scholarly journals Application of the POCS inversion method to cross‐borehole imaging

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 941-948 ◽  
Author(s):  
Ingi Th. Bjarnason ◽  
William Menke
Keyword(s):  
Velocity Field ◽  
Convex Sets ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Synthetic Data ◽  
Inversion Method ◽  
Tomographic Image ◽  
Tomographic Images ◽  
Wavenumber Domain ◽  
Experimental Geometry

Cross‐borehole tomography suffers from a well‐known problem of data incompleteness: the limited ray coverage dictated by the poor experimental geometry implies that certain features of the velocity field are not determined by the data. Construction of a tomographic image of the velocity field therefore requires the addition of prior constraints to the inversion. In the Fourier wavenumber domain (assuming straight‐line rays), the process of adding prior constraints is equivalent to specifying unmeasured wavenumber coefficients. The projection onto convex sets (POCS) algorithm can impose physically plausible constraints that allow high quality tomographic images to be produced. Each constraint is viewed as defining a set (in function space) of images that satisfy that particular constraint. The POCS method finds one or more images in the intersection of the constraining sets, which is equivalent to finding an image that simutaneously satisfies a number of constraints including the observed data. The sets of images that we employ include: those that satisfy the data in the sense of having certain known wavenumber components, those that have bounded energy in certain unmeasured wavenumber components, those that have seismic velocity bounded everywhere (e.g., non‐negative), and those in which the velocity structure is confined to the region between the boreholes. An advantage of the POCS algorithm is that it allows both space‐domain and wavenumber‐domain constraints to be imposed simultaneously. In our implementation of the POCS algorithm, we make use of the fast Fourier transform to rapidly iterate between the space and Fourier‐wavenumber domains. We test the method on synthetic data, and show that it significantly reduces the artifacts in the image, when compared to other methods. We then apply it to data from a cross‐borehole experiment in Manitoba, Canada, that were previously studied by others. We achieve a tomographic image of the velocity field that is similar in many respects to the results of others, but which possesses fewer artifacts.

scholarly journals Delineation of Upper Crustal Structure Beneath the Island of Lombok, Indonesia, Using Ambient Seismic Noise Tomography

2021 ◽  
Vol 9 ◽  
Author(s):  
Achmad F. N. Sarjan ◽  
Zulfakriza Zulfakriza ◽  
Andri D. Nugraha ◽  
Shindy Rosalia ◽  
Shengji Wei ◽  
...  
Keyword(s):  
Group Velocity ◽  
Ambient Noise ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Inversion Method ◽  
Good Resolution ◽  
Ambient Noise Tomography ◽  
Fast Marching ◽  
Waveform Data ◽  
Short Period

We have successfully conducted the first ambient noise tomography on the island of Lombok, Indonesia using local waveform data observed at 20 temporary stations. Ambient noise tomography was used to delineate the seismic velocity structure in the upper crust. The waveform data were recorded from August 3rd to September 9th, 2018, using short-period and broadband sensors. There are 185 Rayleigh waves retrieved from cross-correlating the vertical components of the seismograms. We used frequency-time analysis (FTAN) to acquire the interstation group velocity from the dispersion curves. Group velocity was obtained for the period range of 1 s to 6 s. The group velocity maps were generated using the subspace inversion method and Fast Marching Method (FMM) to trace ray-paths of the surface waves through a heterogeneous medium. To extract the shear wave velocity (Vs) from the Rayleigh wave group velocity maps, we utilize the Neighborhood Algorithm (NA) method. The 2-D tomographic maps provide good resolution in the center and eastern parts of Lombok. The tomograms show prominent features with a low shear velocity that appears up to 4 km depth beneath Rinjani Volcano, Northern Lombok, and Eastern Lombok. We suggest these low velocity anomalies are associated with Quaternary volcanic products, including the Holocene pyroclastic deposits of Samalas Volcano (the ancient Rinjani Volcano) which erupted in 1257. The northeast of Rinjani Volcano is characterized by higher Vs, and we suggest this may be due to the presence of igneous intrusive rock at depth.

scholarly journals A proper methodology aimed at surface wave tomography

1997 ◽  
Vol 40 (1) ◽  
Author(s):  
F. J. Sabadell ◽  
F. J. Serón ◽  
J. Badal
Keyword(s):  
Surface Wave ◽  
Convex Sets ◽  
Velocity Structure ◽  
Imaging Techniques ◽  
Spatial Prediction ◽  
Wave Dispersion ◽  
Inversion Method ◽  
Surface Wave Dispersion ◽  
Wave Tomography ◽  
Ray Path

When applying a methodology for obtaining the 3D shear-wave velocity structure of a medium from surface wave dispersion data, the problem must be considered with caution since one inverts path-averaged velocities and the use of any inversion method entails some drawbacks such as lack of uniqueness, unwarranted stability and constraints affecting the data. In order to avoid the application of consecutive inversions and to overcome these drawbacks, we propose alternative mapping methods, for example spatial prediction methods, or else the use of an algorithm that, from a mathematical viewpoint, can be understood through the application of the orthogonal projection theorem onto convex sets (POCS). Among the first ones, we try inverse weighted distance interpolation. The POCS algorithm we have used discretises a second order differential equation for the velocity field with boundary conditions. All these imaging techniques aimed at volumetric modelling and the visualisation of data are discussed, and finally we show some results based on ray path velocities obtained previously by inversion of phase and group velocities of Rayleigh waves propagating across the Iberian peninsula.

scholarly journals Imaging the subsurface using induced seismicity and ambient noise: 3-D tomographic Monte Carlo joint inversion of earthquake body wave traveltimes and surface wave dispersion

2020 ◽  
Vol 222 (3) ◽  
pp. 1639-1655
Author(s):  
Xin Zhang ◽  
Corinna Roy ◽  
Andrew Curtis ◽  
Andy Nowacki ◽  
Brian Baptie
Keyword(s):  
Surface Wave ◽  
Ambient Noise ◽  
Velocity Structure ◽  
Joint Inversion ◽  
Body Wave ◽  
Source Parameters ◽  
Wave Dispersion ◽  
Inversion Method ◽  
Surface Wave Dispersion ◽  
Wave Data

SUMMARY Seismic body wave traveltime tomography and surface wave dispersion tomography have been used widely to characterize earthquakes and to study the subsurface structure of the Earth. Since these types of problem are often significantly non-linear and have non-unique solutions, Markov chain Monte Carlo methods have been used to find probabilistic solutions. Body and surface wave data are usually inverted separately to produce independent velocity models. However, body wave tomography is generally sensitive to structure around the subvolume in which earthquakes occur and produces limited resolution in the shallower Earth, whereas surface wave tomography is often sensitive to shallower structure. To better estimate subsurface properties, we therefore jointly invert for the seismic velocity structure and earthquake locations using body and surface wave data simultaneously. We apply the new joint inversion method to a mining site in the United Kingdom at which induced seismicity occurred and was recorded on a small local network of stations, and where ambient noise recordings are available from the same stations. The ambient noise is processed to obtain inter-receiver surface wave dispersion measurements which are inverted jointly with body wave arrival times from local earthquakes. The results show that by using both types of data, the earthquake source parameters and the velocity structure can be better constrained than in independent inversions. To further understand and interpret the results, we conduct synthetic tests to compare the results from body wave inversion and joint inversion. The results show that trade-offs between source parameters and velocities appear to bias results if only body wave data are used, but this issue is largely resolved by using the joint inversion method. Thus the use of ambient seismic noise and our fully non-linear inversion provides a valuable, improved method to image the subsurface velocity and seismicity.

scholarly journals Seismic velocity structure at the southern termination of the 2016 Kumamoto Earthquake rupture, Japan

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Yasuhira Aoyagi ◽  
Haruo Kimura ◽  
Kazuo Mizoguchi
Keyword(s):  
Fault Zone ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Earthquake Rupture ◽  
2016 Kumamoto Earthquake ◽  
Seismic Velocity Structure ◽  
Kumamoto Earthquake ◽  
Seismogenic Layer ◽  
The 2016 Kumamoto Earthquake ◽  
Tectonic Line

Abstract The earthquake rupture termination mechanism and size of the ruptured area are crucial parameters for earthquake magnitude estimations and seismic hazard assessments. The 2016 Mw 7.0 Kumamoto Earthquake, central Kyushu, Japan, ruptured a 34-km-long area along previously recognized active faults, eastern part of the Futagawa fault zone and northernmost part of the Hinagu fault zone. Many researchers have suggested that a magma chamber under Aso Volcano terminated the eastward rupture. However, the termination mechanism of the southward rupture has remained unclear. Here, we conduct a local seismic tomographic inversion using a dense temporary seismic network to detail the seismic velocity structure around the southern termination of the rupture. The compressional-wave velocity (Vp) results and compressional- to shear-wave velocity (Vp/Vs) structure indicate several E–W- and ENE–WSW-trending zonal anomalies in the upper to middle crust. These zonal anomalies may reflect regional geological structures that follow the same trends as the Oita–Kumamoto Tectonic Line and Usuki–Yatsushiro Tectonic Line. While the 2016 Kumamoto Earthquake rupture mainly propagated through a low-Vp/Vs area (1.62–1.74) along the Hinagu fault zone, the southern termination of the earthquake at the focal depth of the mainshock is adjacent to a 3-km-diameter high-Vp/Vs body. There is a rapid 5-km step in the depth of the seismogenic layer across the E–W-trending velocity boundary between the low- and high-Vp/Vs areas that corresponds well with the Rokkoku Tectonic Line; this geological boundary is the likely cause of the dislocation of the seismogenic layer because it is intruded by serpentinite veins. A possible factor in the southern rupture termination of the 2016 Kumamoto Earthquake is the existence of a high-Vp/Vs body in the direction of southern rupture propagation. The provided details of this inhomogeneous barrier, which are inferred from the seismic velocity structures, may improve future seismic hazard assessments for a complex fault system composed of multiple segments.

Crustal Structure across Central Scandinavian Peninsula along Silver Road refraction profile

2021 ◽  
Author(s):  
Metin Kahraman ◽  
Hans Thybo ◽  
Irina Artemieva ◽  
Alexey Shulgin ◽  
Alireza Malehmir ◽  
...  
Keyword(s):  
Atlantic Ocean ◽  
North Atlantic ◽  
Baltic Shield ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Seismic Profile ◽  
High Mountain ◽  
Mountain Range ◽  
Air Gun ◽  
The Baltic

<p>The Baltic Shield is located in the northern part of Europe, which formed by amalgamation of a series of terranes and microcontinents during the Archean to the Paleoproterozoic, followed by significant modification in Neoproterozoic to Paleozoic time. The Baltic Shield includes an up-to 2500 m high mountain range, the Scandes , along the western North Atlantic coast, despite being a stable craton located far from any active plate boundary.</p><p>We study a crustal scale seismic profile experiment in northern Scandinavia between 63<sup>o</sup>N and 71<sup>o</sup>N. Our Silverroad seismic profile extends perpendicular to the coastline around Lofoten and extends ~300km in a northwest direction across the shelf into the Atlantic Ocean and ~300km in a southeastern direction across the Baltic Shield. The seismic data were acquired with 5 explosive sources and 270 receivers onshore; 16 ocean bottom seismometers and air gun shooting from the vessel Hakon Mosby were used to collect both offshore and onshore.</p><p>We present the results from raytracing modelling of the seismic velocity structure along the profile. The outputs of this experiment will help to solve high onshore topography and anomalous and heterogeneous bathymetry of the continental lithosphere around the North Atlantic Ocean. The results show crustal thinning from the shield onto the continental shelf and further into the oceanic part. Of particular interest is the velocity below the high topography of the Scandes, which will be discussed in relation to isostatic equilibrium along the profile.</p>

REAL-TIME 2.5D INVERSION OF LWD RESISTIVITY MEASUREMENTS USING DEEP LEARNING FOR GEOSTEERING APPLICATIONS ACROSS FAULTED FORMATIONS

2021 ◽  
Author(s):  
Kyubo Noh ◽  
◽  
Carlos Torres-Verdín ◽  
David Pardo ◽  
◽  
...  
Keyword(s):  
Deep Learning ◽  
Real Time ◽  
Fault Plane ◽  
Synthetic Data ◽  
Field Measurements ◽  
Geological Structure ◽  
Inversion Method ◽  
Adaptive Finite Element ◽  
Resistivity Measurements ◽  
Lwd Resistivity

We develop a Deep Learning (DL) inversion method for the interpretation of 2.5-dimensional (2.5D) borehole resistivity measurements that requires negligible online computational costs. The method is successfully verified with the inversion of triaxial LWD resistivity measurements acquired across faulted and anisotropic formations. Our DL inversion workflow employs four independent DL architectures. The first one identifies the type of geological structure among several predefined types. Subsequently, the second, third, and fourth architectures estimate the corresponding spatial resistivity distributions that are parameterized (1) without the crossings of bed boundaries or fault plane, (2) with the crossing of a bed boundary but without the crossing of a fault plane, and (3) with the crossing of the fault plane, respectively. Each DL architecture employs convolutional layers and is trained with synthetic data obtained from an accurate high-order, mesh-adaptive finite-element forward numerical simulator. Numerical results confirm the importance of using multi-component resistivity measurements -specifically cross-coupling resistivity components- for the successful reconstruction of 2.5D resistivity distributions adjacent to the well trajectory. The feasibility and effectiveness of the developed inversion workflow is assessed with two synthetic examples inspired by actual field measurements. Results confirm that the proposed DL method successfully reconstructs 2.5D resistivity distributions, location and dip angles of bed boundaries, and the location of the fault plane, and is therefore reliable for real-time well geosteering applications.

Seismic tomographic interpretation of Paleozoic sedimentary sequences in the southeastern North Sea

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. R45-R56 ◽  
Author(s):  
Lars Nielsen ◽  
Hans Thybo ◽  
Martin Glendrup
Keyword(s):  
North Sea ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
P Wave ◽  
Wide Angle ◽  
North German Basin ◽  
Sedimentary Sequences ◽  
The North ◽  
Crystalline Crust ◽  
German Basin

Seismic wide-angle data were recorded to more than 300-km offset from powerful airgun sources during the MONA LISA experiments in 1993 and 1995 to determine the seismic-velocity structure of the crust and uppermost mantle along three lines in the southeastern North Sea with a total length of 850 km. We use the first arrivals observed out to an offset of 90 km to obtain high-resolution models of the velocity structure of the sedimentary layers and the upper part of the crystalline crust. Seismic tomographic traveltime inversion reveals 2–8-km-thick Paleozoic sedimentary sequences with P-wave velocities of 4.5–5.2 km/s. These sedimentary rocks are situated below a Mesozoic-Cenozoic sequence with variable thickness: ∼2–3 km on the basement highs, ∼2–4 km in the Horn Graben and the North German Basin, and ∼6–7 km in the Central Graben. The thicknesses of the Paleozoic sedimentary sequences are ∼3–5 km in the Central Graben, more than 4 km in the Horn Graben, up to ∼4 km on the basement highs, and up to 8 km in the North German Basin. The Paleozoic strata are clearly separated from the shallower and younger sequences with velocities of ∼1.8–3.8 km/s and the deeper crystalline crust with velocities of more than 5.8–6.0 km/s in the tomographic P-wave velocity model. Resolution tests show that the existence of the Paleozoic sediments is well constrained by the data. Hence, our wide-angle seismic models document the presence of Paleozoic sediments throughout the southeastern North Sea, both in the graben structures and in deep basins on the basement highs.

scholarly journals Travel Time Tomography to Delineate 3-D Regional Seismic Velocity Structure in the Banyumas Basin, Central Java, Indonesia, Using Dense Borehole Seismographic Stations

2021 ◽  
Vol 9 ◽  
Author(s):  
Hidayat Hidayat ◽  
Andri Dian Nugraha ◽  
Awali Priyono ◽  
Marjiyono Marjiyono ◽  
Januar H. Setiawan ◽  
...  
Keyword(s):  
Velocity Structure ◽  
Seismic Velocity ◽  
Velocity Model ◽  
Crustal Layer ◽  
Central Java ◽  
Resolution Element ◽  
Passive Seismic ◽  
Dextral Strike Slip Fault ◽  
Southern Central ◽  
Well Data

The Banyumas Basin is a tertiary sedimentary basin located in southern Central Java, Indonesia. Due to the presence of volcanic deposits, 2-D seismic reflection methods cannot provide a good estimation of the sediment thickness and the subsurface geology structure in this area. In this study, the passive seismic tomography (PST) method was applied to image the 3-D subsurface Vp, Vs, and Vp/Vs ratio. We used 70 seismograph borehole stations with a recording duration of 177 days. A total of 354 events with 9, 370 P and 9, 368 S phases were used as input for tomographic inversion. The checkshot data of a 4, 400-meter deep exploration well (Jati-1) located within the seismic network were used to constrain the shallow crustal layer of the initial 1-D velocity model. The model resolution of the tomographic inversions was assessed using the checkerboard resolution test (CRT), the diagonal resolution element (DRE), and the derivative weight sum (DWS). Using the obtained Vp, Vs, and Vp/Vs ratio, we were able to sharpen details of the geological structures within the basin from previous geological studies, and a fault could be well-imaged at a depth of 4 km. We interpreted this as the main dextral strike-slip fault that controls the pull apart process of the Banyumas Basin. The thickness of the sediment layers, as well as its layering, were also could be well determined. We found prominent features of the velocity contrast that aligned very well with the boundary between the Halang and Rambatan formations as observed in the Jati-1 well data. Furthermore, an anticline structure, which is a potential structural trap for the petroleum system in the Banyumas Basin, was also well imaged. This was made possible due to the dense borehole seismographic stations which were deployed in the study area.

Seismic velocity structure and gravity anomalies: a comparison

1987 ◽  
Vol 140 (1) ◽  
pp. 115-120
Author(s):  
Yoshibumi Tomoda ◽  
Hiromi Fujimoto
Keyword(s):  
Velocity Structure ◽  
Seismic Velocity ◽  
Gravity Anomalies ◽  
Seismic Velocity Structure
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