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Full-waveform inversion (FWI) utilizes optimization methods to recover an optimal Earth model to best fit the observed seismic record in a sense of a predefined norm. Since FWI combines mathematic inversion and full-wave equations, it has been recognized as one of the key methods for seismic data imaging and Earth model building in the fields of global/regional and exploration seismology. Unfortunately, conventional FWI fixes background velocity mainly relying on refraction and turning waves that are commonly rich in large offsets. By contrast, reflections in the short offsets mainly contribute to the reconstruction of the high-resolution interfaces. Restricted by acquisition geometries, refractions and turning waves in the record usually have limited penetration depth, which may not reach oil/gas reservoirs. Thus, reflections in the record are the only source that carries the information of these reservoirs. Consequently, it is meaningful to develop reflection-waveform inversion (RWI) that utilizes reflections to recover background velocity including the deep part of the model. This review paper includes: analyzing the weaknesses of FWI when inverting reflections; overviewing the principles of RWI, including separation of the tomography and migration components, the objective functions, constraints; summarizing the current status of the technique of RWI; outlooking the future of RWI.

Arc volcanoes are underlain by complex systems of molten‐rock reservoirs ranging from melt‐poor mush zones to melt‐rich magma chambers. Petrological and satellite data indicate that eruptible magma chambers form in the topmost few kilometres of the crust. However, very few chambers have ever been definitively located, suggesting that most are too short‐lived or too small to be imaged, which has direct implications for hazard assessment and modeling of magma differentiation. Here we use a high‐resolution technology based on inverting full seismic waveforms to image a small, high‐melt‐fraction magma chamber that was not detected with standard seismic tomography. The melt reservoir extends from ∼2 to at least 4 km below sea level (b.s.l.) at Kolumbo—a submarine volcano near Santorini, Greece. The chamber coincides with the termination point of the recent earthquake swarms and may be a missing link between a deeper melt reservoir and the high‐temperature hydrothermal system venting at the crater floor. The chamber poses a serious hazard as it could produce a highly explosive, tsunamigenic eruption in the near future. Our results suggest that similar reservoirs (relatively small but high‐melt‐fraction) may have gone undetected at other active volcanoes, challenging the existing eruption forecasts and reactive‐flow models of magma differentiation. Plain Language Summary Arc volcanoes, which mark the curved boundaries between converging tectonic plates, host the most explosive events on Earth. The associated hazard depends on how much mobile magma is currently present shallow beneath a volcano. Standard tomographic methods used so far have relatively low resolution and give a blurred picture of only the largest molten‐rock bodies. In particular, they struggle to distinguish between mobile magma and melt spread between tightly packed mineral grains. This study, a first in volcanology, combines a next‐generation tomographic method with extraordinarily dense seafloor recordings of controlled marine sound sources. This state‐of‐the‐art experiment at Kolumbo volcano, offshore of Santorini allowed us to detect a body of mobile magma which has been growing at an average rate of 4 × 106 m3 per year since the last eruption in 1650 CE. This rate is large enough to counteract the effect of cooling and crystallization. Our results show that Kolumbo poses a serious threat and deserves a real‐time monitoring facility. Despite the excellent data coverage, the small magma body was missed by standard tomography. This suggests that applying next‐generation imaging methods to already‐well‐studied volcanoes may lead to similar discoveries. We envision that small‐volume, high‐melt‐fraction reservoirs may be more widespread than previously thought. Key Points A shallow, very strong negative Vp anomaly imaged under the explosive, submarine Kolumbo volcano, Greece, using full‐waveform inversion The high‐fidelity image and petrologic data indicate the anomaly is a small (∼0.6‐km wide, ∼2‐km deep), magma chamber with ∼42% of melt The chamber was missed by travel‐time tomography indicating similar reservoirs may have gone undetected at other volcanoes

The Tokai area in the eastern Nankai Trough is characterized by the subduction of a rough plate interface caused by bathymetric highs related to the adjacent Izu‐Bonin arc and fault fabrics in the oceanic crust. However, the effect of this process on the structural development of its accretionary wedge and megathrust seismicity is still poorly understood. To get better insight into Tokai area we apply full‐waveform inversion to legacy wide‐angle seismic data exploiting available signal frequency up to 15 Hz. From this model we extract pseudo‐reflectivity attributes, which are complementary to the section obtained with Kirchoff pre‐stack depth migration of streamer data. The high‐resolution images reveal detailed geological characterization of the subducting oceanic crust, the geometry of the megathrust and splay faults, and the structure of the wedge. The latter is characterized by imbricate fans, out‐of‐sequence thrusts, and duplexes that significantly contribute to its thickening. We compare these features to published structural models and propose that the increased structural complexity in the Tokai segment is due to fault reactivation triggered by the subduction of the bathymetric highs. We suggest that this fault reactivation also controls the shallow seismogenic behavior of this region. We show that the evolution of the forearc basin is related to the ongoing underplating process and out‐of‐sequence thrusting within the wedge. We compare our seismic imaging results with bathymetric, magnetic, and gravity data, revealing no evidence of large ridges beneath our profile, which previous studies have proposed as a cause of the persistent Tokai seismic gap. Plain Language Summary The Tokai segment is located at the eastern Nankai Trough, where the Philippine Sea Plate is sliding underneath Japan. This segment is distinct from other parts of the Nankai Trough, showing a more irregular seafloor bathymetry and narrower wedge of deformed sediments. This is thought to be the effect of seamounts and ridges plowing into the wedge during subduction. Here we use novel approaches to process legacy seismic data to create new images, and interpret in detail the faults and deformation caused by this process. Based on the type and intensity of deformation we divide the wedge into three sections. We show how the adding of material to the wedge from below, a process called underplating, is an important process here. This, combined with faults moving in an unexpected order (out‐of‐sequence), contributes significantly to the uplift and thickening of the wedge. We place observational constraints on the variation of the shape of the plate interface, how the new faults develop in the wedge, and how sediments are accumulated and deformed below and above the wedge. Finally, we do not identify a large‐scale subducted ridge beneath our profile, which previous studies had suggested might govern earthquake occurrence in this region. Key Points FWI based pseudo‐reflectivity models reveal detailed geological structure of the Tokai segment Imaged subducting highs are tilted fault blocks in oceanic crust rather than volcanic ridges Their subduction causes fault reactivation, imbricate fan and duplex formation, and basin inversion

We present a new 3‐D seismic structural model of the eastern Indonesian region and its surroundings from full‐waveform inversion (FWI) that exploits seismic data filtered at periods between 15–150 s. SASSY21—a recent 3‐D FWI tomographic model of Southeast Asia—is used as a starting model, and our study region is characterized by particularly good data coverage, which facilitates a more refined image. We use the spectral‐element solver Salvus to determine the full 3‐D wavefield, accounting for the fluid ocean explicitly by solving a coupled system of acoustic and elastic wave equations. This is computationally more expensive but allows seismic waves within the water layer to be simulated, which becomes important for periods ≤20 s. We investigate path‐dependent effects of surface elevation (topography and bathymetry) and the fluid ocean on synthetic waveforms, and compare our final model to the tomographic result obtained with the frequently used ocean loading approximation. Furthermore, we highlight some of the key features of our final model—SASSIER22—after 34 L‐BFGS iterations, which reveals detailed anomalies down to the mantle transition zone, including a convergent double‐subduction zone along the southern segment of the Philippine Trench, which was not evident in the starting model. A more detailed illumination of the slab beneath the North Sulawesi Trench reveals a pronounced positive wavespeed anomaly down to 200 km depth, consistent with the maximum depth of seismicity, and a more diffuse but aseismic positive wavespeed anomaly that continues to the 410 km discontinuity. Plain Language Summary Earthquakes that trigger devastating tsunamis have caused hundreds of thousands of deaths in Southeast Asia in the past two decades. These events are driven by processes in the Earth's interior such as descending (or subducting) tectonic plates. These plates can be imaged using seismic waves generated by earthquakes and recorded at the surface. We have developed a structural image of the Earth's interior beneath the eastern region of Southeast Asia using an advanced imaging methodology, which takes the full physics of seismic wave propagation into account. Its success is strongly dependent on being able to account for potentially complex models of the Earth; here, we investigate the effect of mountain ranges, ocean floor profiles, and the presence of a fluid ocean on the propagation of seismic waves, which are not routinely accounted for in other studies. Our final model reveals several tectonic plates descending down to ∼400 km depth, in particular around Sulawesi (Indonesia) and a collision of two plates south of the Philippines, which results in a reversal of the descent direction. The new images contribute to a better understanding of on‐going processes in the Earth, which has important implications for tracking the evolution of tectonic plates over time, and for assessing earthquake and tsunami hazards. Key Points Double‐subduction with a polarity reversal near the southern segment of the Philippine Trench is revealed The effects arising from surface topography, bathymetry, and the fluid ocean on synthetic waveforms become pronounced at periods ≤20 s For seismic waves that traverse oceanic regions, ignoring the fluid ocean in waveform predictions can compromise the reconstruction of small‐scale features

Restricted by the limited length of the receiver arrays, estimating the seismic properties of deep targets requires inverting reflection data. Reflection-waveform inversion (RWI) utilizes reflection data to recover the background velocity. RWI splits the Earth model into a long-wavelength background velocity and short-wavelength reflectors. Because of the limited apertures of reflection data illuminating targets, and the trade-off between the depth of reflectors and the average velocity above the reflectors, RWI is inherently ill-posed and contains a large null space. One manifestation of the ill-posedness is the existence of characteristic artificial blob-shaped or column-like anomalies in the velocity models estimated with RWI. That erroneous background velocity, which still fits the travel time of reflection arrivals in the recorded data, can lead to inaccurate velocity models and distorted migration images in the subsequent processes. In order to mitigate those artifacts and improve the conditioning of RWI, we incorporate a piece of prior information into RWI, i.e. slow property variation along geological structures. This prior information is expressed mathematically as structure-oriented smoothing. We achieved this smoothing by solving an anisotropic diffusion equation with a finite-difference method. Thus, we formulated a method for RWI regularized with structure-oriented smoothing shaping by alternating the following three steps: building temporary reflectors, updating background velocity, and solving the diffusion equation. We successfully tested this scheme on the Marmousi model and a modified overthrust model. The results show that the regularized RWI yields a stable and accurate background velocity, and it is more effective than conventional Tikhonov regularization approaches. The estimated background model leads to a high-quality final velocity model when used as an initial model in conventional full-waveform inversion.

Because of the combination of optimization algorithms and full wave equations, full-waveform inversion（FWI） has become the frontier of the study of seismic exploration and is gradually becoming one of the essential tools for obtaining the Earth interior information. However, the application of conventional FWI to pure reflection data in the absence of a highly accurate starting velocity model is difficult. Compared to other types of seismic waves, reflections carry the information of the deep part of the subsurface. Reflection FWI, therefore, is able to improve the accuracy of imaging the Earth interior further. Here, we demonstrate a means of achieving this successfully by interleaving least-squares RTM with a version of reflection FWI in which the tomographic gradient that is required to update the background macro-model is separated from the reflectivity gradient using the Born approximation during forward modeling. This provides a good update to the macro-model. This approach is then followed by conventional FWI to obtain a final high-fidelity high-resolution result from a poor starting model using only reflection data.Further analysis reveals the high-resolution result is achieved due to a deconvolution imaging condition implicitly used by FWI.

For the full‐waveform inversion, obtaining a globally optimal solution is difficult when the seismic data do not contain sufficient low‐frequency information and the inversion object is a salt structure with a large‐scale salt dome. The large salt dome presents difficulty for the inversion of the salt structure; however, it also confers a convenience that can be utilized: A large salt dome makes the events in the seismic record sparse and isolated. We use the envelope to obtain the arrival time of the events in the seismic data and apply multiscale strategies to extract the low‐frequency information of the seismic data that relates to the long‐wavelength components of the subsurface. In calculating the gradient, the envelope Fréchet derivative is used to take advantage of the multiscale envelope for the characteristics of the salt structure. Therefore, the multiscale direct envelope inversion using the window‐averaged envelope and the direct envelope Fréchet derivative is proposed. To further improve the computational efficiency and inversion quality of the multiscale direct envelope inversion, several auxiliary strategies are proposed: A joint misfit function is designed to make the inversion method more adaptable, and an offset weighting factor is introduced to implement the multioffset inversion method to improve the inversion quality of subsalt. We analyze the antinoise performance of the multiscale direct envelope inversion. The SEG/EAGE salt model is used to test the application effect of the multiscale direct envelope inversion. The antinoise ability and insensitivity to low‐frequency data of the method are verified in the numerical experiments. Plain Language Summary The salt structure is an important exploration target for oil and gas reservoirs. The large scale of the salt dome and the strong contrast between the salt velocities and surrounding sediments are insurmountable obstacles in the salt structure exploration. However, as each coin has two sides, these so‐called obstacles can also be regarded as a stepping stone to success from another perspective. This paper introduces a full‐waveform inversion method for the salt structure using its characteristics. The numerical test results verify the correctness of our idea. We hope that our approach will provide you with an alternative method that deserves further study. Key Points An inversion algorithm using the multiscale envelope and the envelope Fréchet derivative is proposed for salt structure inversion Joint objective function and multi‐offset inversion as auxiliary strategies to further improve the accuracy and efficiency of the inversion The anti‐noise ability and insensitivity to low‐frequency data of the method are verified using the SEG/EAGE Salt model

The seismometer onboard InSight NASA Mars mission discovered a seismically active planet. We focused on the strongest event named S1222a (4 May 2022, Mw ∼ 4.7), which was recorded by the Very Broad Band sensors and associated channel ELYSE and is located 37.2° away from InSight. We use two different methods based on a point source approach for an elastic, horizontally layered medium to retrieve source parameters of S1222a. In the first case, the seismic moment tensor inversion of high‐frequency seismogram data is calculated using a matrix method for the direct waves. The process includes the generation of records in displacement using the frequency‐wavenumber integration technique. A method of inversion of the moment tensor of direct P‐ and S‐waves, less sensitive to path effects than reflected and transformed waves, is presented, which significantly increases the accuracy and reliability of the method. In the second case, tensors were calculated using common low‐frequency full‐waveform inversion and the tests to verify the plausibility of this solution obtained from the single station calculation were performed and the uncertainty estimations for inversions can be useful in future research. Plain Language Summary The paper presents the seismic moment tensor solution and the focal mechanism for the largest event S1222a (4 May 2022, magnitude Mw4.7) recorded at one seismic station on Mars. We consider two different basic approaches to address the problem of the unavoidable inaccuracy of seismic waves modeling: focusing only on direct waves and using low‐frequency full‐waveform inversion. The moment tensor and focal mechanism of the S1222a event were obtained, as well as the optimal depth of a source. Despite the range of possible, it is encouraging that independent studies based on different methodologies, and using different structural models, point to reasonable solutions. The estimates of the focal mechanism when the single‐station inversion is calculated are taken into account and the stability tests to verify our solutions were performed. The importance of this study lies in expanding the possibilities of how to calculate this kind of tasks. Key Points We consider two different methods based on a point source approach to retrieve source parameters of S1222a A method of inversion of the moment tensor of direct waves, less sensitive to path effects than reflected and transformed waves, is presented We obtained the results of seismic tensor solution and time‐independent focal mechanism

Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l 1 -norm-based objective functions. However, the l 1 -norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l 2 -norm and l 1 -norm objective functions and by applying the three methods to noisy data. Our experiments show that the l 2 -norm is sensitive to noise, whereas the l 1 -norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l 1 - and l 2 -norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l 1 - and l 2 -norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution.

The 1 January 2024 Noto-Hanto (Noto Peninsula) earthquake (M JMA 7.6) generated strong ground motion, large crustal deformation and tsunamis that caused significant damage in the region. Around Noto Peninsula, both offshore submarine and partially inland active faults have been identified by previous projects: Ministry of Land, Infrastructure, Transport and Tourism (MLIT) and Japan Sea Earthquake and Tsunami Research Project (JSPJ). We inverted the tsunami waveforms recorded on 6 wave gauges and 12 tide gauges around Sea of Japan and the GNSS data recorded at 53 stations in Noto Peninsula to estimate the slip amount and seismic moment on each of active faults. The results show that the 2024 coseismic slips were 3.5 m, 3.2 m, and 3.2 m on subfaults NT4, NT5 and NT6 of the JSPJ model, located on the northern coast of Noto Peninsula and dipping toward southeast. A smaller slip, 1.0 m, estimated on NT8 on the southwestern end of the 2024 rupture, may be attributed to its previous rupture during the 2007 Noto earthquake. The total length of these four faults is ~ 100 km, and the seismic moment is 1.90 × 10 20 Nm (Mw = 7.5). Almost no slip was estimated on the northeastern subfaults NT2 and NT3, which dip northwestward, opposite to NT4–NT5–NT6, and western subfault NT8. Aftershocks including the M JMA 6.1 event occurred in the NT2–NT3 region, but they are smaller than the potential magnitude (Mw 7.1) those faults can release in a tsunamigenic earthquake. Similar features are also found for the MLIT model; the 2024 slip was only on F43 along the northern coast of Noto Peninsula, and northeastern F42 did not rupture, leaving potential for future event. Graphical Abstract