its systematic use in real applications. These include the design of optimal sensor locations, the dynamic update of velocity estimates in production conditions, and the real-time determination of hypocenters and their uncertainty. Our method’s reach and effectiveness are illustrated with simulated seismic data on 3D checkerboards, using synthetic and real acquisition geometries, and on a dense 2D velocity grid.

A complex point-source solution of the acoustic eikonal equation for Gaussian beams in transversely isotropic media

The complex traveltime solutions of the complex eikonal equation are the basis of inhomogeneous plane-wave seismic imaging methods, such as Gaussian beam migration and tomography. We have developed analytic approximations for the complex traveltime in transversely isotropic media with a titled symmetry axis, which is defined by a Taylor series expansion over the anisotropy parameters. The formulation for the complex traveltime is developed using perturbation theory and the complex point-source method. The real part of the complex traveltime describes the wavefront, and the imaginary part of the complex traveltime describes the decay of the amplitude of waves away from the central ray. We derive the linearized ordinary differential equations for the coefficients of the Taylor-series expansion using perturbation theory. The analytical solutions for the complex traveltimes are determined by applying the complex point-source method to the background traveltime formula and subsequently obtaining the coefficients from the linearized ordinary differential equations. We investigate the influence of the anisotropy parameters and of the initial width of the ray tube on the accuracy of the computed traveltimes. The analytical formulas, as outlined, are efficient methods for the computation of complex traveltimes from the complex eikonal equation. In addition, those formulas are also effective methods for benchmarking approximated solutions.

A Novel Wavefield-Reconstruction Algorithm for RTM in Attenuating Media

Q-compensated reverse-time migration ( Q-RTM) has been proven as an efficient method for seismic imaging with high fidelity. However, the source (forward) and receiver (backward) wavefields propagate along the opposite direction of time, and the recursive computation with the out-of-order access requires that all the wavefields of source propagation should be stored on the hard disk. For massive amounts of seismic data, saving the source wavefield from the central processing unit (CPU) [or graphics processing unit (GPU)] device to the disk and loading these data from the hard disk to the CPU (or GPU) device become extremely intensive in time and storage, which has been a bottleneck of Q-RTM. Several methods have been developed to reduce the huge wavefield storage in acoustic media, but are not applicable in the attenuated media. In this letter, we present a reversible hybrid absorbing boundary condition for Q-RTM, which is implemented by mixing the reversible attenuation and the random boundary conditions. Based on our developed new boundary, we just need to save the wavefield at the last one or two time steps in the forward process and then reconstruct the source wavefield in the time-reversal order. Numerical results demonstrate that the method can avoid the huge seismic data input and output (I/O) requirement and improve the computational efficiency dramatically.

Eikonal Equation-Based Seismic Tomography of the Source Areas of the 2008 Mw 7.9 Wenchuan Earthquake and the 2013 Mw 6.6 Lushan Earthquake

ABSTRACT We use the eikonal equation-based seismic travel-time tomography method to image the source areas of the 2008 Wenchuan earthquake and the 2013 Lushan earthquake in the Longmenshan fault zone. High-resolution VP and VS models are obtained by inverting 75,686 P-wave and 74,552 S-wave travel times of local earthquakes during the period from 2009 to 2018. The tomographic models reveal strong crustal velocity heterogeneities in the study area. A significant velocity contrast exists across the Longmenshan fault zone: The western Songpan–Ganzi block is a high-velocity body, whereas the eastern Sichuan basin is a low-velocity anomaly. The hypocenter of the 2008 Wenchuan earthquake is between a high-velocity and a low-velocity anomaly. Beneath the Wenchuan mainshock, there is a significant low-velocity structure in the lower crust. The 2013 Lushan earthquake occurred in rocks associated with a high-velocity anomaly. A distinct low-velocity zone with low seismicity is imaged between the 2008 Wenchuan earthquake and the 2013 Lushan earthquake, where the crustal ductile deformation is likely to occur. The Baoxing complex to the northwest of the Lushan hypocenter exhibits as a high-velocity anomaly, which may be a carrier of stress accumulation and more prone to seismic activities in the future.

Landslide monitoring using seismic refraction tomography – The importance of incorporating topographic variations

Seismic refraction tomography provides images of the elastic properties of subsurface materials in landslide settings. Seismic velocities are sensitive to changes in moisture content, which is a triggering factor in the initiation of many landslides. However, the application of the method to long-term monitoring of landslides is rarely used, given the challenges in undertaking repeat surveys and in handling and minimizing the errors arising from processing time-lapse surveys. This work presents a simple method and workflow for producing a reliable time-series of inverted seismic velocity models. This method is tested using data acquired during a recent, novel, long-term seismic refraction monitoring campaign at an active landslide in the UK. Potential sources of error include those arising from inaccurate and inconsistent determination of first-arrival times, inaccurate receiver positioning, and selection of inappropriate inversion starting models. At our site, a comparative analysis of variations in seismic velocity to real-world variations in topography over time shows that topographic error alone can account for changes in seismic velocity of greater than ±10% in a significant proportion (23%) of the data acquired. The seismic velocity variations arising from real material property changes at the near-surface of the landslide, linked to other sources of environmental data, are demonstrated to be of a similar magnitude. Over the monitoring period we observe subtle variations in the bulk seismic velocity of the sliding layer that are demonstrably related to variations in moisture content. This highlights the need to incorporate accurate topographic information for each time-step in the monitoring time-series. The goal of the proposed workflow is to minimize the sources of potential errors, and to preserve the changes observed by real variations in the subsurface. Following the workflow produces spatially comparable, time-lapse velocity cross-sections formulated from disparate, discretely-acquired datasets. These practical steps aim to aid the use of the seismic refraction tomography method for the long-term monitoring of landslides prone to hydrological destabilization.

Source‐Independent Passive Seismic Reverse‐Time Structure Imaging With Grouping Imaging Condition: Method and Application to Microseismic Events Induced by Hydraulic Fracturing

AbstractSeismic imaging with active seismic sources can be used to image subsurface structures such as faults, fractures, and layer interfaces with higher resolutions than tomographic methods. However, for characterizing large‐scale three‐dimensional structures, oftentimes it is too expensive and thus impractical to conduct active seismic survey. Seismic imaging using passive sources has been used to image structures through the “pseudoactive” source imaging by assuming source information is known. However, in practice there exist some uncertainties on source information including location, origin time, source time function, and radiation pattern, which can inevitably affect the final imaging result. In this study, we propose a new source‐independent passive seismic imaging method based on reverse‐time imaging with converted waves and a new imaging condition. This method uses the interference between P and S waves at conversion points for structure imaging by back‐propagating seismograms recorded by all receivers. Since no forward modeling is needed in this method, source information is not needed. A new grouping imaging condition is proposed to improve the image resolution, in which seismic receivers are divided into several groups and the separated P and S wavefields of different groups are multiplied and then stacked over time to get an image. We test the new method on both synthetic and real data sets based on a downhole microseismic system that is used for monitoring a shale gas hydraulic fracturing treatment. The results show that the proposed passive seismic imaging method does not depend on knowing source information and can achieve higher imaging resolution.

Amplitude‐compensated Laplacian filtering of reverse time migration and its application

ABSTRACTReverse time migration is an advanced seismic migration imaging method. When the source wavefield and the receiver wavefield are cross‐correlated, the cross‐correlations of direct arrivals, backscattered waves and overturned waves will produce a lot of low‐frequency noise, which will mask the final imaging results. Laplacian filtering, as a common method to suppress low‐frequency noise, can adapt to any complex media, just adding a little computational cost. However, simple direct Laplacian filtering will destroy the characteristics of the useful signals. Therefore, the amplitude needs to be compensated before filtering when using the Laplacian filtering method. Zhang and Sun proposed an improved Laplacian filtering method and gave a simple calculation formula and explanation. This method can effectively suppress the low‐frequency noise in reverse time migration while retaining the useful signal characteristics, but lacks detailed and strict mathematical derivation. Therefore, this paper gives a detailed and rigorous mathematical derivation of the amplitude‐compensated Laplace filtering method from the point of view of amplitude‐preserved filtering. The source wavelet is used instead of the source wavefield to compensate amplitude, just adding a little calculation cost. Finally, the amplitude‐compensated Laplace filtering method is verified by two theoretical models and compared with the direct Laplacian filtering method.